{"id":47677,"date":"2025-07-30T08:41:59","date_gmt":"2025-07-30T00:41:59","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/47677.html"},"modified":"2025-07-30T08:41:59","modified_gmt":"2025-07-30T00:41:59","slug":"%e9%9b%b6%e5%9f%ba%e7%a1%80%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84%e4%b8%8e%e7%ae%97%e6%b3%95-%e7%ac%ac%e5%85%ad%e7%ab%a0%ef%bc%9a%e7%ae%97%e6%b3%95%e8%ae%be%e8%ae%a1%e8%8c%83%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/47677.html","title":{"rendered":"\u96f6\u57fa\u7840\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u2014\u2014\u7b2c\u516d\u7ae0\uff1a\u7b97\u6cd5\u8bbe\u8ba1\u8303\u5f0f\u4e0e\u9ad8\u7ea7\u4e3b\u9898-\u8bbe\u8ba1\u6280\u5de7(\u4e0b)"},"content":{"rendered":"<h3>6.1 \u7b97\u6cd5\u8bbe\u8ba1\u6280\u5de7<\/h3>\n<h4>\u8bbe\u8ba1\u6280\u5de7(\u4e0a)<\/h4>\n<h4>6.1.3 \u9884\u5904\u7406\u4e0e\u7d22\u5f15<\/h4>\n<h5>\u57fa\u672c\u6982\u5ff5<\/h5>\n<p>\u9884\u5904\u7406\u662f\u6307\u5728\u4e3b\u8981\u7b97\u6cd5\u6267\u884c\u4e4b\u524d&#xff0c;\u5bf9\u8f93\u5165\u6570\u636e\u8fdb\u884c\u4e00\u4e9b\u9884\u5148\u5904\u7406&#xff0c;\u4ee5\u4fbf\u7b80\u5316\u540e\u7eed\u7684\u8ba1\u7b97\u3002\u7d22\u5f15\u662f\u4e00\u79cd\u6570\u636e\u7ed3\u6784&#xff0c;\u7528\u4e8e\u52a0\u901f\u6570\u636e\u67e5\u627e\u64cd\u4f5c\u3002\u8fd9\u5c31\u50cf\u5728\u505a\u4e00\u9053\u590d\u6742\u83dc\u80b4\u524d&#xff0c;\u5148\u628a\u6240\u6709\u98df\u6750\u6d17\u597d\u3001\u5207\u597d\u3001\u5206\u7c7b\u597d&#xff0c;\u8fd9\u6837\u5728\u70f9\u996a\u8fc7\u7a0b\u4e2d\u5c31\u80fd\u66f4\u52a0\u9ad8\u6548\u3002<\/p>\n<p>\u9884\u5904\u7406\u548c\u7d22\u5f15\u7684\u6838\u5fc3\u601d\u60f3\u662f&#xff1a;\u82b1\u8d39\u4e00\u6b21\u6027\u7684\u524d\u671f\u5de5\u4f5c&#xff0c;\u6362\u53d6\u540e\u7eed\u591a\u6b21\u64cd\u4f5c\u7684\u6548\u7387\u63d0\u5347\u3002<\/p>\n<h5>\u751f\u6d3b\u4e2d\u7684\u4f8b\u5b50<\/h5>\n<p>\u56fe\u4e66\u9986\u7684\u56fe\u4e66\u5206\u7c7b\u7cfb\u7edf&#xff1a;<\/p>\n<ul>\n<li>\u56fe\u4e66\u9986\u4e0d\u4f1a\u968f\u673a\u6446\u653e\u4e66\u7c4d&#xff0c;\u800c\u662f\u6309\u7167\u5206\u7c7b\u7cfb\u7edf&#xff08;\u5982\u675c\u5a01\u5341\u8fdb\u5236\u5206\u7c7b\u6cd5&#xff09;\u7ec4\u7ec7\u56fe\u4e66<\/li>\n<li>\u8fd9\u79cd\u9884\u5904\u7406\u9700\u8981\u521d\u59cb\u6295\u5165&#xff08;\u5bf9\u6240\u6709\u4e66\u7c4d\u8fdb\u884c\u5206\u7c7b\u548c\u7f16\u53f7&#xff09;<\/li>\n<li>\u4f46\u5927\u5927\u52a0\u5feb\u4e86\u540e\u7eed\u67e5\u627e\u7279\u5b9a\u4e66\u7c4d\u7684\u901f\u5ea6<\/li>\n<li>\u8fd8\u6709\u76ee\u5f55\u7d22\u5f15\u7cfb\u7edf&#xff0c;\u53ef\u4ee5\u901a\u8fc7\u4f5c\u8005\u3001\u4e66\u540d\u6216\u4e3b\u9898\u5feb\u901f\u627e\u5230\u4e66\u7c4d\u4f4d\u7f6e<\/li>\n<\/ul>\n<p>\u53a8\u623f\u98df\u6750\u7684\u51c6\u5907\u5de5\u4f5c&#xff1a;<\/p>\n<ul>\n<li>\u4e13\u4e1a\u53a8\u5e08\u5728\u70f9\u996a\u524d\u4f1a\u505a&#034;mise en place&#034;&#xff08;\u6cd5\u8bed&#xff0c;\u610f\u4e3a&#034;\u653e\u7f6e\u5230\u4f4d&#034;&#xff09;<\/li>\n<li>\u63d0\u524d\u5c06\u6240\u6709\u98df\u6750\u6d17\u51c0\u3001\u5207\u597d\u3001\u5206\u7c7b\u653e\u597d<\/li>\n<li>\u867d\u7136\u524d\u671f\u9700\u8981\u65f6\u95f4&#xff0c;\u4f46\u5728\u5b9e\u9645\u70f9\u996a\u8fc7\u7a0b\u4e2d\u53ef\u4ee5\u66f4\u52a0\u9ad8\u6548\u6d41\u7545<\/li>\n<\/ul>\n<h5>\u5e38\u89c1\u7684\u9884\u5904\u7406\u4e0e\u7d22\u5f15\u6280\u672f<\/h5>\n<li>\n<p>\u6392\u5e8f\u9884\u5904\u7406&#xff1a;<\/p>\n<ul>\n<li>\u9884\u5148\u5bf9\u6570\u636e\u8fdb\u884c\u6392\u5e8f&#xff0c;\u4ee5\u4fbf\u540e\u7eed\u4f7f\u7528\u4e8c\u5206\u67e5\u627e<\/li>\n<li>\u4f8b\u5982&#xff1a;\u7535\u8bdd\u7c3f\u6309\u59d3\u6c0f\u5b57\u6bcd\u987a\u5e8f\u6392\u5e8f&#xff0c;\u4fbf\u4e8e\u5feb\u901f\u67e5\u627e\u8054\u7cfb\u4eba<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u54c8\u5e0c\u8868\u7d22\u5f15&#xff1a;<\/p>\n<ul>\n<li>\u6784\u5efa\u54c8\u5e0c\u8868\u4ee5\u5b9e\u73b0O(1)\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u67e5\u627e<\/li>\n<li>\u4f8b\u5982&#xff1a;\u6570\u636e\u5e93\u4e2d\u7684\u4e3b\u952e\u7d22\u5f15&#xff0c;\u53ef\u4ee5\u5feb\u901f\u5b9a\u4f4d\u8bb0\u5f55<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u524d\u7f00\u548c\/\u524d\u7f00\u79ef&#xff1a;<\/p>\n<ul>\n<li>\u9884\u8ba1\u7b97\u6570\u7ec4\u7684\u524d\u7f00\u548c\u6216\u524d\u7f00\u79ef&#xff0c;\u4ee5\u4fbf\u5feb\u901f\u8ba1\u7b97\u533a\u95f4\u548c\u6216\u79ef<\/li>\n<li>\u4f8b\u5982&#xff1a;\u5728\u7ebf\u8003\u8bd5\u7cfb\u7edf\u4e2d\u9884\u8ba1\u7b97\u6bcf\u9053\u9898\u7684\u7d2f\u8ba1\u5206\u6570<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u7a7a\u95f4\u5206\u533a\u7d22\u5f15&#xff1a;<\/p>\n<ul>\n<li>\u5c06\u7a7a\u95f4\u6570\u636e\u5212\u5206\u4e3a\u533a\u57df&#xff0c;\u52a0\u901f\u8303\u56f4\u67e5\u8be2<\/li>\n<li>\u4f8b\u5982&#xff1a;\u5730\u56fe\u5e94\u7528\u4e2d\u7684\u56db\u53c9\u6811\u6216R\u6811\u7d22\u5f15<\/li>\n<\/ul>\n<\/li>\n<h5>\u7b97\u6cd5\u793a\u4f8b&#xff1a;\u524d\u7f00\u548c\u4e0e\u533a\u95f4\u67e5\u8be2<\/h5>\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u6574\u6570\u6570\u7ec4&#xff0c;\u9700\u8981\u9891\u7e41\u5730\u8ba1\u7b97\u6570\u7ec4\u4e2d\u67d0\u4e2a\u533a\u95f4\u5185\u6240\u6709\u5143\u7d20\u7684\u548c\u3002<\/p>\n<p>\u65b9\u6cd51&#xff1a;\u76f4\u63a5\u8ba1\u7b97&#xff08;\u65e0\u9884\u5904\u7406&#xff09;<\/p>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">static<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">rangeSum<\/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 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 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> left<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> arr<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><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>\u8fd9\u79cd\u65b9\u6cd5\u6bcf\u6b21\u67e5\u8be2\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n)&#xff0c;\u5176\u4e2dn\u662f\u533a\u95f4\u957f\u5ea6\u3002<\/p>\n<p>\u65b9\u6cd52&#xff1a;\u4f7f\u7528\u524d\u7f00\u548c&#xff08;\u9884\u5904\u7406&#xff09;<\/p>\n<p><span class=\"token comment\">\/\/ \u6784\u5efa\u524d\u7f00\u548c\u6570\u7ec4<\/span><br \/>\n<span class=\"token keyword\">public<\/span> <span class=\"token keyword\">static<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">buildPrefixSum<\/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> n <span class=\"token operator\">&#061;<\/span> arr<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> prefixSum <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> <span class=\"token comment\">\/\/ \u6ce8\u610f\u5927\u5c0f\u4e3an&#043;1<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ prefixSum[i]\u8868\u793aarr[0]\u5230arr[i-1]\u7684\u548c<\/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        prefixSum<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> prefixSum<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> arr<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> prefixSum<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u4f7f\u7528\u524d\u7f00\u548c\u8ba1\u7b97\u533a\u95f4\u548c<\/span><br \/>\n<span class=\"token keyword\">public<\/span> <span class=\"token keyword\">static<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">rangeSum<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> prefixSum<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\">\/\/ \u533a\u95f4[left, right]\u7684\u548c &#061; \u524d\u7f00\u548c[0, right] &#8211; \u524d\u7f00\u548c[0, left-1]<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> prefixSum<span class=\"token punctuation\">[<\/span>right <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#8211;<\/span> prefixSum<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>\u8fd9\u79cd\u65b9\u6cd5\u9884\u5904\u7406\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n)&#xff0c;\u4f46\u6bcf\u6b21\u67e5\u8be2\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u964d\u4e3aO(1)\u3002<\/p>\n<h5>\u56fe\u89e3\u524d\u7f00\u548c<\/h5>\n<p>\u5047\u8bbe\u6709\u6570\u7ec4&#xff1a;[3, 1, 4, 1, 5, 9, 2, 6]<\/p>\n<p>\u524d\u7f00\u548c\u6570\u7ec4&#xff1a;[0, 3, 4, 8, 9, 14, 23, 25, 31]<\/p>\n<ul>\n<li>prefixSum[0] &#061; 0&#xff08;\u7a7a\u524d\u7f00&#xff09;<\/li>\n<li>prefixSum[1] &#061; 3&#xff08;\u524d1\u4e2a\u5143\u7d20\u548c&#xff09;<\/li>\n<li>prefixSum[2] &#061; 4&#xff08;\u524d2\u4e2a\u5143\u7d20\u548c&#xff09;<\/li>\n<li>prefixSum[3] &#061; 8&#xff08;\u524d3\u4e2a\u5143\u7d20\u548c&#xff09;<\/li>\n<li>\u2026<\/li>\n<li>prefixSum[8] &#061; 31&#xff08;\u5168\u90e8\u5143\u7d20\u548c&#xff09;<\/li>\n<\/ul>\n<p>\u8ba1\u7b97\u533a\u95f4\u548c\u793a\u4f8b&#xff1a;<\/p>\n<ul>\n<li>\u533a\u95f4[2, 5]\u7684\u548c &#061; prefixSum[6] &#8211; prefixSum[2] &#061; 23 &#8211; 4 &#061; 19<\/li>\n<li>\u533a\u95f4[0, 7]\u7684\u548c &#061; prefixSum[8] &#8211; prefixSum[0] &#061; 31 &#8211; 0 &#061; 31<\/li>\n<li>\u533a\u95f4[4, 4]\u7684\u548c &#061; prefixSum[5] &#8211; prefixSum[4] &#061; 14 &#8211; 9 &#061; 5<\/li>\n<\/ul>\n<h5>\u4e8c\u7ef4\u524d\u7f00\u548c<\/h5>\n<p>\u5bf9\u4e8e\u4e8c\u7ef4\u6570\u7ec4&#xff0c;\u4e5f\u53ef\u4ee5\u4f7f\u7528\u7c7b\u4f3c\u7684\u6280\u672f&#xff1a;<\/p>\n<p><span class=\"token comment\">\/\/ \u6784\u5efa\u4e8c\u7ef4\u524d\u7f00\u548c<\/span><br \/>\n<span class=\"token keyword\">public<\/span> <span class=\"token keyword\">static<\/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\">build2DPrefixSum<\/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 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 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><\/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><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> prefixSum <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>m <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/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><\/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> m<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> 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            prefixSum<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 punctuation\">[<\/span>j <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> prefixSum<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 punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> prefixSum<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><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><br \/>\n                                     prefixSum<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\">&#043;<\/span> matrix<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 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> prefixSum<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u8ba1\u7b97\u5b50\u77e9\u9635\u548c<\/span><br \/>\n<span class=\"token keyword\">public<\/span> <span class=\"token keyword\">static<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">subMatrixSum<\/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> prefixSum<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> row1<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> col1<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> row2<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> col2<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> prefixSum<span class=\"token punctuation\">[<\/span>row2 <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>col2 <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#8211;<\/span> prefixSum<span class=\"token punctuation\">[<\/span>row2 <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>col1<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#8211;<\/span><br \/>\n           prefixSum<span class=\"token punctuation\">[<\/span>row1<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>col2 <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> prefixSum<span class=\"token punctuation\">[<\/span>row1<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>col1<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h5>\u5e94\u7528\u573a\u666f<\/h5>\n<li>\u6570\u636e\u5e93\u7cfb\u7edf&#xff1a;\u4f7f\u7528\u7d22\u5f15\u52a0\u901f\u67e5\u8be2\u64cd\u4f5c<\/li>\n<li>\u56fe\u50cf\u5904\u7406&#xff1a;\u4f7f\u7528\u79ef\u5206\u56fe\u50cf&#xff08;\u4e8c\u7ef4\u524d\u7f00\u548c&#xff09;\u5feb\u901f\u8ba1\u7b97\u533a\u57df\u7279\u5f81<\/li>\n<li>\u5730\u7406\u4fe1\u606f\u7cfb\u7edf&#xff1a;\u4f7f\u7528\u7a7a\u95f4\u7d22\u5f15\u52a0\u901f\u5730\u7406\u4f4d\u7f6e\u67e5\u8be2<\/li>\n<li>\u641c\u7d22\u5f15\u64ce&#xff1a;\u4f7f\u7528\u5012\u6392\u7d22\u5f15\u52a0\u901f\u5168\u6587\u641c\u7d22<\/li>\n<li>\u6e38\u620f\u5f00\u53d1&#xff1a;\u9884\u8ba1\u7b97\u5149\u7167\u8d34\u56fe&#xff0c;\u52a0\u901f\u6e32\u67d3<\/li>\n<h4>6.1.4 \u589e\u91cf\u66f4\u65b0<\/h4>\n<h5>\u57fa\u672c\u6982\u5ff5<\/h5>\n<p>\u589e\u91cf\u66f4\u65b0\u662f\u4e00\u79cd\u53ea\u66f4\u65b0\u5fc5\u8981\u90e8\u5206\u800c\u4e0d\u662f\u91cd\u65b0\u8ba1\u7b97\u6574\u4e2a\u7ed3\u679c\u7684\u6280\u672f\u3002\u8fd9\u79cd\u65b9\u6cd5\u5728\u5904\u7406\u52a8\u6001\u53d8\u5316\u7684\u6570\u636e\u65f6\u7279\u522b\u6709\u7528&#xff0c;\u53ef\u4ee5\u5927\u5927\u63d0\u9ad8\u7b97\u6cd5\u7684\u6548\u7387\u3002\u5c31\u50cf\u4fee\u6539\u6587\u6863\u65f6&#xff0c;\u6211\u4eec\u53ea\u9700\u8981\u4fee\u6539\u53d8\u52a8\u7684\u90e8\u5206&#xff0c;\u800c\u4e0d\u662f\u91cd\u65b0\u6253\u5b57\u6574\u4e2a\u6587\u6863\u3002<\/p>\n<p>\u589e\u91cf\u66f4\u65b0\u7684\u6838\u5fc3\u601d\u60f3\u662f&#xff1a;\u5229\u7528\u524d\u4e00\u4e2a\u72b6\u6001\u7684\u7ed3\u679c\u548c\u65b0\u7684\u53d8\u5316&#xff0c;\u5feb\u901f\u8ba1\u7b97\u51fa\u65b0\u72b6\u6001\u7684\u7ed3\u679c\u3002<\/p>\n<h5>\u751f\u6d3b\u4e2d\u7684\u4f8b\u5b50<\/h5>\n<p>\u94f6\u884c\u8d26\u6237\u4f59\u989d&#xff1a;<\/p>\n<ul>\n<li>\u94f6\u884c\u4e0d\u4f1a\u6bcf\u6b21\u4ea4\u6613\u540e\u91cd\u65b0\u8ba1\u7b97\u4f60\u7684\u6240\u6709\u5386\u53f2\u4ea4\u6613<\/li>\n<li>\u800c\u662f\u57fa\u4e8e\u5f53\u524d\u4f59\u989d\u52a0\u4e0a\u6216\u51cf\u53bb\u65b0\u7684\u4ea4\u6613\u91d1\u989d<\/li>\n<li>\u4f8b\u5982&#xff1a;\u4f59\u989d1000\u5143&#xff0c;\u6d88\u8d39200\u5143&#xff0c;\u65b0\u4f59\u989d &#061; 1000 &#8211; 200 &#061; 800\u5143<\/li>\n<\/ul>\n<p>\u7535\u5b50\u8868\u683c\u8ba1\u7b97&#xff1a;<\/p>\n<ul>\n<li>\u5f53\u4f60\u4fee\u6539\u7535\u5b50\u8868\u683c\u4e2d\u7684\u4e00\u4e2a\u5355\u5143\u683c\u65f6<\/li>\n<li>\u53ea\u6709\u4f9d\u8d56\u4e8e\u8be5\u5355\u5143\u683c\u7684\u516c\u5f0f\u4f1a\u88ab\u91cd\u65b0\u8ba1\u7b97<\/li>\n<li>\u5176\u4ed6\u65e0\u5173\u7684\u8ba1\u7b97\u4fdd\u6301\u4e0d\u53d8<\/li>\n<\/ul>\n<p>\u793e\u4ea4\u5a92\u4f53\u4fe1\u606f\u6d41&#xff1a;<\/p>\n<ul>\n<li>\u5f53\u4f60\u6253\u5f00\u793e\u4ea4\u5a92\u4f53\u5e94\u7528\u65f6&#xff0c;\u5b83\u4e0d\u4f1a\u91cd\u65b0\u52a0\u8f7d\u6240\u6709\u5185\u5bb9<\/li>\n<li>\u800c\u662f\u53ea\u52a0\u8f7d\u81ea\u4e0a\u6b21\u67e5\u770b\u540e\u7684\u65b0\u5185\u5bb9<\/li>\n<li>\u901a\u5e38\u4f1a\u663e\u793a&#034;\u52a0\u8f7d\u65b0\u5185\u5bb9&#034;\u7684\u9009\u9879<\/li>\n<\/ul>\n<h5>\u5e38\u89c1\u7684\u589e\u91cf\u66f4\u65b0\u6280\u672f<\/h5>\n<li>\n<p>\u6ed1\u52a8\u7a97\u53e3&#xff1a;<\/p>\n<ul>\n<li>\u5728\u7a97\u53e3\u79fb\u52a8\u65f6\u53ea\u66f4\u65b0\u7a97\u53e3\u8fb9\u754c\u7684\u5143\u7d20<\/li>\n<li>\u4f8b\u5982&#xff1a;\u8ba1\u7b97\u6570\u7ec4\u7684\u79fb\u52a8\u5e73\u5747\u503c<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u5dee\u5206\u66f4\u65b0&#xff1a;<\/p>\n<ul>\n<li>\u53ea\u8bb0\u5f55\u548c\u5904\u7406\u53d8\u5316\u7684\u90e8\u5206<\/li>\n<li>\u4f8b\u5982&#xff1a;\u7248\u672c\u63a7\u5236\u7cfb\u7edf\u53ea\u5b58\u50a8\u6587\u4ef6\u7684\u53d8\u5316<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u589e\u91cf\u7ef4\u62a4\u6570\u636e\u7ed3\u6784&#xff1a;<\/p>\n<ul>\n<li>\u52a8\u6001\u7ef4\u62a4\u6811\u3001\u5806\u3001\u56fe\u7b49\u6570\u636e\u7ed3\u6784<\/li>\n<li>\u4f8b\u5982&#xff1a;\u52a8\u6001\u7ef4\u62a4\u6700\u5c0f\u751f\u6210\u6811<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6d41\u5904\u7406&#xff1a;<\/p>\n<ul>\n<li>\u5904\u7406\u8fde\u7eed\u5230\u8fbe\u7684\u6570\u636e\u6d41<\/li>\n<li>\u4f8b\u5982&#xff1a;\u5b9e\u65f6\u6570\u636e\u5206\u6790\u7cfb\u7edf<\/li>\n<\/ul>\n<\/li>\n<h5>\u7b97\u6cd5\u793a\u4f8b&#xff1a;\u6ed1\u52a8\u7a97\u53e3\u6700\u5927\u503c<\/h5>\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u6574\u6570\u6570\u7ec4\u548c\u4e00\u4e2a\u5927\u5c0f\u4e3ak\u7684\u6ed1\u52a8\u7a97\u53e3&#xff0c;\u7a97\u53e3\u4ece\u6570\u7ec4\u7684\u6700\u5de6\u8fb9\u6ed1\u52a8\u5230\u6700\u53f3\u8fb9&#xff0c;\u6211\u4eec\u9700\u8981\u627e\u51fa\u7a97\u53e3\u4e2d\u7684\u6700\u5927\u503c\u3002<\/p>\n<p>\u65b9\u6cd51&#xff1a;\u66b4\u529b\u6cd5&#xff08;\u65e0\u589e\u91cf\u66f4\u65b0&#xff09;<\/p>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">static<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">maxSlidingWindow<\/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\">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 operator\">||<\/span> k <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 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><\/p>\n<p>    <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 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><\/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 operator\">&#8211;<\/span> k<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> max <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\">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> i <span class=\"token operator\">&#043;<\/span> k<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            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>max<span class=\"token punctuation\">,<\/span> nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <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> max<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>\u8fd9\u79cd\u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n*k)&#xff0c;\u56e0\u4e3a\u5bf9\u4e8e\u6bcf\u4e2a\u7a97\u53e3\u4f4d\u7f6e&#xff0c;\u6211\u4eec\u90fd\u9700\u8981\u904d\u5386k\u4e2a\u5143\u7d20\u627e\u51fa\u6700\u5927\u503c\u3002<\/p>\n<p>\u65b9\u6cd52&#xff1a;\u4f7f\u7528\u53cc\u7aef\u961f\u5217&#xff08;\u589e\u91cf\u66f4\u65b0&#xff09;<\/p>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">static<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">maxSlidingWindow<\/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\">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 operator\">||<\/span> k <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 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><\/p>\n<p>    <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 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><br \/>\n    <span class=\"token comment\">\/\/ \u4f7f\u7528\u53cc\u7aef\u961f\u5217\u5b58\u50a8\u53ef\u80fd\u6210\u4e3a\u7a97\u53e3\u6700\u5927\u503c\u7684\u5143\u7d20\u7684\u7d22\u5f15<\/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;<\/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\u6240\u6709\u5c0f\u4e8e\u5f53\u524d\u5143\u7d20\u7684\u503c&#xff08;\u5b83\u4eec\u4e0d\u53ef\u80fd\u662f\u540e\u7eed\u7a97\u53e3\u7684\u6700\u5927\u503c&#xff09;<\/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> nums<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\">&lt;<\/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            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>        <span class=\"token comment\">\/\/ \u6dfb\u52a0\u5f53\u524d\u5143\u7d20\u7d22\u5f15\u5230\u961f\u5217<\/span><br \/>\n        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><\/p>\n<p>        <span class=\"token comment\">\/\/ \u79fb\u9664\u961f\u5217\u4e2d\u6240\u6709\u4e0d\u5728\u5f53\u524d\u7a97\u53e3\u8303\u56f4\u5185\u7684\u5143\u7d20<\/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> 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\">&lt;<\/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><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\">\/\/ \u5f53\u7a97\u53e3\u81f3\u5c11\u6709k\u4e2a\u5143\u7d20\u65f6&#xff0c;\u8bb0\u5f55\u5f53\u524d\u7a97\u53e3\u7684\u6700\u5927\u503c<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>i <span class=\"token operator\">&gt;&#061;<\/span> k <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            result<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 operator\">&#061;<\/span> nums<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><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>\u8fd9\u79cd\u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n)&#xff0c;\u56e0\u4e3a\u6bcf\u4e2a\u5143\u7d20\u6700\u591a\u88ab\u5904\u7406\u4e24\u6b21&#xff08;\u5165\u961f\u548c\u51fa\u961f&#xff09;\u3002<\/p>\n<h5>\u53e6\u4e00\u4e2a\u4f8b\u5b50&#xff1a;\u6700\u5927\u5b50\u6570\u7ec4\u548c&#xff08;Kadane\u7b97\u6cd5&#xff09;<\/h5>\n<p>\u6700\u5927\u5b50\u6570\u7ec4\u548c\u95ee\u9898\u662f\u5bfb\u627e\u4e00\u4e2a\u6570\u7ec4\u4e2d\u5177\u6709\u6700\u5927\u548c\u7684\u8fde\u7eed\u5b50\u6570\u7ec4\u3002<\/p>\n<p><span class=\"token keyword\">public<\/span> <span class=\"token keyword\">static<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxSubArraySum<\/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 comment\">\/\/ \u5982\u679c\u6570\u7ec4\u4e3a\u7a7a&#xff0c;\u8fd4\u56de0<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>arr<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 keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token keyword\">int<\/span> maxSoFar <span class=\"token operator\">&#061;<\/span> arr<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\">\/\/ \u8bb0\u5f55\u5168\u5c40\u6700\u5927\u5b50\u6570\u7ec4\u548c<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> maxEndingHere <span class=\"token operator\">&#061;<\/span> arr<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\">\/\/ \u8bb0\u5f55\u4ee5\u5f53\u524d\u5143\u7d20\u7ed3\u5c3e\u7684\u6700\u5927\u5b50\u6570\u7ec4\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> arr<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\">\/\/ \u589e\u91cf\u66f4\u65b0&#xff1a;\u5f53\u524d\u5143\u7d20\u8981\u4e48\u81ea\u5df1\u5f00\u59cb\u4e00\u4e2a\u65b0\u7684\u5b50\u6570\u7ec4&#xff0c;\u8981\u4e48\u52a0\u5165\u5230\u524d\u9762\u7684\u5b50\u6570\u7ec4<\/span><br \/>\n        maxEndingHere <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>arr<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> maxEndingHere <span class=\"token operator\">&#043;<\/span> arr<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\u5168\u5c40\u6700\u5927\u503c<\/span><br \/>\n        maxSoFar <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>maxSoFar<span class=\"token punctuation\">,<\/span> maxEndingHere<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> maxSoFar<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h5>\u56fe\u89e3Kadane\u7b97\u6cd5<\/h5>\n<p>\u5047\u8bbe\u6570\u7ec4\u4e3a&#xff1a;[-2, 1, -3, 4, -1, 2, 1, -5, 4]<\/p>\n<table>\n<tr>\u7d22\u5f15\u6570\u7ec4\u503cmaxEndingHere\u8ba1\u7b97maxEndingHeremaxSoFar<\/tr>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>-2<\/td>\n<td>\u521d\u59cb\u503c<\/td>\n<td>-2<\/td>\n<td>-2<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>max(1, -2&#043;1)<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>-3<\/td>\n<td>max(-3, 1&#043;(-3))<\/td>\n<td>-2<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>4<\/td>\n<td>max(4, -2&#043;4)<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>-1<\/td>\n<td>max(-1, 4&#043;(-1))<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>2<\/td>\n<td>max(2, 3&#043;2)<\/td>\n<td>5<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>1<\/td>\n<td>max(1, 5&#043;1)<\/td>\n<td>6<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>-5<\/td>\n<td>max(-5, 6&#043;(-5))<\/td>\n<td>1<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>4<\/td>\n<td>max(4, 1&#043;4)<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u6700\u7ec8\u7ed3\u679c&#xff1a;\u6700\u5927\u5b50\u6570\u7ec4\u548c\u4e3a6&#xff0c;\u5bf9\u5e94\u7684\u5b50\u6570\u7ec4\u662f[4, -1, 2, 1]\u3002<\/p>\n<h5>\u5e94\u7528\u573a\u666f<\/h5>\n<li>\u5b9e\u65f6\u6570\u636e\u5206\u6790&#xff1a;\u5904\u7406\u8fde\u7eed\u5230\u8fbe\u7684\u6570\u636e\u6d41<\/li>\n<li>\u52a8\u6001\u89c4\u5212\u4f18\u5316&#xff1a;\u51cf\u5c11\u91cd\u590d\u8ba1\u7b97<\/li>\n<li>\u56fe\u5f62\u6e32\u67d3&#xff1a;\u53ea\u66f4\u65b0\u5c4f\u5e55\u4e0a\u53d8\u5316\u7684\u90e8\u5206<\/li>\n<li>\u6570\u636e\u5e93\u66f4\u65b0&#xff1a;\u589e\u91cf\u5907\u4efd\u548c\u540c\u6b65<\/li>\n<li>\u7f16\u8bd1\u5668\u4f18\u5316&#xff1a;\u589e\u91cf\u7f16\u8bd1\u53ea\u91cd\u65b0\u7f16\u8bd1\u4fee\u6539\u7684\u90e8\u5206<\/li>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb523\u6b21\uff0c\u70b9\u8d5e23\u6b21\uff0c\u6536\u85cf11\u6b21\u3002\u9884\u5904\u7406\u4e0e\u7d22\u5f15\u6280\u672f\u901a\u8fc7\u9884\u5148\u7ec4\u7ec7\u6570\u636e\uff08\u5982\u6392\u5e8f\u3001\u54c8\u5e0c\u8868\uff09\u6765\u52a0\u901f\u540e\u7eed\u67e5\u8be2\uff0c\u7c7b\u4f3c\u4e8e\u56fe\u4e66\u9986\u5206\u7c7b\u7cfb\u7edf\u6216\u53a8\u623f\u5907\u83dc\u3002\u5e38\u89c1\u65b9\u6cd5\u5305\u62ec\u524d\u7f00\u548c\uff08O(n)\u9884\u5904\u7406\u540eO(1)\u533a\u95f4\u67e5\u8be2\uff09\u3001\u4e8c\u7ef4\u524d\u7f00\u548c\u7b49\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6570\u636e\u5e93\u3001\u56fe\u50cf\u5904\u7406\u548c\u641c\u7d22\u5f15\u64ce\u3002\u589e\u91cf\u66f4\u65b0\u5219\u901a\u8fc7\u53ea\u5904\u7406\u6570\u636e\u53d8\u5316\u90e8\u5206\u63d0\u5347\u6548\u7387\uff0c\u5982\u6ed1\u52a8\u7a97\u53e3\u53cc\u7aef\u961f\u5217\u6cd5\u5c06\u7a97\u53e3\u6700\u5927\u503c\u67e5\u627e\u4eceO(nk)\u4f18\u5316\u5230O(n)\u3002\u8fd9\u4e24\u79cd\u6280\u672f\u90fd\u4f53\u73b0\u4e86&quot;\u524d\u671f\u6295\u5165\u6362\u53d6\u957f\u671f\u6548\u7387&quot;\u7684\u6838\u5fc3\u601d\u60f3\uff0c\u5728\u52a8\u6001\u6570\u636e\u5904\u7406\u573a\u666f\u4e2d\u5c24\u4e3a\u91cd\u8981\u3002<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[99,4582,4579,427,4581,4578,4580],"topic":[],"class_list":["post-47677","post","type-post","status-publish","format-standard","hentry","category-server","tag-java","tag-4582","tag-4579","tag-427","tag-4581","tag-4578","tag-4580"],"yoast_head":"<!-- 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