{"id":61825,"date":"2026-01-18T18:17:46","date_gmt":"2026-01-18T10:17:46","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/61825.html"},"modified":"2026-01-18T18:17:46","modified_gmt":"2026-01-18T10:17:46","slug":"%e4%b8%80%e7%af%87%e6%96%87%e7%ab%a0%e8%ae%a9%e4%bd%a0%e7%86%9f%e6%82%89%e6%bb%91%e5%8a%a8%e7%aa%97%e5%8f%a3","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/61825.html","title":{"rendered":"\u4e00\u7bc7\u6587\u7ae0\u8ba9\u4f60\u719f\u6089\u6ed1\u52a8\u7a97\u53e3"},"content":{"rendered":"<p>\u6ed1\u52a8\u7a97\u53e3\u662f\u5904\u7406\u6570\u7ec4 \/ \u5b57\u7b26\u4e32\u5b50\u95ee\u9898\u7684\u9ad8\u6548\u7b97\u6cd5\u601d\u60f3&#xff0c;\u6838\u5fc3\u662f\u7528\u4e00\u4e2a \u201c\u53ef\u79fb\u52a8\u7684\u7a97\u53e3\u201d&#xff08;\u8fde\u7eed\u7684\u5b50\u533a\u95f4&#xff09;\u8986\u76d6\u6570\u636e&#xff0c;\u901a\u8fc7 \u201c\u6ed1\u52a8\u201d \u7a97\u53e3&#xff08;\u6269\u5927 \/ \u7f29\u5c0f\u8fb9\u754c&#xff09;\u4ee3\u66ff\u66b4\u529b\u679a\u4e3e&#xff0c;\u5c06\u65f6\u95f4\u590d\u6742\u5ea6\u4ece O (n\u00b2) \u964d\u5230 O (n)\u3002<\/p>\n<h3>\u4e00\u3001\u5148\u641e\u61c2&#xff1a;\u4ec0\u4e48\u662f\u6ed1\u52a8\u7a97\u53e3&#xff1f;<\/h3>\n<h4>1. \u901a\u4fd7\u7406\u89e3&#xff1a;\u201c\u79fb\u52a8\u7684\u671b\u8fdc\u955c\u201d<\/h4>\n<p>\u60f3\u8c61\u4f60\u7528\u4e00\u4e2a\u56fa\u5b9a\u957f\u5ea6\u7684\u671b\u8fdc\u955c\u89c2\u5bdf\u4e00\u6392\u6811\u6728&#xff08;\u6570\u7ec4&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\u7a97\u53e3&#xff1a;\u671b\u8fdc\u955c\u7684\u89c6\u91ce\u8303\u56f4&#xff08;\u5bf9\u5e94\u6570\u7ec4\u7684\u8fde\u7eed\u5b50\u533a\u95f4&#xff09;&#xff1b;<\/li>\n<li>\u6ed1\u52a8&#xff1a;\u671b\u8fdc\u955c\u5411\u53f3\u79fb\u52a8\u65f6&#xff0c;\u5de6\u8fb9\u7684\u6811\u6728\u79fb\u51fa\u89c6\u91ce&#xff0c;\u53f3\u8fb9\u7684\u6811\u6728\u8fdb\u5165\u89c6\u91ce&#xff08;\u7a97\u53e3\u8fb9\u754c\u79fb\u52a8&#xff0c;\u4e0d\u91cd\u590d\u626b\u63cf\u5df2\u89c2\u5bdf\u7684\u6811\u6728&#xff09;&#xff1b;<\/li>\n<li>\u6838\u5fc3&#xff1a;\u901a\u8fc7 \u201c\u6ed1\u52a8\u201d \u907f\u514d\u91cd\u590d\u8ba1\u7b97&#xff0c;\u63d0\u9ad8\u6548\u7387\u3002<\/li>\n<\/ul>\n<h4>2. \u751f\u6d3b\u4f8b\u5b50&#xff1a;\u8d85\u5e02\u7ed3\u8d26\u6392\u961f<\/h4>\n<p>\u5047\u8bbe\u8d85\u5e02\u8981\u6c42 \u201c\u6bcf\u6b21\u6700\u591a 3 \u4eba\u540c\u65f6\u7ed3\u8d26\u201d&#xff08;\u7a97\u53e3\u957f\u5ea6\u56fa\u5b9a\u4e3a 3&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\u521d\u59cb\u7a97\u53e3&#xff1a;\u7b2c 1\u30012\u30013 \u4eba&#xff08;\u5904\u7406\u8fd9 3 \u4eba\u7684\u7ed3\u8d26&#xff09;&#xff1b;<\/li>\n<li>\u6ed1\u52a8\u7a97\u53e3&#xff1a;\u7b2c 3 \u4eba\u7ed3\u5b8c\u8d26\u540e&#xff0c;\u7a97\u53e3\u5411\u53f3\u79fb&#xff0c;\u53d8\u6210\u7b2c 2\u30013\u30014 \u4eba&#xff08;\u4e0d\u7528\u91cd\u65b0\u5904\u7406\u7b2c 2\u30013 \u4eba&#xff0c;\u53ea\u65b0\u589e\u7b2c 4 \u4eba&#xff09;&#xff1b;<\/li>\n<li>\u4f18\u52bf&#xff1a;\u4e0d\u7528\u6bcf\u6b21\u90fd\u4ece\u7b2c 1 \u4eba\u5f00\u59cb\u91cd\u65b0\u7edf\u8ba1&#xff0c;\u8282\u7701\u65f6\u95f4\u3002<\/li>\n<\/ul>\n<h4>3. \u6838\u5fc3\u5206\u7c7b&#xff08;\u4e24\u79cd&#xff09;<\/h4>\n<table>\n<tr>\u7a97\u53e3\u7c7b\u578b\u7279\u70b9\u5178\u578b\u95ee\u9898<\/tr>\n<tbody>\n<tr>\n<td>\u56fa\u5b9a\u7a97\u53e3&#xff08;\u957f\u5ea6\u56fa\u5b9a&#xff09;<\/td>\n<td>\u7a97\u53e3\u5927\u5c0f\u4e0d\u53d8&#xff0c;\u53ea\u5de6\u53f3\u6ed1\u52a8<\/td>\n<td>\u957f\u5ea6\u4e3a k \u7684\u5b50\u6570\u7ec4\u6700\u5927\u548c\u3001\u5b57\u7b26\u4e32\u4e2d\u6240\u6709\u957f\u5ea6\u4e3a k \u7684\u5b50\u4e32<\/td>\n<\/tr>\n<tr>\n<td>\u53ef\u53d8\u7a97\u53e3&#xff08;\u957f\u5ea6\u53ef\u53d8&#xff09;<\/td>\n<td>\u7a97\u53e3\u5927\u5c0f\u6839\u636e\u6761\u4ef6\u6269\u5927 \/ \u7f29\u5c0f<\/td>\n<td>\u65e0\u91cd\u590d\u5b57\u7b26\u7684\u6700\u957f\u5b50\u4e32\u3001\u548c\u5927\u4e8e\u7b49\u4e8e target \u7684\u6700\u77ed\u5b50\u6570\u7ec4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 style=\"background-color:transparent\">\u4e8c\u3001\u6838\u5fc3\u539f\u7406&#xff1a;\u4e3a\u4ec0\u4e48\u6ed1\u52a8\u7a97\u53e3\u9ad8\u6548&#xff1f;<\/h3>\n<p>\u66b4\u529b\u679a\u4e3e\u4f1a\u91cd\u590d\u626b\u63cf\u5927\u91cf\u5143\u7d20&#xff08;\u6bd4\u5982\u627e\u5b50\u6570\u7ec4\u6700\u5927\u548c&#xff0c;\u66b4\u529b\u679a\u4e3e\u6240\u6709\u5b50\u6570\u7ec4&#xff0c;\u65f6\u95f4 O (n\u00b2)&#xff09;&#xff0c;\u800c\u6ed1\u52a8\u7a97\u53e3\u7684\u6838\u5fc3\u662f \u201c\u53ea\u5904\u7406\u65b0\u589e\u548c\u79fb\u51fa\u7684\u5143\u7d20\u201d&#xff1a;<\/p>\n<ul>\n<li>\u56fa\u5b9a\u7a97\u53e3&#xff1a;\u6ed1\u52a8\u65f6&#xff0c;\u5de6\u8fb9\u79fb\u51fa 1 \u4e2a\u5143\u7d20&#xff0c;\u53f3\u8fb9\u65b0\u589e 1 \u4e2a\u5143\u7d20&#xff0c;\u53ea\u9700\u8ba1\u7b97 \u201c\u603b\u548c &#061; \u539f\u603b\u548c &#8211; \u79fb\u51fa\u5143\u7d20 &#043; \u65b0\u589e\u5143\u7d20\u201d&#xff08;O (1) \u64cd\u4f5c&#xff09;&#xff1b;<\/li>\n<li>\u53ef\u53d8\u7a97\u53e3&#xff1a;\u901a\u8fc7\u6269\u5927\u53f3\u8fb9\u754c\u52a0\u5165\u5143\u7d20&#xff0c;\u4e0d\u6ee1\u8db3\u6761\u4ef6\u65f6\u7f29\u5c0f\u5de6\u8fb9\u754c&#xff0c;\u5168\u7a0b\u6bcf\u4e2a\u5143\u7d20\u53ea\u8fdb\u7a97\u53e3 1 \u6b21\u3001\u51fa\u7a97\u53e3 1 \u6b21&#xff08;\u603b\u65f6\u95f4 O (n)&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u5c31\u50cf\u7528\u671b\u8fdc\u955c\u89c2\u5bdf\u6811\u6728&#xff0c;\u79fb\u52a8\u65f6\u4e0d\u7528\u91cd\u65b0\u770b\u6240\u6709\u6811&#xff0c;\u53ea\u770b\u65b0\u8fdb\u5165\u89c6\u91ce\u7684\u6811\u548c\u79bb\u5f00\u89c6\u91ce\u7684\u6811&#xff0c;\u6548\u7387\u81ea\u7136\u9ad8\u3002<\/p>\n<h3>\u4e09\u3001\u5178\u578b\u95ee\u9898\u62c6\u89e3&#xff08;\u4ee3\u7801\u5b9e\u73b0&#xff09;<\/h3>\n<h4>1. \u56fa\u5b9a\u7a97\u53e3&#xff1a;\u957f\u5ea6\u4e3a k \u7684\u5b50\u6570\u7ec4\u6700\u5927\u548c&#xff08;LeetCode 643&#xff09;<\/h4>\n<h5>\u95ee\u9898\u63cf\u8ff0&#xff1a;<\/h5>\n<p>\u7ed9\u5b9a\u6570\u7ec4 nums &#061; [1,12,-5,-6,50,3]&#xff0c;k&#061;4&#xff0c;\u6c42\u957f\u5ea6\u4e3a 4 \u7684\u5b50\u6570\u7ec4\u7684\u6700\u5927\u548c&#xff08;\u7b54\u6848&#xff1a;12 &#043; (-5) &#043; (-6) &#043; 50 &#061; 51&#xff09;\u3002<\/p>\n<h5>\u6ed1\u52a8\u7a97\u53e3\u601d\u8def&#xff1a;<\/h5>\n<ul>\n<li>\u521d\u59cb\u7a97\u53e3&#xff1a;\u524d 4 \u4e2a\u5143\u7d20&#xff08;1,12,-5,-6&#xff09;&#xff0c;\u603b\u548c &#061; 2&#xff1b;<\/li>\n<li>\u6ed1\u52a8\u7a97\u53e3&#xff1a;\u6bcf\u6b21\u5411\u53f3\u79fb 1 \u4f4d&#xff0c;\u603b\u548c &#061; \u539f\u603b\u548c &#8211; \u5de6\u8fb9\u79fb\u51fa\u5143\u7d20 &#043; \u53f3\u8fb9\u65b0\u589e\u5143\u7d20&#xff1b;\n<ul>\n<li>\u7b2c 1 \u6b21\u6ed1\u52a8&#xff1a;\u79fb\u51fa 1&#xff0c;\u65b0\u589e 50 \u2192 \u603b\u548c &#061; 2-1&#043;50&#061;51&#xff1b;<\/li>\n<li>\u7b2c 2 \u6b21\u6ed1\u52a8&#xff1a;\u79fb\u51fa 12&#xff0c;\u65b0\u589e 3 \u2192 \u603b\u548c &#061; 51-12&#043;3&#061;42&#xff1b;<\/li>\n<\/ul>\n<\/li>\n<li>\u8bb0\u5f55\u8fc7\u7a0b\u4e2d\u6700\u5927\u7684\u603b\u548c&#xff08;51&#xff09;\u3002<\/li>\n<\/ul>\n<h5>\u4ee3\u7801\u5b9e\u73b0&#xff08;Java&#xff09;&#xff1a;<\/h5>\n<p>public double findMaxAverage(int[] nums, int k) {<br \/>\n    int n &#061; nums.length;<br \/>\n    int windowSum &#061; 0;<br \/>\n    \/\/ \u521d\u59cb\u5316\u7a97\u53e3&#xff08;\u524dk\u4e2a\u5143\u7d20\u6c42\u548c&#xff09;<br \/>\n    for (int i &#061; 0; i &lt; k; i&#043;&#043;) {<br \/>\n        windowSum &#043;&#061; nums[i];<br \/>\n    }<br \/>\n    int maxSum &#061; windowSum;<br \/>\n    \/\/ \u6ed1\u52a8\u7a97\u53e3&#xff08;\u4ecek\u5f00\u59cb&#xff0c;\u6bcf\u6b21\u53f3\u79fb1\u4f4d&#xff09;<br \/>\n    for (int i &#061; k; i &lt; n; i&#043;&#043;) {<br \/>\n        windowSum &#061; windowSum &#8211; nums[i &#8211; k] &#043; nums[i]; \/\/ \u79fb\u51fa\u5de6\u5143\u7d20&#xff0c;\u52a0\u5165\u53f3\u5143\u7d20<br \/>\n        maxSum &#061; Math.max(maxSum, windowSum);<br \/>\n    }<br \/>\n    return (double) maxSum \/ k;<br \/>\n}<\/p>\n<h4>2. \u53ef\u53d8\u7a97\u53e3&#xff1a;\u65e0\u91cd\u590d\u5b57\u7b26\u7684\u6700\u957f\u5b50\u4e32&#xff08;LeetCode 3&#xff09;<\/h4>\n<h5>\u95ee\u9898\u63cf\u8ff0&#xff1a;<\/h5>\n<p>\u7ed9\u5b9a\u5b57\u7b26\u4e32 s &#061; &#034;abcabcbb&#034;&#xff0c;\u6c42\u65e0\u91cd\u590d\u5b57\u7b26\u7684\u6700\u957f\u5b50\u4e32\u957f\u5ea6&#xff08;\u7b54\u6848&#xff1a;3&#xff0c;\u5bf9\u5e94 &#034;abc&#034;&#xff09;\u3002<\/p>\n<h5>\u6ed1\u52a8\u7a97\u53e3\u601d\u8def&#xff1a;<\/h5>\n<ul>\n<li>\u7a97\u53e3\u8fb9\u754c&#xff1a;\u5de6\u6307\u9488left\u3001\u53f3\u6307\u9488right&#xff08;\u521d\u59cb\u90fd\u4e3a 0&#xff09;&#xff0c;\u7a97\u53e3\u4e3a[left, right]&#xff1b;<\/li>\n<li>\u6269\u5927\u7a97\u53e3&#xff1a;right\u5411\u53f3\u79fb&#xff0c;\u52a0\u5165\u5f53\u524d\u5b57\u7b26&#xff0c;\u7528\u54c8\u5e0c\u8868\u8bb0\u5f55\u5b57\u7b26\u662f\u5426\u5b58\u5728&#xff1b;<\/li>\n<li>\u7f29\u5c0f\u7a97\u53e3&#xff1a;\u5982\u679c\u5f53\u524d\u5b57\u7b26\u5df2\u5728\u7a97\u53e3\u4e2d&#xff0c;left\u5411\u53f3\u79fb&#xff0c;\u76f4\u5230\u7a97\u53e3\u4e2d\u65e0\u91cd\u590d\u5b57\u7b26&#xff1b;<\/li>\n<li>\u8bb0\u5f55\u8fc7\u7a0b\u4e2d\u7a97\u53e3\u7684\u6700\u5927\u957f\u5ea6\u3002<\/li>\n<\/ul>\n<h5>\u4ee3\u7801\u5b9e\u73b0&#xff08;Java&#xff09;&#xff1a;<\/h5>\n<p>public int lengthOfLongestSubstring(String s) {<br \/>\n    Map&lt;Character, Integer&gt; map &#061; new HashMap&lt;&gt;();<br \/>\n    int maxLen &#061; 0;<br \/>\n    int left &#061; 0;<br \/>\n    for (int right &#061; 0; right &lt; s.length(); right&#043;&#043;) {<br \/>\n        char c &#061; s.charAt(right);<br \/>\n        \/\/ \u5982\u679c\u5b57\u7b26\u5df2\u5b58\u5728&#xff0c;\u4e14\u4f4d\u7f6e\u5728\u5f53\u524d\u7a97\u53e3\u5185&#xff0c;\u79fb\u52a8left\u5230\u91cd\u590d\u5b57\u7b26\u7684\u4e0b\u4e00\u4f4d<br \/>\n        if (map.containsKey(c) &amp;&amp; map.get(c) &gt;&#061; left) {<br \/>\n            left &#061; map.get(c) &#043; 1;<br \/>\n        }<br \/>\n        map.put(c, right); \/\/ \u66f4\u65b0\u5b57\u7b26\u7684\u6700\u65b0\u4f4d\u7f6e<br \/>\n        maxLen &#061; Math.max(maxLen, right &#8211; left &#043; 1); \/\/ \u8ba1\u7b97\u7a97\u53e3\u957f\u5ea6<br \/>\n    }<br \/>\n    return maxLen;<br \/>\n}<\/p>\n<h3>\u56db\u3001\u6838\u5fc3\u603b\u7ed3&#xff08;\u4e00\u53e5\u8bdd\u8bb0\u7262&#xff09;<\/h3>\n<ul>\n<li>\u6ed1\u52a8\u7a97\u53e3\u7684\u672c\u8d28&#xff1a;\u7528\u8fde\u7eed\u7684\u7a97\u53e3\u8986\u76d6\u5b50\u95ee\u9898&#xff0c;\u901a\u8fc7\u6ed1\u52a8\u907f\u514d\u91cd\u590d\u8ba1\u7b97&#xff1b;<\/li>\n<li>\u56fa\u5b9a\u7a97\u53e3&#xff1a;\u5148\u521d\u59cb\u5316&#xff0c;\u518d\u6ed1\u52a8&#xff08;\u53ea\u66f4\u65b0\u8fb9\u754c\u5143\u7d20&#xff09;&#xff1b;<\/li>\n<li>\u53ef\u53d8\u7a97\u53e3&#xff1a;\u53f3\u6269\u627e\u53ef\u884c\u89e3&#xff0c;\u5de6\u7f29\u4f18\u5316\u89e3&#xff08;\u5168\u7a0b O (n) \u6548\u7387&#xff09;\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u6ed1\u52a8\u7a97\u53e3\u662f\u5904\u7406\u6570\u7ec4 \/ \u5b57\u7b26\u4e32\u5b50\u95ee\u9898\u7684\u9ad8\u6548\u7b97\u6cd5\u601d\u60f3&#xff0c;\u6838\u5fc3\u662f\u7528\u4e00\u4e2a 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