{"id":61301,"date":"2026-01-17T11:58:43","date_gmt":"2026-01-17T03:58:43","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/61301.html"},"modified":"2026-01-17T11:58:43","modified_gmt":"2026-01-17T03:58:43","slug":"leetcode%e7%ae%97%e6%b3%95%e9%a2%98%e8%af%a6%e8%a7%a3-53%ef%bc%9a%e6%9c%80%e5%a4%a7%e5%ad%90%e6%95%b0%e7%bb%84%e5%92%8c","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/61301.html","title":{"rendered":"LeetCode\u7b97\u6cd5\u9898\u8be6\u89e3 53\uff1a\u6700\u5927\u5b50\u6570\u7ec4\u548c"},"content":{"rendered":"<\/p>\n<h4>\u76ee\u5f55<\/h4>\n<ul>\n<li>1. \u95ee\u9898\u63cf\u8ff0<\/li>\n<li>2. \u95ee\u9898\u5206\u6790<\/li>\n<li>\n<ul>\n<li>2.1 \u9898\u76ee\u7406\u89e3<\/li>\n<li>2.2 \u6838\u5fc3\u6d1e\u5bdf<\/li>\n<li>2.3 \u7834\u9898\u5173\u952e<\/li>\n<\/ul>\n<\/li>\n<li>3. \u7b97\u6cd5\u8bbe\u8ba1\u4e0e\u5b9e\u73b0<\/li>\n<li>\n<ul>\n<li>3.1 \u66b4\u529b\u679a\u4e3e\u6cd5<\/li>\n<li>3.2 \u52a8\u6001\u89c4\u5212&#xff08;Kadane\u7b97\u6cd5&#xff09;<\/li>\n<li>3.3 \u5206\u6cbb\u6cd5&#xff08;\u8fdb\u9636\u6311\u6218&#xff09;<\/li>\n<li>3.4 \u524d\u7f00\u548c\u4f18\u5316<\/li>\n<\/ul>\n<\/li>\n<li>4. \u6027\u80fd\u5bf9\u6bd4<\/li>\n<li>5. \u6269\u5c55\u4e0e\u53d8\u4f53<\/li>\n<li>\n<ul>\n<li>5.1 \u6700\u5927\u5b50\u6570\u7ec4\u4e58\u79ef<\/li>\n<li>5.2 \u73af\u5f62\u5b50\u6570\u7ec4\u7684\u6700\u5927\u548c<\/li>\n<li>5.3 \u6700\u5927\u5b50\u77e9\u9635\u548c<\/li>\n<li>5.4 \u5e26\u957f\u5ea6\u9650\u5236\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/li>\n<\/ul>\n<\/li>\n<li>6. \u603b\u7ed3<\/li>\n<li>\n<ul>\n<li>6.1 \u6838\u5fc3\u77e5\u8bc6\u603b\u7ed3<\/li>\n<li>6.2 \u7b97\u6cd5\u9009\u62e9\u6307\u5357<\/li>\n<li>6.3 \u5e94\u7528\u573a\u666f<\/li>\n<li>6.4 \u9762\u8bd5\u6280\u5de7<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>1. \u95ee\u9898\u63cf\u8ff0<\/h2>\n<p>\u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 nums &#xff0c;\u8bf7\u4f60\u627e\u51fa\u4e00\u4e2a\u5177\u6709\u6700\u5927\u548c\u7684\u8fde\u7eed\u5b50\u6570\u7ec4&#xff08;\u5b50\u6570\u7ec4\u6700\u5c11\u5305\u542b\u4e00\u4e2a\u5143\u7d20&#xff09;&#xff0c;\u8fd4\u56de\u5176\u6700\u5927\u548c\u3002<\/p>\n<p>\u5b50\u6570\u7ec4 \u662f\u6570\u7ec4\u4e2d\u7684\u4e00\u4e2a\u8fde\u7eed\u90e8\u5206\u3002<\/p>\n<p>\u793a\u4f8b 1&#xff1a;<\/p>\n<p>\u8f93\u5165&#xff1a;nums &#061; [-2,1,-3,4,-1,2,1,-5,4]<br \/>\n\u8f93\u51fa&#xff1a;6<br \/>\n\u89e3\u91ca&#xff1a;\u8fde\u7eed\u5b50\u6570\u7ec4 [4,-1,2,1] \u7684\u548c\u6700\u5927&#xff0c;\u4e3a 6\u3002<\/p>\n<p>\u793a\u4f8b 2&#xff1a;<\/p>\n<p>\u8f93\u5165&#xff1a;nums &#061; [1]<br \/>\n\u8f93\u51fa&#xff1a;1<\/p>\n<p>\u793a\u4f8b 3&#xff1a;<\/p>\n<p>\u8f93\u5165&#xff1a;nums &#061; [5,4,-1,7,8]<br \/>\n\u8f93\u51fa&#xff1a;23<\/p>\n<p>\u63d0\u793a&#xff1a;<\/p>\n<ul>\n<li>1 &lt;&#061; nums.length &lt;&#061; 10^5<\/li>\n<li>-10^4 &lt;&#061; nums[i] &lt;&#061; 10^4<\/li>\n<\/ul>\n<p>\u8fdb\u9636&#xff1a; \u5982\u679c\u4f60\u5df2\u7ecf\u5b9e\u73b0\u590d\u6742\u5ea6\u4e3a O(n) \u7684\u89e3\u6cd5&#xff0c;\u5c1d\u8bd5\u4f7f\u7528\u66f4\u4e3a\u7cbe\u5999\u7684 \u5206\u6cbb\u6cd5 \u6c42\u89e3\u3002<\/p>\n<h2>2. \u95ee\u9898\u5206\u6790<\/h2>\n<h3>2.1 \u9898\u76ee\u7406\u89e3<\/h3>\n<p>\u6211\u4eec\u9700\u8981\u5728\u6570\u7ec4\u4e2d\u627e\u5230\u4e00\u4e2a\u8fde\u7eed\u7684\u5b50\u6570\u7ec4&#xff0c;\u4f7f\u5f97\u8be5\u5b50\u6570\u7ec4\u7684\u5143\u7d20\u4e4b\u548c\u6700\u5927\u3002\u6ce8\u610f\u5b50\u6570\u7ec4\u81f3\u5c11\u5305\u542b\u4e00\u4e2a\u5143\u7d20&#xff0c;\u4e14\u5fc5\u987b\u662f\u8fde\u7eed\u7684\u3002<\/p>\n<h3>2.2 \u6838\u5fc3\u6d1e\u5bdf<\/h3>\n<ul>\n<li>\u8fde\u7eed\u6027\u7ea6\u675f&#xff1a;\u5b50\u6570\u7ec4\u8981\u6c42\u8fde\u7eed&#xff0c;\u8fd9\u6392\u9664\u4e86\u9009\u62e9\u4e0d\u76f8\u90bb\u5143\u7d20\u7684\u53ef\u80fd\u6027<\/li>\n<li>\u8d1f\u6570\u5f71\u54cd&#xff1a;\u6570\u7ec4\u53ef\u80fd\u5305\u542b\u8d1f\u6570&#xff0c;\u8fd9\u610f\u5473\u7740\u4e0d\u80fd\u7b80\u5355\u5730\u9009\u62e9\u6240\u6709\u6b63\u6570<\/li>\n<li>\u5c40\u90e8\u4e0e\u5168\u5c40&#xff1a;\u5f53\u524d\u5143\u7d20\u53ef\u4ee5\u5f00\u59cb\u65b0\u7684\u5b50\u6570\u7ec4&#xff0c;\u6216\u52a0\u5165\u4e4b\u524d\u7684\u5b50\u6570\u7ec4<\/li>\n<\/ul>\n<h3>2.3 \u7834\u9898\u5173\u952e<\/h3>\n<p>\u95ee\u9898\u7684\u6838\u5fc3\u5728\u4e8e\u5982\u4f55\u9ad8\u6548\u5730\u51b3\u5b9a\u6bcf\u4e2a\u5143\u7d20\u662f\u5e94\u8be5\u5f00\u59cb\u65b0\u7684\u5b50\u6570\u7ec4\u8fd8\u662f\u52a0\u5165\u73b0\u6709\u7684\u5b50\u6570\u7ec4\u3002\u8fd9\u5f15\u5bfc\u6211\u4eec\u601d\u8003\u4e24\u79cd\u4e3b\u8981\u601d\u8def&#xff1a;<\/p>\n<li>\u52a8\u6001\u89c4\u5212&#xff1a;\u7ef4\u62a4\u4ee5\u6bcf\u4e2a\u4f4d\u7f6e\u7ed3\u5c3e\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/li>\n<li>\u5206\u6cbb\u6cd5&#xff1a;\u5c06\u95ee\u9898\u5206\u89e3\u4e3a\u5b50\u95ee\u9898&#xff0c;\u5206\u522b\u89e3\u51b3\u540e\u5408\u5e76<\/li>\n<h2>3. \u7b97\u6cd5\u8bbe\u8ba1\u4e0e\u5b9e\u73b0<\/h2>\n<h3>3.1 \u66b4\u529b\u679a\u4e3e\u6cd5<\/h3>\n<p>\u6838\u5fc3\u601d\u60f3<\/p>\n<p>\u679a\u4e3e\u6240\u6709\u53ef\u80fd\u7684\u5b50\u6570\u7ec4&#xff0c;\u8ba1\u7b97\u6bcf\u4e2a\u5b50\u6570\u7ec4\u7684\u548c&#xff0c;\u627e\u51fa\u6700\u5927\u503c\u3002<\/p>\n<p>\u7b97\u6cd5\u601d\u8def<\/p>\n<li>\u904d\u5386\u6240\u6709\u53ef\u80fd\u7684\u8d77\u59cb\u4f4d\u7f6e i (0\u5230n-1)<\/li>\n<li>\u5bf9\u4e8e\u6bcf\u4e2a\u8d77\u59cb\u4f4d\u7f6e&#xff0c;\u904d\u5386\u7ed3\u675f\u4f4d\u7f6e j (i\u5230n-1)<\/li>\n<li>\u8ba1\u7b97\u5b50\u6570\u7ec4 nums[i..j] \u7684\u548c<\/li>\n<li>\u8bb0\u5f55\u6240\u6709\u548c\u4e2d\u7684\u6700\u5927\u503c<\/li>\n<p>Java\u4ee3\u7801\u5b9e\u73b0<\/p>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">class<\/span> <span class=\"token class-name\">MaximumSubarrayBruteForce<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/**<br \/>\n     * \u66b4\u529b\u89e3\u6cd5 &#8211; \u4e09\u5c42\u5faa\u73af<br \/>\n     * \u65f6\u95f4\u590d\u6742\u5ea6: O(n\u00b3)<br \/>\n     * \u7a7a\u95f4\u590d\u6742\u5ea6: O(1)<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubArrayBruteForce1<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> sum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token comment\">\/\/ \u8ba1\u7b97\u5b50\u6570\u7ec4\u7684\u548c<\/span><br \/>\n                <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> k <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span> k <span class=\"token operator\">&lt;&#061;<\/span> j<span class=\"token punctuation\">;<\/span> k<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                    sum <span class=\"token operator\">&#043;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token punctuation\">}<\/span><br \/>\n                maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxSum<span class=\"token punctuation\">,<\/span> sum<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> maxSum<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * \u4f18\u5316\u7248\u66b4\u529b\u89e3\u6cd5 &#8211; \u51cf\u5c11\u91cd\u590d\u8ba1\u7b97<br \/>\n     * \u65f6\u95f4\u590d\u6742\u5ea6: O(n\u00b2)<br \/>\n     * \u7a7a\u95f4\u590d\u6742\u5ea6: O(1)<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubArrayBruteForce2<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> sum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                sum <span class=\"token operator\">&#043;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u7d2f\u52a0\u8ba1\u7b97<\/span><br \/>\n                maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxSum<span class=\"token punctuation\">,<\/span> sum<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> maxSum<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * \u8fdb\u4e00\u6b65\u4f18\u5316\u7684\u66b4\u529b\u89e3\u6cd5 &#8211; \u4f7f\u7528\u524d\u7f00\u548c<br \/>\n     * \u65f6\u95f4\u590d\u6742\u5ea6: O(n\u00b2)<br \/>\n     * \u7a7a\u95f4\u590d\u6742\u5ea6: O(n)<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubArrayBruteForce3<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u524d\u7f00\u548c<\/span><br \/>\n        <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> prefix <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        prefix<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            prefix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> prefix<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> nums<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u5b50\u6570\u7ec4 nums[i..j] \u7684\u548c &#061; prefix[j&#043;1] &#8211; prefix[i]<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> sum <span class=\"token operator\">&#061;<\/span> prefix<span class=\"token punctuation\">[<\/span>j <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#8211;<\/span> prefix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxSum<span class=\"token punctuation\">,<\/span> sum<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> maxSum<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>\u6027\u80fd\u5206\u6790<\/p>\n<ul>\n<li>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;O(n\u00b2)&#xff0c;\u5176\u4e2dn\u4e3a\u6570\u7ec4\u957f\u5ea6\u3002\u9700\u8981\u68c0\u67e5\u6240\u6709\u53ef\u80fd\u7684\u5b50\u6570\u7ec4\u3002<\/li>\n<li>\u7a7a\u95f4\u590d\u6742\u5ea6&#xff1a;O(1) \u6216 O(n)&#xff0c;\u53d6\u51b3\u4e8e\u662f\u5426\u4f7f\u7528\u524d\u7f00\u548c\u6570\u7ec4\u3002<\/li>\n<li>\u9002\u7528\u573a\u666f&#xff1a;\u4ec5\u9002\u7528\u4e8e\u975e\u5e38\u5c0f\u7684\u8f93\u5165\u89c4\u6a21&#xff08;n \u2264 100&#xff09;\u3002<\/li>\n<\/ul>\n<h3>3.2 \u52a8\u6001\u89c4\u5212&#xff08;Kadane\u7b97\u6cd5&#xff09;<\/h3>\n<p>\u6838\u5fc3\u601d\u60f3<\/p>\n<p>\u4f7f\u7528\u52a8\u6001\u89c4\u5212\u601d\u60f3&#xff0c;\u7ef4\u62a4\u4e24\u4e2a\u53d8\u91cf&#xff1a;<\/p>\n<li>currentMax&#xff1a;\u4ee5\u5f53\u524d\u4f4d\u7f6e\u7ed3\u5c3e\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/li>\n<li>globalMax&#xff1a;\u5168\u5c40\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/li>\n<p>\u5bf9\u4e8e\u6bcf\u4e2a\u4f4d\u7f6e&#xff0c;\u51b3\u5b9a\u662f\u5f00\u59cb\u65b0\u7684\u5b50\u6570\u7ec4&#xff0c;\u8fd8\u662f\u5c06\u5f53\u524d\u5143\u7d20\u52a0\u5165\u4e4b\u524d\u7684\u5b50\u6570\u7ec4\u3002<\/p>\n<p>\u7b97\u6cd5\u601d\u8def<\/p>\n<li>\u521d\u59cb\u5316 currentMax &#061; nums[0]&#xff0c;globalMax &#061; nums[0]<\/li>\n<li>\u4ece\u7b2c\u4e8c\u4e2a\u5143\u7d20\u5f00\u59cb\u904d\u5386\u6570\u7ec4&#xff1a;\n<ul>\n<li>currentMax &#061; max(nums[i], currentMax &#043; nums[i])<\/li>\n<li>globalMax &#061; max(globalMax, currentMax)<\/li>\n<\/ul>\n<\/li>\n<li>\u8fd4\u56de globalMax<\/li>\n<p>Java\u4ee3\u7801\u5b9e\u73b0<\/p>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">class<\/span> <span class=\"token class-name\">MaximumSubarrayKadane<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/**<br \/>\n     * Kadane\u7b97\u6cd5 &#8211; \u6807\u51c6\u7248<br \/>\n     * \u65f6\u95f4\u590d\u6742\u5ea6: O(n)<br \/>\n     * \u7a7a\u95f4\u590d\u6742\u5ea6: O(1)<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubArray<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> currentMax <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> globalMax <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token comment\">\/\/ \u5173\u952e\u51b3\u7b56&#xff1a;\u662f\u5f00\u59cb\u65b0\u7684\u5b50\u6570\u7ec4&#xff0c;\u8fd8\u662f\u52a0\u5165\u4e4b\u524d\u7684\u5b50\u6570\u7ec4<\/span><br \/>\n            currentMax <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> currentMax <span class=\"token operator\">&#043;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            globalMax <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>globalMax<span class=\"token punctuation\">,<\/span> currentMax<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> globalMax<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * Kadane\u7b97\u6cd5 &#8211; \u8be6\u7ec6\u6ce8\u91ca\u7248<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubArrayDetailed<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ dp[i] \u8868\u793a\u4ee5\u7b2c i \u4e2a\u5143\u7d20\u7ed3\u5c3e\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u5b9e\u9645\u4e0a\u53ea\u9700\u8981\u524d\u4e00\u4e2a\u72b6\u6001&#xff0c;\u6240\u4ee5\u53ef\u4ee5\u538b\u7f29\u7a7a\u95f4<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> prev <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u4ee5\u7b2c0\u4e2a\u5143\u7d20\u7ed3\u5c3e\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5168\u5c40\u6700\u5927\u548c<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token comment\">\/\/ \u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b&#xff1a;<\/span><br \/>\n            <span class=\"token comment\">\/\/ dp[i] &#061; max(nums[i], dp[i-1] &#043; nums[i])<\/span><br \/>\n            <span class=\"token comment\">\/\/ \u89e3\u91ca&#xff1a;\u8981\u4e48\u4ece\u5f53\u524d\u4f4d\u7f6e\u5f00\u59cb\u65b0\u7684\u5b50\u6570\u7ec4&#xff0c;\u8981\u4e48\u52a0\u5165\u4e4b\u524d\u7684\u5b50\u6570\u7ec4<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> current <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> prev <span class=\"token operator\">&#043;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxSum<span class=\"token punctuation\">,<\/span> current<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            prev <span class=\"token operator\">&#061;<\/span> current<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u66f4\u65b0prev\u4e3a\u5f53\u524d\u72b6\u6001<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> maxSum<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * Kadane\u7b97\u6cd5 &#8211; \u8fd4\u56de\u5b50\u6570\u7ec4\u672c\u8eab<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">maxSubArrayWithIndices<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> currentMax <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> globalMax <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> currentStart <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> globalStart <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> globalEnd <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&gt;<\/span> currentMax <span class=\"token operator\">&#043;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token comment\">\/\/ \u5f00\u59cb\u65b0\u7684\u5b50\u6570\u7ec4<\/span><br \/>\n                currentMax <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                currentStart <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">else<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token comment\">\/\/ \u52a0\u5165\u4e4b\u524d\u7684\u5b50\u6570\u7ec4<\/span><br \/>\n                currentMax <span class=\"token operator\">&#061;<\/span> currentMax <span class=\"token operator\">&#043;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u66f4\u65b0\u5168\u5c40\u6700\u5927\u503c<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>currentMax <span class=\"token operator\">&gt;<\/span> globalMax<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                globalMax <span class=\"token operator\">&#061;<\/span> currentMax<span class=\"token punctuation\">;<\/span><br \/>\n                globalStart <span class=\"token operator\">&#061;<\/span> currentStart<span class=\"token punctuation\">;<\/span><br \/>\n                globalEnd <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8fd4\u56de\u5b50\u6570\u7ec4<\/span><br \/>\n        <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> result <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>globalEnd <span class=\"token operator\">&#8211;<\/span> globalStart <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token class-name\">System<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">arraycopy<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> globalStart<span class=\"token punctuation\">,<\/span> result<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> result<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> result<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * \u5904\u7406\u5168\u8d1f\u6570\u60c5\u51b5\u7684\u7248\u672c<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubArrayAllNegative<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> maxElement <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">boolean<\/span> allNegative <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u68c0\u67e5\u662f\u5426\u5168\u4e3a\u8d1f\u6570<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> num <span class=\"token operator\">:<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>num <span class=\"token operator\">&gt;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                allNegative <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token keyword\">break<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n            maxElement <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxElement<span class=\"token punctuation\">,<\/span> num<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>allNegative<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> maxElement<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5168\u8d1f\u6570\u60c5\u51b5&#xff0c;\u8fd4\u56de\u6700\u5927\u5143\u7d20<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u6b63\u5e38Kadane\u7b97\u6cd5<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> currentMax <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> globalMax <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> num <span class=\"token operator\">:<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            currentMax <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> currentMax <span class=\"token operator\">&#043;<\/span> num<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            globalMax <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>globalMax<span class=\"token punctuation\">,<\/span> currentMax<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> globalMax<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>\u56fe\u89e3\u7b97\u6cd5<\/p>\n<p>\u793a\u4f8b&#xff1a;nums &#061; [-2, 1, -3, 4, -1, 2, 1, -5, 4]<\/p>\n<p>\u521d\u59cb\u5316&#xff1a;currentMax &#061; -2, globalMax &#061; -2<\/p>\n<p>i&#061;1: num&#061;1<br \/>\n  currentMax &#061; max(1, -2&#043;1&#061; -1) &#061; 1<br \/>\n  globalMax &#061; max(-2, 1) &#061; 1<\/p>\n<p>i&#061;2: num&#061;-3<br \/>\n  currentMax &#061; max(-3, 1&#043;(-3)&#061; -2) &#061; -2<br \/>\n  globalMax &#061; max(1, -2) &#061; 1<\/p>\n<p>i&#061;3: num&#061;4<br \/>\n  currentMax &#061; max(4, -2&#043;4&#061; 2) &#061; 4<br \/>\n  globalMax &#061; max(1, 4) &#061; 4<\/p>\n<p>i&#061;4: num&#061;-1<br \/>\n  currentMax &#061; max(-1, 4&#043;(-1)&#061; 3) &#061; 3<br \/>\n  globalMax &#061; max(4, 3) &#061; 4<\/p>\n<p>i&#061;5: num&#061;2<br \/>\n  currentMax &#061; max(2, 3&#043;2&#061; 5) &#061; 5<br \/>\n  globalMax &#061; max(4, 5) &#061; 5<\/p>\n<p>i&#061;6: num&#061;1<br \/>\n  currentMax &#061; max(1, 5&#043;1&#061; 6) &#061; 6<br \/>\n  globalMax &#061; max(5, 6) &#061; 6<\/p>\n<p>i&#061;7: num&#061;-5<br \/>\n  currentMax &#061; max(-5, 6&#043;(-5)&#061; 1) &#061; 1<br \/>\n  globalMax &#061; max(6, 1) &#061; 6<\/p>\n<p>i&#061;8: num&#061;4<br \/>\n  currentMax &#061; max(4, 1&#043;4&#061; 5) &#061; 5<br \/>\n  globalMax &#061; max(6, 5) &#061; 6<\/p>\n<p>\u8fd4\u56de&#xff1a;6<\/p>\n<p>\u6027\u80fd\u5206\u6790<\/p>\n<ul>\n<li>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;O(n)&#xff0c;\u53ea\u9700\u8981\u4e00\u6b21\u904d\u5386<\/li>\n<li>\u7a7a\u95f4\u590d\u6742\u5ea6&#xff1a;O(1)&#xff0c;\u53ea\u4f7f\u7528\u4e86\u5e38\u6570\u7ea7\u522b\u7684\u989d\u5916\u7a7a\u95f4<\/li>\n<li>\u4f18\u52bf&#xff1a;\u9ad8\u6548\u3001\u7b80\u6d01&#xff0c;\u662f\u6700\u4f18\u89e3\u6cd5<\/li>\n<\/ul>\n<h3>3.3 \u5206\u6cbb\u6cd5&#xff08;\u8fdb\u9636\u6311\u6218&#xff09;<\/h3>\n<p>\u6838\u5fc3\u601d\u60f3<\/p>\n<p>\u5c06\u6570\u7ec4\u5206\u6210\u4e24\u534a&#xff0c;\u6700\u5927\u5b50\u6570\u7ec4\u53ef\u80fd\u51fa\u73b0\u5728&#xff1a;<\/p>\n<li>\u5de6\u534a\u90e8\u5206<\/li>\n<li>\u53f3\u534a\u90e8\u5206<\/li>\n<li>\u8de8\u8d8a\u4e2d\u95f4\u70b9\u7684\u90e8\u5206<\/li>\n<p>\u5206\u522b\u8ba1\u7b97\u8fd9\u4e09\u79cd\u60c5\u51b5&#xff0c;\u53d6\u6700\u5927\u503c\u3002<\/p>\n<p>\u7b97\u6cd5\u601d\u8def<\/p>\n<li>\u5c06\u6570\u7ec4\u5206\u6210\u5de6\u53f3\u4e24\u534a<\/li>\n<li>\u9012\u5f52\u8ba1\u7b97\u5de6\u534a\u90e8\u5206\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/li>\n<li>\u9012\u5f52\u8ba1\u7b97\u53f3\u534a\u90e8\u5206\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/li>\n<li>\u8ba1\u7b97\u8de8\u8d8a\u4e2d\u95f4\u70b9\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/li>\n<li>\u8fd4\u56de\u4e09\u8005\u4e2d\u7684\u6700\u5927\u503c<\/li>\n<p>Java\u4ee3\u7801\u5b9e\u73b0<\/p>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">class<\/span> <span class=\"token class-name\">MaximumSubarrayDivideConquer<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/**<br \/>\n     * \u5206\u6cbb\u6cd5<br \/>\n     * \u65f6\u95f4\u590d\u6742\u5ea6: O(n log n)<br \/>\n     * \u7a7a\u95f4\u590d\u6742\u5ea6: O(log n) \u9012\u5f52\u6808\u7a7a\u95f4<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubArray<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> <span class=\"token function\">divideAndConquer<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token keyword\">private<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">divideAndConquer<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> left<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u57fa\u672c\u60c5\u51b5&#xff1a;\u53ea\u6709\u4e00\u4e2a\u5143\u7d20<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&#061;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> nums<span class=\"token punctuation\">[<\/span>left<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u627e\u5230\u4e2d\u95f4\u70b9<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> mid <span class=\"token operator\">&#061;<\/span> left <span class=\"token operator\">&#043;<\/span> <span class=\"token punctuation\">(<\/span>right <span class=\"token operator\">&#8211;<\/span> left<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u9012\u5f52\u8ba1\u7b97\u5de6\u534a\u90e8\u5206\u548c\u53f3\u534a\u90e8\u5206\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> leftMax <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">divideAndConquer<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> left<span class=\"token punctuation\">,<\/span> mid<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> rightMax <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">divideAndConquer<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u8de8\u8d8a\u4e2d\u95f4\u70b9\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> crossMax <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">maxCrossingSum<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> left<span class=\"token punctuation\">,<\/span> mid<span class=\"token punctuation\">,<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8fd4\u56de\u4e09\u8005\u4e2d\u7684\u6700\u5927\u503c<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span><span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>leftMax<span class=\"token punctuation\">,<\/span> rightMax<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> crossMax<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * \u8ba1\u7b97\u8de8\u8d8a\u4e2d\u95f4\u70b9\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">private<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxCrossingSum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> left<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> mid<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u5de6\u534a\u90e8\u5206&#xff08;\u4ecemid\u5411\u5de6&#xff09;\u7684\u6700\u5927\u548c<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> leftSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> sum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> mid<span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&gt;&#061;<\/span> left<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#8212;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            sum <span class=\"token operator\">&#043;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            leftSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>leftSum<span class=\"token punctuation\">,<\/span> sum<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u53f3\u534a\u90e8\u5206&#xff08;\u4ecemid&#043;1\u5411\u53f3&#xff09;\u7684\u6700\u5927\u548c<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> rightSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><br \/>\n        sum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            sum <span class=\"token operator\">&#043;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            rightSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>rightSum<span class=\"token punctuation\">,<\/span> sum<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8de8\u8d8a\u4e2d\u95f4\u70b9\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c &#061; \u5de6\u534a\u90e8\u5206\u6700\u5927\u548c &#043; \u53f3\u534a\u90e8\u5206\u6700\u5927\u548c<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> leftSum <span class=\"token operator\">&#043;<\/span> rightSum<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * \u5206\u6cbb\u6cd5\u7684\u8fed\u4ee3\u7248\u672c&#xff08;\u907f\u514d\u9012\u5f52\u6808\u6ea2\u51fa&#xff09;<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubArrayIterative<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u4f7f\u7528\u6808\u6a21\u62df\u9012\u5f52<\/span><br \/>\n        <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> result <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u5904\u7406\u957f\u5ea6\u4e3a1\u7684\u5b50\u6570\u7ec4<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            result<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u5408\u5e76\u76f8\u90bb\u7684\u5b50\u6570\u7ec4<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> size <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> size <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> size <span class=\"token operator\">*&#061;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> left <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> left <span class=\"token operator\">&lt;<\/span> n <span class=\"token operator\">&#8211;<\/span> size<span class=\"token punctuation\">;<\/span> left <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> size<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> mid <span class=\"token operator\">&#061;<\/span> left <span class=\"token operator\">&#043;<\/span> size <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> right <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> size <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> n <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>                <span class=\"token comment\">\/\/ \u8ba1\u7b97\u8de8\u8d8a\u4e2d\u95f4\u70b9\u7684\u6700\u5927\u548c<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> crossMax <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">maxCrossingSum<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> left<span class=\"token punctuation\">,<\/span> mid<span class=\"token punctuation\">,<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>                <span class=\"token comment\">\/\/ \u66f4\u65b0\u7ed3\u679c<\/span><br \/>\n                result<span class=\"token punctuation\">[<\/span>left<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span><br \/>\n                    <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>result<span class=\"token punctuation\">[<\/span>left<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> result<span class=\"token punctuation\">[<\/span>mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n                    crossMax<br \/>\n                <span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> result<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>\u6027\u80fd\u5206\u6790<\/p>\n<ul>\n<li>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;O(n log n)&#xff0c;\u6bcf\u6b21\u9012\u5f52\u5c06\u95ee\u9898\u5206\u6210\u4e24\u534a&#xff0c;\u4f46\u5408\u5e76\u9700\u8981O(n)\u65f6\u95f4<\/li>\n<li>\u7a7a\u95f4\u590d\u6742\u5ea6&#xff1a;O(log n)&#xff0c;\u9012\u5f52\u6808\u7684\u6df1\u5ea6<\/li>\n<li>\u4f18\u52bf&#xff1a;\u5c55\u793a\u4e86\u5206\u6cbb\u601d\u60f3\u7684\u4f18\u96c5&#xff0c;\u9002\u5408\u5e76\u884c\u8ba1\u7b97<\/li>\n<li>\u52a3\u52bf&#xff1a;\u6bd4Kadane\u7b97\u6cd5\u6162&#xff0c;\u4f46\u5bf9\u4e8e\u7406\u89e3\u7b97\u6cd5\u8bbe\u8ba1\u6709\u6559\u80b2\u610f\u4e49<\/li>\n<\/ul>\n<h3>3.4 \u524d\u7f00\u548c\u4f18\u5316<\/h3>\n<p>\u6838\u5fc3\u601d\u60f3<\/p>\n<p>\u4f7f\u7528\u524d\u7f00\u548c\u5c06\u95ee\u9898\u8f6c\u5316\u4e3a&#xff1a;\u627e\u5230\u4e24\u4e2a\u7d22\u5f15 i \u548c j (i \u2264 j)&#xff0c;\u4f7f\u5f97 prefix[j&#043;1] &#8211; prefix[i] \u6700\u5927\u3002 \u8fd9\u7b49\u4ef7\u4e8e\u5728\u904d\u5386\u8fc7\u7a0b\u4e2d\u7ef4\u62a4\u6700\u5c0f\u524d\u7f00\u548c\u3002<\/p>\n<p>\u7b97\u6cd5\u601d\u8def<\/p>\n<li>\u8ba1\u7b97\u524d\u7f00\u548c\u6570\u7ec4 prefix&#xff0c;\u5176\u4e2d prefix[i] \u8868\u793a\u524d i \u4e2a\u5143\u7d20\u7684\u548c<\/li>\n<li>\u904d\u5386\u6570\u7ec4&#xff0c;\u5bf9\u4e8e\u6bcf\u4e2a\u4f4d\u7f6e j&#xff1a;\n<ul>\n<li>\u5f53\u524d\u5b50\u6570\u7ec4\u548c &#061; prefix[j&#043;1] &#8211; minPrefix&#xff0c;\u5176\u4e2d minPrefix \u662f prefix[0\u2026j] \u7684\u6700\u5c0f\u503c<\/li>\n<li>\u66f4\u65b0\u5168\u5c40\u6700\u5927\u503c<\/li>\n<li>\u66f4\u65b0\u6700\u5c0f\u524d\u7f00\u548c<\/li>\n<\/ul>\n<\/li>\n<p>Java\u4ee3\u7801\u5b9e\u73b0<\/p>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">class<\/span> <span class=\"token class-name\">MaximumSubarrayPrefixSum<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/**<br \/>\n     * \u524d\u7f00\u548c\u4f18\u5316\u89e3\u6cd5<br \/>\n     * \u65f6\u95f4\u590d\u6742\u5ea6: O(n)<br \/>\n     * \u7a7a\u95f4\u590d\u6742\u5ea6: O(1)<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubArray<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> minPrefixSum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u6700\u5c0f\u524d\u7f00\u548c&#xff0c;\u521d\u59cb\u4e3a0&#xff08;\u7a7a\u6570\u7ec4&#xff09;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> prefixSum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> num <span class=\"token operator\">:<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            prefixSum <span class=\"token operator\">&#043;&#061;<\/span> num<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5f53\u524d\u524d\u7f00\u548c<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u5f53\u524d\u6700\u5927\u5b50\u6570\u7ec4\u548c &#061; \u5f53\u524d\u524d\u7f00\u548c &#8211; \u6700\u5c0f\u524d\u7f00\u548c<\/span><br \/>\n            maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxSum<span class=\"token punctuation\">,<\/span> prefixSum <span class=\"token operator\">&#8211;<\/span> minPrefixSum<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u66f4\u65b0\u6700\u5c0f\u524d\u7f00\u548c<\/span><br \/>\n            minPrefixSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>minPrefixSum<span class=\"token punctuation\">,<\/span> prefixSum<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> maxSum<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * \u524d\u7f00\u548c\u89e3\u6cd5\u7684\u8be6\u7ec6\u7248\u672c<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubArrayDetailed<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u524d\u7f00\u548c\u6570\u7ec4<\/span><br \/>\n        <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> prefix <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        prefix<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u7a7a\u6570\u7ec4\u7684\u524d\u7f00\u548c\u4e3a0<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            prefix<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> prefix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> minPrefix <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u6700\u5c0f\u524d\u7f00\u548c&#xff0c;\u521d\u59cb\u4e3aprefix[0] &#061; 0<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token comment\">\/\/ \u4ee5\u7b2ci\u4e2a\u5143\u7d20\u7ed3\u5c3e\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c &#061; prefix[i] &#8211; \u6700\u5c0f\u524d\u7f00\u548c<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> currentSum <span class=\"token operator\">&#061;<\/span> prefix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#8211;<\/span> minPrefix<span class=\"token punctuation\">;<\/span><br \/>\n            maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxSum<span class=\"token punctuation\">,<\/span> currentSum<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u66f4\u65b0\u6700\u5c0f\u524d\u7f00\u548c<\/span><br \/>\n            minPrefix <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>minPrefix<span class=\"token punctuation\">,<\/span> prefix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> maxSum<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * \u8fd4\u56de\u5b50\u6570\u7ec4\u7684\u524d\u7f00\u548c\u89e3\u6cd5<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">maxSubArrayWithIndicesPrefix<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> minPrefixSum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> minPrefixIndex <span class=\"token operator\">&#061;<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u6700\u5c0f\u524d\u7f00\u548c\u7684\u7d22\u5f15<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> prefixSum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> start <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> end <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            prefixSum <span class=\"token operator\">&#043;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u8ba1\u7b97\u5f53\u524d\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> currentSum <span class=\"token operator\">&#061;<\/span> prefixSum <span class=\"token operator\">&#8211;<\/span> minPrefixSum<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>currentSum <span class=\"token operator\">&gt;<\/span> maxSum<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                maxSum <span class=\"token operator\">&#061;<\/span> currentSum<span class=\"token punctuation\">;<\/span><br \/>\n                start <span class=\"token operator\">&#061;<\/span> minPrefixIndex <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5b50\u6570\u7ec4\u4ece\u6700\u5c0f\u524d\u7f00\u548c\u7684\u4e0b\u4e00\u4e2a\u4f4d\u7f6e\u5f00\u59cb<\/span><br \/>\n                end <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u66f4\u65b0\u6700\u5c0f\u524d\u7f00\u548c<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>prefixSum <span class=\"token operator\">&lt;<\/span> minPrefixSum<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                minPrefixSum <span class=\"token operator\">&#061;<\/span> prefixSum<span class=\"token punctuation\">;<\/span><br \/>\n                minPrefixIndex <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8fd4\u56de\u5b50\u6570\u7ec4<\/span><br \/>\n        <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> result <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>end <span class=\"token operator\">&#8211;<\/span> start <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token class-name\">System<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">arraycopy<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> start<span class=\"token punctuation\">,<\/span> result<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> result<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> result<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h2>4. \u6027\u80fd\u5bf9\u6bd4<\/h2>\n<table>\n<tr>\u7b97\u6cd5\u65f6\u95f4\u590d\u6742\u5ea6\u7a7a\u95f4\u590d\u6742\u5ea6\u4f18\u52bf\u52a3\u52bf<\/tr>\n<tbody>\n<tr>\n<td>\u66b4\u529b\u679a\u4e3e&#xff08;\u57fa\u7840&#xff09;<\/td>\n<td>O(n\u00b3)<\/td>\n<td>O(1)<\/td>\n<td>\u5b9e\u73b0\u7b80\u5355<\/td>\n<td>\u6548\u7387\u6781\u4f4e<\/td>\n<\/tr>\n<tr>\n<td>\u66b4\u529b\u679a\u4e3e&#xff08;\u4f18\u5316&#xff09;<\/td>\n<td>O(n\u00b2)<\/td>\n<td>O(1)<\/td>\n<td>\u6bd4\u57fa\u7840\u7248\u7a0d\u597d<\/td>\n<td>\u4ecd\u7136\u6548\u7387\u4f4e<\/td>\n<\/tr>\n<tr>\n<td>\u52a8\u6001\u89c4\u5212&#xff08;Kadane&#xff09;<\/td>\n<td>O(n)<\/td>\n<td>O(1)<\/td>\n<td>\u6700\u4f18\u65f6\u95f4\u590d\u6742\u5ea6<\/td>\n<td>\u9700\u8981\u7406\u89e3\u52a8\u6001\u89c4\u5212\u601d\u60f3<\/td>\n<\/tr>\n<tr>\n<td>\u5206\u6cbb\u6cd5<\/td>\n<td>O(n log n)<\/td>\n<td>O(log n)<\/td>\n<td>\u5c55\u793a\u5206\u6cbb\u601d\u60f3<\/td>\n<td>\u6bd4Kadane\u6162<\/td>\n<\/tr>\n<tr>\n<td>\u524d\u7f00\u548c\u4f18\u5316<\/td>\n<td>O(n)<\/td>\n<td>O(1)<\/td>\n<td>\u53e6\u4e00\u79cdO(n)\u89e3\u6cd5<\/td>\n<td>\u9700\u8981\u7406\u89e3\u524d\u7f00\u548c<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u6027\u80fd\u6d4b\u8bd5\u7ed3\u679c&#xff08;\u6570\u7ec4\u957f\u5ea6&#061;100000&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\u66b4\u529b\u679a\u4e3e&#xff08;\u4f18\u5316&#xff09;&#xff1a;\u8d85\u65f6&#xff08;&gt;10\u79d2&#xff09;<\/li>\n<li>\u52a8\u6001\u89c4\u5212&#xff08;Kadane&#xff09;&#xff1a;~2 ms<\/li>\n<li>\u5206\u6cbb\u6cd5&#xff1a;~10 ms<\/li>\n<li>\u524d\u7f00\u548c\u4f18\u5316&#xff1a;~3 ms<\/li>\n<\/ul>\n<p>\u5185\u5b58\u5360\u7528\u5bf9\u6bd4&#xff1a;<\/p>\n<ul>\n<li>Kadane\u7b97\u6cd5&#xff1a;\u5e38\u6570\u7a7a\u95f4&#xff0c;\u51e0\u4e2a\u53d8\u91cf<\/li>\n<li>\u5206\u6cbb\u6cd5&#xff1a;\u9012\u5f52\u6808\u6df1\u5ea6O(log n)&#xff0c;\u7ea617\u5c42&#xff08;n&#061;100000&#xff09;<\/li>\n<li>\u524d\u7f00\u548c\u4f18\u5316&#xff1a;\u5e38\u6570\u7a7a\u95f4&#xff0c;\u51e0\u4e2a\u53d8\u91cf<\/li>\n<\/ul>\n<h2>5. \u6269\u5c55\u4e0e\u53d8\u4f53<\/h2>\n<h3>5.1 \u6700\u5927\u5b50\u6570\u7ec4\u4e58\u79ef<\/h3>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">class<\/span> <span class=\"token class-name\">MaximumProductSubarray<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/**<br \/>\n     * \u6700\u5927\u5b50\u6570\u7ec4\u4e58\u79ef<br \/>\n     * \u7531\u4e8e\u8d1f\u6570\u4e58\u8d1f\u6570\u5f97\u6b63&#xff0c;\u9700\u8981\u540c\u65f6\u7ef4\u62a4\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxProduct<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> maxProd <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> minProd <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> result <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token comment\">\/\/ \u5982\u679c\u662f\u8d1f\u6570&#xff0c;\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u4f1a\u4ea4\u6362<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> temp <span class=\"token operator\">&#061;<\/span> maxProd<span class=\"token punctuation\">;<\/span><br \/>\n                maxProd <span class=\"token operator\">&#061;<\/span> minProd<span class=\"token punctuation\">;<\/span><br \/>\n                minProd <span class=\"token operator\">&#061;<\/span> temp<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u66f4\u65b0\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c<\/span><br \/>\n            maxProd <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> maxProd <span class=\"token operator\">*<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            minProd <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> minProd <span class=\"token operator\">*<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u66f4\u65b0\u7ed3\u679c<\/span><br \/>\n            result <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>result<span class=\"token punctuation\">,<\/span> maxProd<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> result<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * \u53e6\u4e00\u79cd\u5199\u6cd5&#xff1a;\u540c\u65f6\u8ba1\u7b97\u4e09\u79cd\u53ef\u80fd\u6027<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxProduct2<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> max <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> min <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> result <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> temp <span class=\"token operator\">&#061;<\/span> max<span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u6700\u5927\u503c\u6709\u4e09\u79cd\u53ef\u80fd&#xff1a;\u5f53\u524d\u5143\u7d20&#xff0c;\u5f53\u524d\u5143\u7d20\u00d7\u4e4b\u524d\u7684\u6700\u5927\u503c&#xff0c;\u5f53\u524d\u5143\u7d20\u00d7\u4e4b\u524d\u7684\u6700\u5c0f\u503c<\/span><br \/>\n            max <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span><span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> max <span class=\"token operator\">*<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> min <span class=\"token operator\">*<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            min <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span><span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> temp <span class=\"token operator\">*<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> min <span class=\"token operator\">*<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>            result <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>result<span class=\"token punctuation\">,<\/span> max<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> result<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h3>5.2 \u73af\u5f62\u5b50\u6570\u7ec4\u7684\u6700\u5927\u548c<\/h3>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">class<\/span> <span class=\"token class-name\">MaximumCircularSubarray<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/**<br \/>\n     * \u73af\u5f62\u5b50\u6570\u7ec4\u7684\u6700\u5927\u548c<br \/>\n     * \u6709\u4e24\u79cd\u60c5\u51b5&#xff1a;<br \/>\n     * 1. \u6700\u5927\u5b50\u6570\u7ec4\u5728\u6570\u7ec4\u4e2d\u95f4&#xff08;\u975e\u73af\u5f62&#xff09;<br \/>\n     * 2. \u6700\u5927\u5b50\u6570\u7ec4\u8de8\u8d8a\u6570\u7ec4\u9996\u5c3e&#xff08;\u73af\u5f62&#xff09; &#061; \u603b\u548c &#8211; \u6700\u5c0f\u5b50\u6570\u7ec4\u548c<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubarraySumCircular<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> totalSum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> minSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MAX_VALUE<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> currentMax <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> currentMin <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> num <span class=\"token operator\">:<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            totalSum <span class=\"token operator\">&#043;&#061;<\/span> num<span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ Kadane\u7b97\u6cd5\u8ba1\u7b97\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/span><br \/>\n            currentMax <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>num<span class=\"token punctuation\">,<\/span> currentMax <span class=\"token operator\">&#043;<\/span> num<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxSum<span class=\"token punctuation\">,<\/span> currentMax<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ Kadane\u7b97\u6cd5\u8ba1\u7b97\u6700\u5c0f\u5b50\u6570\u7ec4\u548c<\/span><br \/>\n            currentMin <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>num<span class=\"token punctuation\">,<\/span> currentMin <span class=\"token operator\">&#043;<\/span> num<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            minSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>minSum<span class=\"token punctuation\">,<\/span> currentMin<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u7279\u6b8a\u60c5\u51b5&#xff1a;\u6240\u6709\u5143\u7d20\u90fd\u662f\u8d1f\u6570<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>maxSum <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> maxSum<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u73af\u5f62\u60c5\u51b5\u7684\u6700\u5927\u548c &#061; max(\u975e\u73af\u5f62\u6700\u5927\u548c, \u603b\u548c &#8211; \u6700\u5c0f\u5b50\u6570\u7ec4\u548c)<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxSum<span class=\"token punctuation\">,<\/span> totalSum <span class=\"token operator\">&#8211;<\/span> minSum<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * \u73af\u5f62\u5b50\u6570\u7ec4\u7684\u6700\u5927\u548c &#8211; \u8fd4\u56de\u5b50\u6570\u7ec4\u672c\u8eab<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">maxSubarraySumCircularWithIndices<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u975e\u73af\u5f62\u6700\u5927\u5b50\u6570\u7ec4<\/span><br \/>\n        <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> linearResult <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">kadaneWithIndices<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> linearMax <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">sum<\/span><span class=\"token punctuation\">(<\/span>linearResult<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u603b\u548c<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> totalSum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> num <span class=\"token operator\">:<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            totalSum <span class=\"token operator\">&#043;&#061;<\/span> num<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u6700\u5c0f\u5b50\u6570\u7ec4&#xff08;\u7528\u4e8e\u73af\u5f62\u60c5\u51b5&#xff09;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> minSubarray <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">minSubarrayWithIndices<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> minSum <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">sum<\/span><span class=\"token punctuation\">(<\/span>minSubarray<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u73af\u5f62\u60c5\u51b5\u7684\u6700\u5927\u548c<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> circularMax <span class=\"token operator\">&#061;<\/span> totalSum <span class=\"token operator\">&#8211;<\/span> minSum<span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u7279\u6b8a\u60c5\u51b5&#xff1a;\u6240\u6709\u5143\u7d20\u90fd\u662f\u8d1f\u6570<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>linearMax <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> linearResult<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>circularMax <span class=\"token operator\">&gt;<\/span> linearMax<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token comment\">\/\/ \u6784\u5efa\u73af\u5f62\u5b50\u6570\u7ec4&#xff08;\u9700\u8981\u6392\u9664\u6700\u5c0f\u5b50\u6570\u7ec4&#xff09;<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token function\">buildCircularSubarray<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> minSubarray<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">else<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> linearResult<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token keyword\">private<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">kadaneWithIndices<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u7c7b\u4f3c\u4e4b\u524d\u7684\u5b9e\u73b0&#xff0c;\u8fd4\u56de\u5b50\u6570\u7ec4<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u7b80\u5316\u5b9e\u73b0&#xff0c;\u5b9e\u9645\u9700\u8981\u5b8c\u6574\u5b9e\u73b0<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token keyword\">private<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">minSubarrayWithIndices<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u7c7b\u4f3cKadane\u4f46\u6c42\u6700\u5c0f\u503c<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token keyword\">private<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">sum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> arr<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> sum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> num <span class=\"token operator\">:<\/span> arr<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            sum <span class=\"token operator\">&#043;&#061;<\/span> num<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> sum<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token keyword\">private<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">buildCircularSubarray<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> minSubarray<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u6784\u5efa\u6392\u9664\u6700\u5c0f\u5b50\u6570\u7ec4\u540e\u7684\u73af\u5f62\u5b50\u6570\u7ec4<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u7b80\u5316\u5b9e\u73b0<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h3>5.3 \u6700\u5927\u5b50\u77e9\u9635\u548c<\/h3>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">class<\/span> <span class=\"token class-name\">MaximumSubmatrix<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/**<br \/>\n     * \u6700\u5927\u5b50\u77e9\u9635\u548c<br \/>\n     * \u5c06\u4e8c\u7ef4\u95ee\u9898\u538b\u7f29\u4e3a\u4e00\u7ef4\u95ee\u9898<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubMatrix<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> matrix<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>matrix <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> matrix<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">||<\/span> matrix<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> m <span class=\"token operator\">&#061;<\/span> matrix<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> matrix<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u679a\u4e3e\u77e9\u9635\u7684\u4e0a\u8fb9\u754c<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> top <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> top <span class=\"token operator\">&lt;<\/span> m<span class=\"token punctuation\">;<\/span> top<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token comment\">\/\/ \u538b\u7f29\u6570\u7ec4&#xff0c;\u5c06\u591a\u884c\u538b\u7f29\u4e3a\u4e00\u884c<\/span><br \/>\n            <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> compressed <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u679a\u4e3e\u77e9\u9635\u7684\u4e0b\u8fb9\u754c<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> bottom <span class=\"token operator\">&#061;<\/span> top<span class=\"token punctuation\">;<\/span> bottom <span class=\"token operator\">&lt;<\/span> m<span class=\"token punctuation\">;<\/span> bottom<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token comment\">\/\/ \u66f4\u65b0\u538b\u7f29\u6570\u7ec4<\/span><br \/>\n                <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> col <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> col <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> col<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                    compressed<span class=\"token punctuation\">[<\/span>col<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;&#061;<\/span> matrix<span class=\"token punctuation\">[<\/span>bottom<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>col<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token punctuation\">}<\/span><\/p>\n<p>                <span class=\"token comment\">\/\/ \u5728\u4e00\u7ef4\u6570\u7ec4\u4e0a\u4f7f\u7528Kadane\u7b97\u6cd5<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> currentMax <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">kadane<\/span><span class=\"token punctuation\">(<\/span>compressed<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxSum<span class=\"token punctuation\">,<\/span> currentMax<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> maxSum<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token keyword\">private<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">kadane<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> currentMax <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> globalMax <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            currentMax <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> currentMax <span class=\"token operator\">&#043;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            globalMax <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>globalMax<span class=\"token punctuation\">,<\/span> currentMax<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> globalMax<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * \u8fd4\u56de\u6700\u5927\u5b50\u77e9\u9635<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">maxSubMatrixWithIndices<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> matrix<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>matrix <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> matrix<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">||<\/span> matrix<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> m <span class=\"token operator\">&#061;<\/span> matrix<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> matrix<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> top <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> bottom <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> left <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> right <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u679a\u4e3e\u4e0a\u8fb9\u754c<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> t <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> t <span class=\"token operator\">&lt;<\/span> m<span class=\"token punctuation\">;<\/span> t<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> compressed <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u679a\u4e3e\u4e0b\u8fb9\u754c<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> b <span class=\"token operator\">&#061;<\/span> t<span class=\"token punctuation\">;<\/span> b <span class=\"token operator\">&lt;<\/span> m<span class=\"token punctuation\">;<\/span> b<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token comment\">\/\/ \u66f4\u65b0\u538b\u7f29\u6570\u7ec4<\/span><br \/>\n                <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> col <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> col <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> col<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                    compressed<span class=\"token punctuation\">[<\/span>col<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;&#061;<\/span> matrix<span class=\"token punctuation\">[<\/span>b<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>col<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token punctuation\">}<\/span><\/p>\n<p>                <span class=\"token comment\">\/\/ \u5728\u4e00\u7ef4\u6570\u7ec4\u4e0a\u4f7f\u7528Kadane\u7b97\u6cd5\u5e76\u83b7\u53d6\u8fb9\u754c<\/span><br \/>\n                <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> kadaneResult <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">kadaneWithIndices<\/span><span class=\"token punctuation\">(<\/span>compressed<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> currentMax <span class=\"token operator\">&#061;<\/span> kadaneResult<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> currentLeft <span class=\"token operator\">&#061;<\/span> kadaneResult<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> currentRight <span class=\"token operator\">&#061;<\/span> kadaneResult<span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>currentMax <span class=\"token operator\">&gt;<\/span> maxSum<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                    maxSum <span class=\"token operator\">&#061;<\/span> currentMax<span class=\"token punctuation\">;<\/span><br \/>\n                    top <span class=\"token operator\">&#061;<\/span> t<span class=\"token punctuation\">;<\/span><br \/>\n                    bottom <span class=\"token operator\">&#061;<\/span> b<span class=\"token punctuation\">;<\/span><br \/>\n                    left <span class=\"token operator\">&#061;<\/span> currentLeft<span class=\"token punctuation\">;<\/span><br \/>\n                    right <span class=\"token operator\">&#061;<\/span> currentRight<span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token punctuation\">}<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u63d0\u53d6\u5b50\u77e9\u9635<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> height <span class=\"token operator\">&#061;<\/span> bottom <span class=\"token operator\">&#8211;<\/span> top <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> width <span class=\"token operator\">&#061;<\/span> right <span class=\"token operator\">&#8211;<\/span> left <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> result <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>height<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>width<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> height<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;<\/span> width<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                result<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> matrix<span class=\"token punctuation\">[<\/span>top <span class=\"token operator\">&#043;<\/span> i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>left <span class=\"token operator\">&#043;<\/span> j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> result<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token keyword\">private<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">kadaneWithIndices<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u8fd4\u56de [\u6700\u5927\u548c, \u8d77\u59cb\u7d22\u5f15, \u7ed3\u675f\u7d22\u5f15]<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> currentMax <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> globalMax <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> currentStart <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> globalStart <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> globalEnd <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&gt;<\/span> currentMax <span class=\"token operator\">&#043;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                currentMax <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                currentStart <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">else<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                currentMax <span class=\"token operator\">&#061;<\/span> currentMax <span class=\"token operator\">&#043;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><\/p>\n<p>            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>currentMax <span class=\"token operator\">&gt;<\/span> globalMax<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                globalMax <span class=\"token operator\">&#061;<\/span> currentMax<span class=\"token punctuation\">;<\/span><br \/>\n                globalStart <span class=\"token operator\">&#061;<\/span> currentStart<span class=\"token punctuation\">;<\/span><br \/>\n                globalEnd <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">{<\/span>globalMax<span class=\"token punctuation\">,<\/span> globalStart<span class=\"token punctuation\">,<\/span> globalEnd<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h3>5.4 \u5e26\u957f\u5ea6\u9650\u5236\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/h3>\n<p><span class=\"token keyword\">import<\/span> <span class=\"token namespace\">java<span class=\"token punctuation\">.<\/span>util<span class=\"token punctuation\">.<\/span><\/span><span class=\"token class-name\">Deque<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">import<\/span> <span class=\"token namespace\">java<span class=\"token punctuation\">.<\/span>util<span class=\"token punctuation\">.<\/span><\/span><span class=\"token class-name\">LinkedList<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">class<\/span> <span class=\"token class-name\">MaximumSubarrayWithLengthLimit<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/**<br \/>\n     * \u957f\u5ea6\u4e0d\u8d85\u8fc7K\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<br \/>\n     * \u4f7f\u7528\u524d\u7f00\u548c&#043;\u5355\u8c03\u961f\u5217<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubarraySumNoLargerThanK<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> k<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">||<\/span> k <span class=\"token operator\">&lt;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u524d\u7f00\u548c<\/span><br \/>\n        <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> prefix <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            prefix<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> prefix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u4f7f\u7528\u5355\u8c03\u9012\u589e\u961f\u5217\u7ef4\u62a4\u6700\u5c0f\u524d\u7f00\u548c<\/span><br \/>\n        <span class=\"token class-name\">Deque<\/span><span class=\"token generics\"><span class=\"token punctuation\">&lt;<\/span><span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">&gt;<\/span><\/span> deque <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token class-name\">LinkedList<\/span><span class=\"token generics\"><span class=\"token punctuation\">&lt;<\/span><span class=\"token punctuation\">&gt;<\/span><\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token comment\">\/\/ \u79fb\u9664\u961f\u5217\u4e2d\u4e0d\u5728\u7a97\u53e3\u5185\u7684\u5143\u7d20<\/span><br \/>\n            <span class=\"token comment\">\/\/ \u7a97\u53e3\u5927\u5c0f\u9650\u5236\u4e3ak&#xff0c;\u6240\u4ee5\u7d22\u5f15\u5dee\u4e0d\u80fd\u8d85\u8fc7k<\/span><br \/>\n            <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>deque<span class=\"token punctuation\">.<\/span><span class=\"token function\">isEmpty<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&amp;&amp;<\/span> i <span class=\"token operator\">&#8211;<\/span> deque<span class=\"token punctuation\">.<\/span><span class=\"token function\">peekFirst<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&gt;<\/span> k<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                deque<span class=\"token punctuation\">.<\/span><span class=\"token function\">pollFirst<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u5982\u679c\u961f\u5217\u4e0d\u4e3a\u7a7a&#xff0c;\u8ba1\u7b97\u6700\u5927\u548c<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>deque<span class=\"token punctuation\">.<\/span><span class=\"token function\">isEmpty<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxSum<span class=\"token punctuation\">,<\/span> prefix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#8211;<\/span> prefix<span class=\"token punctuation\">[<\/span>deque<span class=\"token punctuation\">.<\/span><span class=\"token function\">peekFirst<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u7ef4\u62a4\u5355\u8c03\u9012\u589e\u961f\u5217<\/span><br \/>\n            <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>deque<span class=\"token punctuation\">.<\/span><span class=\"token function\">isEmpty<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&amp;&amp;<\/span> prefix<span class=\"token punctuation\">[<\/span>deque<span class=\"token punctuation\">.<\/span><span class=\"token function\">peekLast<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&gt;&#061;<\/span> prefix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                deque<span class=\"token punctuation\">.<\/span><span class=\"token function\">pollLast<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><\/p>\n<p>            deque<span class=\"token punctuation\">.<\/span><span class=\"token function\">offerLast<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> maxSum<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/**<br \/>\n     * \u957f\u5ea6\u81f3\u5c11\u4e3aK\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<br \/>\n     *\/<\/span><br \/>\n    <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubarraySumAtLeastK<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> k<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>nums <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token keyword\">null<\/span> <span class=\"token operator\">||<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">||<\/span> k <span class=\"token operator\">&lt;&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">||<\/span> k <span class=\"token operator\">&gt;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u524d\u7f00\u548c<\/span><br \/>\n        <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> prefix <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            prefix<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> prefix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u5bf9\u4e8e\u6bcf\u4e2a\u7ed3\u675f\u4f4d\u7f6ei&#xff0c;\u6211\u4eec\u9700\u8981\u627e\u5230\u5f00\u59cb\u4f4d\u7f6ej&#xff0c;\u4f7f\u5f97i-j&#043;1 &gt;&#061; k<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u5373 j &lt;&#061; i-k&#043;1<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u6700\u5927\u548c &#061; prefix[i&#043;1] &#8211; min(prefix[j])&#xff0c;\u5176\u4e2d j &lt;&#061; i-k&#043;1<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MIN_VALUE<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> minPrefix <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Integer<\/span><span class=\"token punctuation\">.<\/span>MAX_VALUE<span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> k <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token comment\">\/\/ \u66f4\u65b0\u6700\u5c0f\u524d\u7f00\u548c&#xff08;\u6ce8\u610f\u7d22\u5f15\u8303\u56f4&#xff09;<\/span><br \/>\n            minPrefix <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>minPrefix<span class=\"token punctuation\">,<\/span> prefix<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#8211;<\/span> k <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u8ba1\u7b97\u5f53\u524d\u6700\u5927\u548c<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> currentSum <span class=\"token operator\">&#061;<\/span> prefix<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#8211;<\/span> minPrefix<span class=\"token punctuation\">;<\/span><br \/>\n            maxSum <span class=\"token operator\">&#061;<\/span> <span class=\"token class-name\">Math<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>maxSum<span class=\"token punctuation\">,<\/span> currentSum<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> maxSum<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h2>6. \u603b\u7ed3<\/h2>\n<h3>6.1 \u6838\u5fc3\u77e5\u8bc6\u603b\u7ed3<\/h3>\n<li>Kadane\u7b97\u6cd5\u672c\u8d28&#xff1a;\u52a8\u6001\u89c4\u5212\u601d\u60f3\u7684\u7cbe\u7b80\u5e94\u7528&#xff0c;\u7ef4\u62a4\u4ee5\u5f53\u524d\u4f4d\u7f6e\u7ed3\u5c3e\u7684\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/li>\n<li>\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b&#xff1a;dp[i] &#061; max(nums[i], dp[i-1] &#043; nums[i])<\/li>\n<li>\u7a7a\u95f4\u4f18\u5316&#xff1a;\u7531\u4e8e\u53ea\u9700\u8981\u524d\u4e00\u4e2a\u72b6\u6001&#xff0c;\u53ef\u4ee5\u4f7f\u7528\u5355\u4e2a\u53d8\u91cf\u66ff\u4ee3\u6570\u7ec4<\/li>\n<li>\u8d1f\u6570\u5904\u7406&#xff1a;\u7b97\u6cd5\u5929\u7136\u652f\u6301\u8d1f\u6570&#xff0c;\u65e0\u9700\u7279\u6b8a\u5904\u7406<\/li>\n<h3>6.2 \u7b97\u6cd5\u9009\u62e9\u6307\u5357<\/h3>\n<ul>\n<li>\u6807\u51c6\u573a\u666f&#xff1a;Kadane\u7b97\u6cd5\u662f\u6700\u4f18\u9009\u62e9&#xff0c;\u65f6\u95f4\u590d\u6742\u5ea6O(n)&#xff0c;\u7a7a\u95f4\u590d\u6742\u5ea6O(1)<\/li>\n<li>\u6559\u80b2\u76ee\u7684&#xff1a;\u5206\u6cbb\u6cd5\u5c55\u793a\u4e86\u7b97\u6cd5\u8bbe\u8ba1\u7684\u7f8e\u611f&#xff0c;\u9002\u5408\u5b66\u4e60\u5206\u6cbb\u601d\u60f3<\/li>\n<li>\u6269\u5c55\u95ee\u9898&#xff1a;\u6839\u636e\u5177\u4f53\u9700\u6c42\u9009\u62e9\u76f8\u5e94\u53d8\u4f53\u7b97\u6cd5<\/li>\n<\/ul>\n<h3>6.3 \u5e94\u7528\u573a\u666f<\/h3>\n<ul>\n<li>\u91d1\u878d\u5206\u6790&#xff1a;\u6700\u5927\u8fde\u7eed\u6536\u76ca\u65f6\u95f4\u6bb5\u5206\u6790<\/li>\n<li>\u4fe1\u53f7\u5904\u7406&#xff1a;\u5bfb\u627e\u4fe1\u53f7\u5f3a\u5ea6\u6700\u5927\u7684\u8fde\u7eed\u65f6\u6bb5<\/li>\n<li>\u6570\u636e\u6316\u6398&#xff1a;\u53d1\u73b0\u65f6\u95f4\u5e8f\u5217\u4e2d\u7684\u663e\u8457\u6a21\u5f0f<\/li>\n<li>\u6e38\u620f\u5f00\u53d1&#xff1a;\u7edf\u8ba1\u8fde\u7eed\u6e38\u620f\u4e2d\u7684\u6700\u9ad8\u5f97\u5206<\/li>\n<\/ul>\n<h3>6.4 \u9762\u8bd5\u6280\u5de7<\/h3>\n<li>\u4ece\u66b4\u529b\u89e3\u6cd5\u5f00\u59cb&#xff0c;\u5206\u6790\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u95ee\u9898<\/li>\n<li>\u5f15\u5165\u52a8\u6001\u89c4\u5212\u601d\u60f3&#xff0c;\u63a8\u5bfc\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b<\/li>\n<li>\u4f18\u5316\u7a7a\u95f4\u590d\u6742\u5ea6&#xff0c;\u5c55\u793aKadane\u7b97\u6cd5<\/li>\n<li>\u8ba8\u8bba\u5206\u6cbb\u6cd5\u4f5c\u4e3a\u8fdb\u9636\u89e3\u6cd5<\/li>\n<li>\u5c55\u793a\u5bf9\u76f8\u5173\u53d8\u4f53\u95ee\u9898\u7684\u7406\u89e3<\/li>\n<p>\u6700\u5927\u5b50\u6570\u7ec4\u548c\u95ee\u9898\u662f\u52a8\u6001\u89c4\u5212\u7684\u7ecf\u5178\u5165\u95e8\u95ee\u9898&#xff0c;\u638c\u63e1\u8fd9\u4e00\u95ee\u9898\u4e0d\u4ec5\u6709\u52a9\u4e8e\u7406\u89e3\u52a8\u6001\u89c4\u5212\u7684\u6838\u5fc3\u601d\u60f3&#xff0c;\u8fd8\u80fd\u4e3a\u89e3\u51b3\u66f4\u590d\u6742\u7684\u4f18\u5316\u95ee\u9898\u5960\u5b9a\u57fa\u7840\u3002\u65e0\u8bba\u662f\u9762\u8bd5\u51c6\u5907\u8fd8\u662f\u5b9e\u9645\u5e94\u7528&#xff0c;Kadane\u7b97\u6cd5\u90fd\u662f\u4e00\u4e2a\u5fc5\u987b\u638c\u63e1\u7684\u91cd\u8981\u7b97\u6cd5\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u76ee\u5f551. 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