{"id":34191,"date":"2025-04-29T09:13:44","date_gmt":"2025-04-29T01:13:44","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/34191.html"},"modified":"2025-04-29T09:13:44","modified_gmt":"2025-04-29T01:13:44","slug":"%e6%b7%b1%e5%ba%a6%e8%a7%a3%e6%9e%90%e7%ae%97%e6%b3%95%e4%b9%8b%e5%88%86%e6%b2%bb%ef%bc%88%e5%bd%92%e5%b9%b6%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/34191.html","title":{"rendered":"\u6df1\u5ea6\u89e3\u6790\u7b97\u6cd5\u4e4b\u5206\u6cbb\uff08\u5f52\u5e76\uff09"},"content":{"rendered":"<h3>48.\u6392\u5e8f\u6570\u7ec4<\/h3>\n<p>\u9898\u76ee\u94fe\u63a5 \u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4\u00a0nums&#xff0c;\u8bf7\u4f60\u5c06\u8be5\u6570\u7ec4\u5347\u5e8f\u6392\u5217\u3002<\/p>\n<p>\u4f60\u5fc5\u987b\u5728\u00a0\u4e0d\u4f7f\u7528\u4efb\u4f55\u5185\u7f6e\u51fd\u6570\u00a0\u7684\u60c5\u51b5\u4e0b\u89e3\u51b3\u95ee\u9898&#xff0c;\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a\u00a0O(nlog(n))&#xff0c;\u5e76\u4e14\u7a7a\u95f4\u590d\u6742\u5ea6\u5c3d\u53ef\u80fd\u5c0f\u3002<\/p>\n<p>\u793a\u4f8b 1&#xff1a;<\/p>\n<p>\u8f93\u5165&#xff1a; nums &#061; [5,2,3,1] \u8f93\u51fa&#xff1a;[1,2,3,5]<\/p>\n<p>\u793a\u4f8b 2&#xff1a;<\/p>\n<p>\u8f93\u5165&#xff1a; nums &#061; [5,1,1,2,0,0] \u8f93\u51fa&#xff1a;[0,0,1,1,2,5]<\/p>\n<p>\u6211\u4eec\u4e0a\u6b21\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u662f\u4f7f\u7528\u5feb\u6392\u8fdb\u884c\u89e3\u51b3\u7684&#xff0c;\u90a3\u4e48\u8fd9\u91cc\u662f\u4f7f\u7528\u5f52\u5e76\u6392\u5e8f\u8fdb\u884c\u89e3\u51b3\u7684<\/p>\n<p>\u5f52\u5e76\u662f\u4ec0\u4e48\u5462&#xff1f;\u8bf4\u767d\u4e86\u5c31\u662f\u9012\u5f52 \u5c06\u4e00\u4e2a\u6570\u7ec4\u6839\u636e\u4e2d\u95f4\u70b9\u5206\u6210\u4e24\u90e8\u5206&#xff0c;\u6211\u4eec\u518d\u4ece\u5de6\u8fb9\u533a\u95f4\u627e\u4e2d\u95f4\u70b9&#xff0c;\u4f9d\u6b21\u8fd9\u6837&#xff0c;\u76f4\u5230\u6211\u4eec\u6700\u540e\u53ea\u5269\u4e0b\u4e00\u4e2a\u5143\u7d20&#xff0c;\u6211\u4eec\u4f9d\u6b21\u8fdb\u884c\u8fd4\u56de\u7684\u64cd\u4f5c&#xff0c;\u7136\u540e\u8fdb\u884c\u4e0a\u4e00\u5c42\u7684\u53f3\u533a\u95f4\u8fdb\u884c\u9012\u5f52\u9012\u5f52 \u5f53\u6211\u4eec\u8fd9\u4e00\u5c42\u7684\u5224\u65ad\u90fd\u641e\u5b9a\u4e86&#xff0c;\u90a3\u4e48\u6211\u4eec\u5c31\u8fdb\u884c\u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4<\/p>\n<p>\u5f53\u6211\u4eec\u5de6\u8fb9\u548c\u53f3\u8fb9\u90fd\u6392\u5b8c\u5e8f\u4e4b\u540e&#xff0c;\u90a3\u4e48\u6211\u4eec\u5c31\u5c06\u8fd9\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4\u8fdb\u884c\u5408\u5e76\u64cd\u4f5c <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011340-681027c4068c7.png\" alt=\"image.png\" \/> \u8fd9\u79cd\u975e\u5e38\u50cf\u4e8c\u53c9\u6811\u7684\u540e\u7eed\u904d\u5386&#xff0c;\u5148\u628a\u5de6\u8fb9\u641e\u597d&#xff0c;\u518d\u628a\u53f3\u8fb9\u641e\u597d&#xff0c;\u518d\u56de\u5230\u6839\u8282\u70b9<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011340-681027c447252.png\" alt=\"image.png\" \/> \u5feb\u6392\u7684\u8fc7\u7a0b\u6709\u70b9\u7c7b\u4f3c\u4e8c\u53c9\u6811\u7684\u524d\u5e8f\u904d\u5386<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011340-681027c47a7f6.png\" alt=\"image.png\" \/><\/p>\n<p>class Solution<\/p>\n<p>{<\/p>\n<p>public:<\/p>\n<p>\u00a0 \u00a0 vector&lt;int&gt; sortArray(vector&lt;int&gt;&amp; nums)<\/p>\n<p>\u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 mergesort(nums,0,nums.size()-1);\/\/\u5c06\u8fd9\u6bb5\u533a\u95f4\u8fdb\u884c\u6392\u5e8f&#xff0c;\u6392\u5b8c\u5e8f\u76f4\u63a5\u8fd4\u56de\u5c31\u884c\u4e86<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 return nums;<\/p>\n<p>\u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 void mergesort(vector&lt;int&gt;&amp;nums,int left,int right)<\/p>\n<p>\u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 if(left&gt;&#061;right) return;\/\/\u7279\u6b8a\u60c5\u51b5&#xff0c;\u5982\u679c\u533a\u95f4\u4e0d\u5b58\u5728\u6216\u8005\u662f\u53ea\u6709\u4e00\u4e2a\u5143\u7d20\u7684\u8bdd<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/1.\u5148\u9009\u62e9\u4e2d\u95f4\u70b9\u5212\u5206\u533a\u95f4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int mid&#061;(left&#043;right)&gt;&gt;1;\/\/ &gt;&gt; 1 \u662f\u4f4d\u8fd0\u7b97\u4e2d\u7684\u53f3\u79fb\u64cd\u4f5c&#xff0c;\u5b83\u5c06\u7ed3\u679c\u53f3\u79fb\u4e00\u4f4d&#xff0c;\u76f8\u5f53\u4e8e\u5c06\u7ed3\u679c\u9664\u4ee52\u5e76\u5411\u4e0b\u53d6\u6574\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/[left,mid][mid&#043;1,right]<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/2.\u5c06\u5de6\u53f3\u533a\u95f4\u8fdb\u884c\u6392\u5e8f\u7684\u64cd\u4f5c<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 mergesort(nums,left,mid);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 mergesort(nums,mid&#043;1,right);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/3.\u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 vector&lt;int&gt;tmp(right-left&#043;1);\/\/\u8f85\u52a9\u6570\u7ec4&#xff0c;\u5927\u5c0f\u548c\u6211\u4eec\u7684nums\u5927\u5c0f\u4e00\u6837<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int cur1&#061;left;\/\/\u6307\u5411\u7b2c\u4e00\u4e2a\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int cur2&#061;mid&#043;1;\/\/\u6307\u5411\u7b2c\u4e8c\u4e2a\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int i&#061;0;\/\/\u8f85\u52a9\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid&amp;&amp;cur2&lt;&#061;right)<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmp[i&#043;&#043;]&#061;nums[cur1]&lt;&#061;nums[cur2]?nums[cur1&#043;&#043;]:nums[cur2&#043;&#043;];\/\/\u8fdb\u884c\u5224\u65ad&#xff0c;\u5982\u679ccur1\u7684\u5927\u5c0f\u5c0f\u4e8e\u7b49\u4e8ecur2\u7684\u8bdd&#xff0c;\u90a3\u4e48\u5c31\u8ba9\u6211\u4eec\u7684tmp[i]&#061;nums[cur1]\u7684\u503c<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/\u5c31\u662f\u8bf4\u767d\u4e86\u6301\u7eed\u8fdb\u884c\u5bf9\u6bd4&#xff0c;\u8c01\u5c0f\u8c01\u5148\u653e\u5230tmp\u8fd9\u4e2a\u6570\u7ec4\u4e2d\u53bb<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/i\u3001cur1\u3001cur2\u8fd9\u4e09\u4e2a\u6307\u9488\u90fd\u5f97\u5f80\u540e\u8fdb\u884c\u79fb\u52a8&#xff0c;\u6211\u4eec\u76f4\u63a5\u653e\u5728\u4e0a\u9762\u7684\u90a3\u4e2a\u4ee3\u7801\u4e2d\u53bb<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/\u5230\u8fd9\u91cc\u7684\u8bdd\u53ef\u80fd\u5b58\u5728\u4e00\u4e2a\u6570\u7ec4\u4e2d\u8fd8\u6709\u6570\u636e\u6ca1\u6709\u79fb\u52a8\u5230tmp\u4e2d\u53bb&#xff0c;\u4e0b\u9762\u4e24\u53e5\u4ee3\u7801\u5c31\u662f\u5904\u7406\u6ca1\u6709\u904d\u5386\u5b8c\u7684\u60c5\u51b5<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid)tmp[i&#043;&#043;]&#061;nums[cur1&#043;&#043;];\/\/\u56e0\u4e3a\u6b64\u65f6\u7684\u6307\u9488\u8fd8\u6ca1\u5230mid\u7684\u4f4d\u7f6e&#xff0c;\u5c31\u662f\u5927\u5c0f\u6bd4mid\u5c0f&#xff0c;\u90a3\u4e48\u6211\u4eec\u76f4\u63a5\u5c06cur1\u8fd9\u4e2a\u6570\u5b57\u4e2d\u5269\u4e0b\u7684\u5143\u7d20\u90fd\u653e\u5230tmp\u4e2d<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur2&lt;&#061;right)tmp[i&#043;&#043;]&#061;nums[cur2&#043;&#043;];\/\/\u548c\u4e0a\u9762\u4e00\u6837<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/\u8fd8\u539f<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 for(int i&#061;left;i&lt;&#061;right;i&#043;&#043;)<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 nums[i]&#061;tmp[i-left];\/\/\u6211\u4eec\u7684tmp\u6570\u7ec4\u9700\u8981\u4ece0\u5f00\u59cb\u8fdb\u884c\u8ba1\u6570\u64cd\u4f5c\u5417&#xff0c;\u6240\u4ee5\u6211\u4eec\u8fd9\u91cc\u4f7f\u7528i-left\u53ef\u4ee5\u8fbe\u5230\u4ece\u4e0b\u68070\u5f00\u59cb\u8fdb\u884c\u8d4b\u503c\u64cd\u4f5c<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 }<\/p>\n<p>};<\/p>\n<p>\u6211\u4eec\u5148\u627e\u51fa\u4e2d\u95f4\u70b9\u5bf9\u8fd9\u6bb5\u6570\u7ec4\u8fdb\u884c\u5212\u5206\u64cd\u4f5c&#xff0c;\u7136\u540e\u4f9d\u6b21\u5bf9\u5de6\u53f3\u533a\u95f4\u8fdb\u884c\u6392\u5e8f\u7684\u64cd\u4f5c&#xff0c;\u8fd9\u91cc\u5c31\u662f\u9012\u5f52\u8c03\u7528&#xff0c;\u7136\u540e\u6211\u4eec\u518d\u5408\u5e76\u4e24\u4e2a\u6570\u7ec4\u5c31\u884c\u4e86 \u6700\u540e\u6211\u4eec\u5c06\u6211\u4eec\u8f85\u52a9\u6570\u7ec4\u4e2d\u7684\u503c\u76f4\u63a5\u8d4b\u503c\u5230\u6211\u4eec\u7684nums\u4e2d\u5c31\u884c\u4e86<\/p>\n<p>\u8fd9\u79cd\u4ee3\u7801\u6211\u4eec\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u8fd9\u6837\u7684 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011340-681027c4b2bed.png\" alt=\"image.png\" \/> \u56e0\u4e3a\u6211\u4eec\u6bcf\u6b21\u5408\u5e76\u7684\u65f6\u5019\u90fd\u4f1a\u521b\u5efa\u4e00\u4e2a\u8f85\u52a9\u6570\u7ec4&#xff0c;\u8fd9\u91cc\u7684\u5f00\u9500\u5176\u5b9e\u4e5f\u5f88\u5927\u7684 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011340-681027c4df241.png\" alt=\"image.png\" \/> \u6211\u4eec\u53ef\u4ee5\u5c06\u521b\u5efa\u6570\u7ec4\u7684\u8fd9\u4e2a\u64cd\u4f5c\u653e\u5728\u5168\u5c40\u7684\u4f4d\u7f6e<\/p>\n<p>class Solution<\/p>\n<p>{<\/p>\n<p>\u00a0 \u00a0 vector&lt;int&gt;tmp;\/\/\u521b\u5efa\u8f85\u52a9\u6570\u7ec4<\/p>\n<p>public:<\/p>\n<p>\u00a0 \u00a0 vector&lt;int&gt; sortArray(vector&lt;int&gt;&amp; nums)<\/p>\n<p>\u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 tmp.resize(nums.size());<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 mergesort(nums,0,nums.size()-1);\/\/\u5c06\u8fd9\u6bb5\u533a\u95f4\u8fdb\u884c\u6392\u5e8f&#xff0c;\u6392\u5b8c\u5e8f\u76f4\u63a5\u8fd4\u56de\u5c31\u884c\u4e86<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 return nums;<\/p>\n<p>\u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 void mergesort(vector&lt;int&gt;&amp;nums,int left,int right)<\/p>\n<p>\u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 if(left&gt;&#061;right) return;\/\/\u7279\u6b8a\u60c5\u51b5&#xff0c;\u5982\u679c\u533a\u95f4\u4e0d\u5b58\u5728\u6216\u8005\u662f\u53ea\u6709\u4e00\u4e2a\u5143\u7d20\u7684\u8bdd<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/1.\u5148\u9009\u62e9\u4e2d\u95f4\u70b9\u5212\u5206\u533a\u95f4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int mid&#061;(left&#043;right)&gt;&gt;1;\/\/ &gt;&gt; 1 \u662f\u4f4d\u8fd0\u7b97\u4e2d\u7684\u53f3\u79fb\u64cd\u4f5c&#xff0c;\u5b83\u5c06\u7ed3\u679c\u53f3\u79fb\u4e00\u4f4d&#xff0c;\u76f8\u5f53\u4e8e\u5c06\u7ed3\u679c\u9664\u4ee52\u5e76\u5411\u4e0b\u53d6\u6574\u3002<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/[left,mid][mid&#043;1,right]<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/2.\u5c06\u5de6\u53f3\u533a\u95f4\u8fdb\u884c\u6392\u5e8f\u7684\u64cd\u4f5c<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 mergesort(nums,left,mid);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 mergesort(nums,mid&#043;1,right);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/3.\u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int cur1&#061;left;\/\/\u6307\u5411\u7b2c\u4e00\u4e2a\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int cur2&#061;mid&#043;1;\/\/\u6307\u5411\u7b2c\u4e8c\u4e2a\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int i&#061;0;\/\/\u8f85\u52a9\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid&amp;&amp;cur2&lt;&#061;right)<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmp[i&#043;&#043;]&#061;nums[cur1]&lt;&#061;nums[cur2]?nums[cur1&#043;&#043;]:nums[cur2&#043;&#043;];\/\/\u8fdb\u884c\u5224\u65ad&#xff0c;\u5982\u679ccur1\u7684\u5927\u5c0f\u5c0f\u4e8e\u7b49\u4e8ecur2\u7684\u8bdd&#xff0c;\u90a3\u4e48\u5c31\u8ba9\u6211\u4eec\u7684tmp[i]&#061;nums[cur1]\u7684\u503c<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/\u5c31\u662f\u8bf4\u767d\u4e86\u6301\u7eed\u8fdb\u884c\u5bf9\u6bd4&#xff0c;\u8c01\u5c0f\u8c01\u5148\u653e\u5230tmp\u8fd9\u4e2a\u6570\u7ec4\u4e2d\u53bb<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/i\u3001cur1\u3001cur2\u8fd9\u4e09\u4e2a\u6307\u9488\u90fd\u5f97\u5f80\u540e\u8fdb\u884c\u79fb\u52a8&#xff0c;\u6211\u4eec\u76f4\u63a5\u653e\u5728\u4e0a\u9762\u7684\u90a3\u4e2a\u4ee3\u7801\u4e2d\u53bb<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/\u5230\u8fd9\u91cc\u7684\u8bdd\u53ef\u80fd\u5b58\u5728\u4e00\u4e2a\u6570\u7ec4\u4e2d\u8fd8\u6709\u6570\u636e\u6ca1\u6709\u79fb\u52a8\u5230tmp\u4e2d\u53bb&#xff0c;\u4e0b\u9762\u4e24\u53e5\u4ee3\u7801\u5c31\u662f\u5904\u7406\u6ca1\u6709\u904d\u5386\u5b8c\u7684\u60c5\u51b5<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid)tmp[i&#043;&#043;]&#061;nums[cur1&#043;&#043;];\/\/\u56e0\u4e3a\u6b64\u65f6\u7684\u6307\u9488\u8fd8\u6ca1\u5230mid\u7684\u4f4d\u7f6e&#xff0c;\u5c31\u662f\u5927\u5c0f\u6bd4mid\u5c0f&#xff0c;\u90a3\u4e48\u6211\u4eec\u76f4\u63a5\u5c06cur1\u8fd9\u4e2a\u6570\u5b57\u4e2d\u5269\u4e0b\u7684\u5143\u7d20\u90fd\u653e\u5230tmp\u4e2d<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur2&lt;&#061;right)tmp[i&#043;&#043;]&#061;nums[cur2&#043;&#043;];\/\/\u548c\u4e0a\u9762\u4e00\u6837<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/\u8fd8\u539f<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 for(int i&#061;left;i&lt;&#061;right;i&#043;&#043;)<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 nums[i]&#061;tmp[i-left];\/\/\u6211\u4eec\u7684tmp\u6570\u7ec4\u9700\u8981\u4ece0\u5f00\u59cb\u8fdb\u884c\u8ba1\u6570\u64cd\u4f5c\u5417&#xff0c;\u6240\u4ee5\u6211\u4eec\u8fd9\u91cc\u4f7f\u7528i-left\u53ef\u4ee5\u8fbe\u5230\u4ece\u4e0b\u68070\u5f00\u59cb\u8fdb\u884c\u8d4b\u503c\u64cd\u4f5c<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 }<\/p>\n<p>};<\/p>\n<p>\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u770b\u770b\u65f6\u95f4\u5f00\u9500 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011341-681027c51671e.png\" alt=\"image.png\" \/> \u5982\u679c\u5728\u9012\u5f52\u4e2d\u9700\u8981\u521b\u5efa\u7a7a\u95f4\u7684\u8bdd&#xff0c;\u90a3\u4e48\u6211\u4eec\u5c31\u5c06\u8fd9\u4e2a\u64cd\u4f5c\u653e\u5728\u5168\u5c40\u4e0a<\/p>\n<h3>49.\u6570\u7ec4\u4e2d\u7684\u9006\u5e8f\u5bf9<\/h3>\n<p>\u9898\u76ee\u94fe\u63a5 \u5728\u6570\u7ec4\u4e2d\u7684\u4e24\u4e2a\u6570\u5b57\u5982\u679c\u524d\u9762\u4e00\u4e2a\u6570\u5b57\u5927\u4e8e\u540e\u9762\u7684\u6570\u5b57&#xff0c;\u5219\u8fd9\u4e24\u4e2a\u6570\u5b57\u7ec4\u6210\u4e00\u4e2a\u9006\u5e8f\u5bf9\u3002<\/p>\n<p>\u8f93\u5165\u4e00\u4e2a\u6570\u7ec4&#xff0c;\u6c42\u51fa\u8fd9\u4e2a\u6570\u7ec4\u4e2d\u7684\u9006\u5e8f\u5bf9\u7684\u603b\u6570\u3002<\/p>\n<p>\u6570\u636e\u8303\u56f4<\/p>\n<p>\u7ed9\u5b9a\u6570\u7ec4\u7684\u957f\u5ea6\u00a0[0,100][0,100]\u3002<\/p>\n<p>\u6837\u4f8b<\/p>\n<p>\u8f93\u5165&#xff1a;[1,2,3,4,5,6,0]<\/p>\n<p>\u8f93\u51fa&#xff1a;6<\/p>\n<p>\u66b4\u529b\u89e3\u6cd5&#xff1a;\u66b4\u529b\u679a\u4e3e \u4e24\u5c42for\u5faa\u73af\u5c31\u80fd\u66b4\u529b\u51fa\u6240\u6709\u7684\u60c5\u51b5&#xff0c;\u4f46\u662f\u4f1a\u8d85\u65f6\u7684<\/p>\n<p>\u6211\u4eec\u6c42\u51fa\u4e00\u4e2a\u4e2d\u5fc3\u70b9&#xff0c;\u5c06\u6574\u4e2a\u6570\u7ec4\u5206\u6210\u4e24\u6bb5&#xff0c;\u5206\u522b\u8fdb\u884c\u5224\u65ad &#xff0c;\u9012\u5f52\u8fdb\u884c\u6c42 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011341-681027c54e864.png\" alt=\"image.png\" \/> \u5229\u7528\u5f52\u5e76\u6392\u5e8f\u89e3\u51b3\u8be5\u95ee\u9898<\/p>\n<p>\u9006\u5e8f\u5bf9\u5c31\u662f\u4e00\u4e2a\u6570\u4e4b\u524d\u6709\u591a\u5c11\u4e2a\u6570\u6bd4\u81ea\u8eab\u5927&#xff0c;\u90a3\u4e48\u5c31\u6709\u591a\u5c11\u7ec4\u9006\u5e8f\u5bf9 \u90a3\u4e48\u6211\u4eec\u76ef\u7740cur2\u8fd9\u4e2a\u533a\u57df\u770b\u5c31\u884c\u4e86<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011341-681027c588a12.png\" alt=\"image.png\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011341-681027c5b47e4.png\" alt=\"\" \/>\u56e0\u4e3a\u6211\u4eec\u8fd9\u91cc\u7ecf\u8fc7\u4e86\u6392\u5e8f\u4e86&#xff0c;\u6240\u4ee5\u4e24\u4e2a\u533a\u57df\u90fd\u662f\u5347\u5e8f\u7684&#xff0c; \u5982\u679cnums[cur1]&lt;&#061;nums[cur2]\u7684\u8bdd&#xff0c;\u90a3\u4e48\u5c31\u8ba9cur1&#043;&#043; \u5982\u679cnums[cur1]&gt;nums[cur2]\u7684\u8bdd&#xff0c;\u56e0\u4e3a\u533a\u57df\u662f\u5347\u5e8f\u7684\u5417&#xff0c;\u6240\u4ee5\u5f53\u524dcur1\u540e\u9762\u7684\u90fd\u662f\u6bd4cur2\u5927\u7684\u6570\u5b57&#xff0c;\u6240\u4ee5\u6211\u4eec\u5c31\u627e\u5230\u4e86\u4e00\u5806\u7684\u9006\u5e8f\u6570&#xff0c;\u6240\u4ee5\u6211\u4eec\u7684\u9006\u5e8f\u6570\u603b\u548c\u5c31\u52a0\u4e0a\u4e86mid-cur1&#043;1<\/p>\n<p>\u6240\u4ee5\u8fd9\u4e2a\u9898\u5229\u7528\u5f52\u5e76\u6392\u5e8f\u7684\u8bdd\u65f6\u95f4\u590d\u6742\u5ea6\u5c31\u662fnlogn <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011341-681027c5e32c6.png\" alt=\"image.png\" \/><\/p>\n<p>\u6211\u4eec\u8fd9\u4e2a\u9898\u662f\u5347\u5e8f\u7684&#xff0c;\u5982\u679c\u662f\u964d\u5e8f\u7684\u8bdd\u8fd9\u4e2a\u9898\u600e\u4e48\u505a\u5462&#xff1f; \u5982\u679cnums[cur1]&gt;nums[cur2]\u7684\u8bdd&#xff0c;\u90a3\u4e48\u6211\u4eec\u5c31\u7edf\u8ba1cur1\u524d\u9762\u7684\u533a\u57df&#xff0c;\u7136\u540e\u6211\u4eec\u5c06cur1&#043;&#043;&#xff0c;\u4f46\u662f\u5982\u679c\u6b64\u65f6\u7684nums[cur1]&gt;nums[cur2]&#xff0c;\u90a3\u4e48\u6211\u4eec\u5c31\u4f1a\u51fa\u73b0\u91cd\u590d\u8ba1\u7b97\u7684\u95ee\u9898\u4e86 \u5982\u679c\u6211\u4eec\u5c06\u539f\u5148\u7684\u7b56\u7565\u6539\u6210&#xff1a;\u627e\u51fa\u67d0\u4e2a\u6570\u4e4b\u540e&#xff0c;\u6709\u591a\u5c11\u4e2a\u6570\u6bd4\u8f83\u5c0f&#xff0c;\u7136\u540e\u6211\u4eec\u6b64\u65f6\u5c31\u53ef\u4ee5\u5229\u7528\u5230\u4e86\u8fd9\u4e2a\u964d\u5e8f\u64cd\u4f5c\u4e86 \u5982\u679c\u6211\u4eec\u5f53\u524dcur1\u5927\u4e8ecur2\u7684\u8bdd&#xff0c;\u56e0\u4e3a\u8fd9\u4e2a\u662f\u964d\u5e8f\u7684&#xff0c;\u6240\u4ee5cur2\u540e\u9762\u7684\u90fd\u6bd4cur2\u5c0f&#xff0c;\u6240\u4ee5\u6211\u4eec\u627e\u5230\u6bd4cur1\u5c0f\u7684\u6570\u5c31\u884c\u4e86&#xff0c;\u90a3\u4e48cur2\u540e\u9762\u4e00\u5927\u5806\u6bd4cur1\u5c0f\u7684&#xff0c;\u7edf\u8ba1\u5b8c\u5f53\u524d\u6570\u4e2d\u6709\u591a\u5c11\u4e2a\u6570\u6bd4cur1\u5c0f\u7684&#xff0c;\u7136\u540e\u6211\u4eec\u7684cur1\u8fdb\u884c\u53f3\u79fb\u64cd\u4f5c <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011342-681027c61d97d.png\" alt=\"image.png\" \/> \u4e0b\u9762\u662f\u6570\u7ec4\u4e3a\u5347\u5e8f\u7684\u7248\u672c<\/p>\n<p>class Solution<br \/>\n{<br \/>\n    int tmp[999999];\/\/\u521b\u5efa\u4e00\u4e2a\u8f85\u52a9\u6570\u7ec4\u8fdb\u884c\u6570\u7ec4\u5408\u5e76\u7684<br \/>\npublic:<br \/>\n    int inversePairs(vector&lt;int&gt;&amp; nums)<br \/>\n    {<br \/>\n        return mergeSort(nums,0,nums.size()-1);\/\/\u5c060~n-1\u8fd9\u6bb5\u533a\u95f4\u7684\u9006\u5e8f\u5bf9\u90fd\u627e\u5230<\/p>\n<p>    }<br \/>\n    int mergeSort(vector&lt;int&gt;&amp;nums,int left,int right)<br \/>\n    {<br \/>\n        if(left&gt;&#061;right) return 0;\/\/\u5904\u7406\u7279\u6b8a\u60c5\u51b5&#xff0c;\u8fd9\u4e2a\u533a\u95f4\u6ca1\u6709\u9006\u5e8f\u5bf9\u6216\u8005\u662f \u53ea\u5b58\u5728\u4e00\u4e2a\u5143\u7d20\u7684\u8bdd<\/p>\n<p>        int ret&#061;0;\/\/\u8bb0\u5f55\u6700\u7ec8\u7684\u7ed3\u679c<br \/>\n        \/\/1.\u627e\u4e00\u4e2a\u4e2d\u95f4\u70b9<br \/>\n        int mid&#061;(right&#043;left)&gt;&gt;1;<br \/>\n        \/\/\u5212\u5206\u4e3a\u4e0b\u9762\u7684\u4e24\u4e2a\u533a\u95f4\u4e86<br \/>\n        \/\/[left,mid][mid&#043;1,right]<\/p>\n<p>        \/\/2.\u5de6\u8fb9\u7684\u9006\u5e8f\u5bf9\u7684\u4e2a\u6570&#043;\u6392\u5e8f&#043;\u53f3\u8fb9\u7684\u9006\u5e8f\u5bf9\u7684\u4e2a\u6570&#043;\u6392\u5e8f<br \/>\n        ret&#043;&#061;mergeSort(nums,left,mid);<br \/>\n        ret&#043;&#061;mergeSort(nums,mid&#043;1,right);<\/p>\n<p>        \/\/3.\u4e00\u5de6\u4e00\u53f3\u7684\u60c5\u51b5<br \/>\n        int cur1&#061;left,cur2&#061;mid&#043;1,i&#061;0;<br \/>\n        while(cur1&lt;&#061;mid&amp;&amp;cur2&lt;&#061;right)<br \/>\n        {<br \/>\n            if(nums[cur1]&lt;&#061;nums[cur2]) tmp[i&#043;&#043;]&#061;nums[cur1&#043;&#043;];<br \/>\n            else \/\/\u8fd9\u4e2a\u5c31\u662fcur1\u7684\u6570\u5927\u4e8ecur2\u7684\u6570<br \/>\n            {<br \/>\n                ret&#043;&#061;mid-cur1&#043;1;<br \/>\n                tmp[i&#043;&#043;]&#061;nums[cur2&#043;&#043;];\/\/\u5c06\u5c0f\u7684\u653e\u8fdb\u53bb<br \/>\n            }<br \/>\n        }<br \/>\n        \/\/4.\u5904\u7406\u4e0b\u6392\u5e8f,\u5c06\u5269\u4e0b\u7684\u5143\u7d20\u653e\u8fdb\u53bb<br \/>\n        while(cur1&lt;&#061;mid)tmp[i&#043;&#043;]&#061;nums[cur1&#043;&#043;];<br \/>\n        while(cur2&lt;&#061;right)tmp[i&#043;&#043;]&#061;nums[cur2&#043;&#043;];<br \/>\n        for(int j&#061;left;j&lt;&#061;right;j&#043;&#043;)<br \/>\n        {<br \/>\n            nums[j]&#061;tmp[j-left];<br \/>\n        }<br \/>\n        return ret;<br \/>\n    }<br \/>\n};<\/p>\n<p>\u5f52\u5e76\u6392\u5e8f\u7684\u7b2c\u4e00\u6b65\u662f\u9012\u5f52\u5730\u5c06\u6570\u7ec4\u62c6\u5206\u6210\u8d8a\u6765\u8d8a\u5c0f\u7684\u5b50\u6570\u7ec4&#xff0c;\u76f4\u5230\u6bcf\u4e2a\u5b50\u6570\u7ec4\u53ea\u6709\u4e00\u4e2a\u5143\u7d20\u4e3a\u6b62\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u662f\u901a\u8fc7 mergeSort(nums, left, mid) \u548c mergeSort(nums, mid &#043; 1, right) \u5b8c\u6210\u7684\u3002\u6bcf\u6b21\u9012\u5f52\u90fd\u4f1a\u627e\u5230\u6570\u7ec4\u7684\u4e2d\u95f4\u70b9 mid&#xff0c;\u7136\u540e\u5bf9\u5de6\u53f3\u4e24\u90e8\u5206\u9012\u5f52\u8c03\u7528 mergeSort\u3002<\/p>\n<p>\u5728\u5f52\u5e76\u7684\u8fc7\u7a0b\u4e2d&#xff0c;\u6211\u4eec\u5c06\u5de6\u53f3\u4e24\u4e2a\u5b50\u6570\u7ec4\u5408\u5e76\u6210\u4e00\u4e2a\u5df2\u6392\u5e8f\u7684\u6570\u7ec4\u3002\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d&#xff0c;\u5982\u679c\u5de6\u4fa7\u7684\u67d0\u4e2a\u5143\u7d20\u5927\u4e8e\u53f3\u4fa7\u7684\u67d0\u4e2a\u5143\u7d20&#xff0c;\u90a3\u4e48\u8fd9\u4e9b\u5143\u7d20\u5c31\u6784\u6210\u4e86\u9006\u5e8f\u5bf9\u3002<\/p>\n<p>\u5269\u4f59\u5143\u7d20\u5904\u7406&#xff1a; \u5982\u679c\u5728\u5408\u5e76\u7684\u8fc7\u7a0b\u4e2d&#xff0c;\u67d0\u4e00\u4fa7\u7684\u6570\u7ec4\u5df2\u7ecf\u5904\u7406\u5b8c\u4e86&#xff0c;\u800c\u53e6\u4e00\u4fa7\u4ecd\u7136\u6709\u5143\u7d20\u5269\u4f59&#xff0c;\u8fd9\u65f6\u5269\u4e0b\u7684\u5143\u7d20\u5df2\u7ecf\u662f\u6709\u5e8f\u7684&#xff0c;\u56e0\u6b64\u53ef\u4ee5\u76f4\u63a5\u5c06\u5b83\u4eec\u653e\u5165\u5230 tmp \u6570\u7ec4\u4e2d&#xff0c;\u4e0d\u9700\u8981\u505a\u4efb\u4f55\u6bd4\u8f83\u3002<\/p>\n<p>\u5c06\u6392\u5e8f\u540e\u7684\u5143\u7d20\u653e\u56de\u539f\u6570\u7ec4&#xff1a; \u5408\u5e76\u5b8c\u6210\u540e&#xff0c;\u6211\u4eec\u5c06 tmp \u6570\u7ec4\u4e2d\u7684\u5143\u7d20\u590d\u5236\u56de nums \u6570\u7ec4&#xff0c;\u8fd9\u6837\u5728\u4e0a\u5c42\u9012\u5f52\u4e2d\u4f1a\u4f7f\u7528\u5230\u6700\u65b0\u6392\u5e8f\u597d\u7684\u6570\u7ec4\u3002<\/p>\n<p>\u4e0b\u9762\u662f\u964d\u5e8f\u7684\u4ee3\u7801<\/p>\n<p>class Solution<br \/>\n{<br \/>\n    int tmp[999999];\/\/\u521b\u5efa\u4e00\u4e2a\u8f85\u52a9\u6570\u7ec4\u8fdb\u884c\u6570\u7ec4\u5408\u5e76\u7684<br \/>\npublic:<br \/>\n    int inversePairs(vector&lt;int&gt;&amp; nums)<br \/>\n    {<br \/>\n        return mergeSort(nums,0,nums.size()-1);\/\/\u5c060~n-1\u8fd9\u6bb5\u533a\u95f4\u7684\u9006\u5e8f\u5bf9\u90fd\u627e\u5230<\/p>\n<p>    }<br \/>\n    int mergeSort(vector&lt;int&gt;&amp;nums,int left,int right)<br \/>\n    {<br \/>\n        if(left&gt;&#061;right) return 0;\/\/\u5904\u7406\u7279\u6b8a\u60c5\u51b5&#xff0c;\u8fd9\u4e2a\u533a\u95f4\u6ca1\u6709\u9006\u5e8f\u5bf9\u6216\u8005\u662f \u53ea\u5b58\u5728\u4e00\u4e2a\u5143\u7d20\u7684\u8bdd<\/p>\n<p>        int ret&#061;0;\/\/\u8bb0\u5f55\u6700\u7ec8\u7684\u7ed3\u679c<br \/>\n        \/\/1.\u627e\u4e00\u4e2a\u4e2d\u95f4\u70b9<br \/>\n        int mid&#061;(right&#043;left)&gt;&gt;1;<br \/>\n        \/\/\u5212\u5206\u4e3a\u4e0b\u9762\u7684\u4e24\u4e2a\u533a\u95f4\u4e86<br \/>\n        \/\/[left,mid][mid&#043;1,right]<\/p>\n<p>        \/\/2.\u5de6\u8fb9\u7684\u9006\u5e8f\u5bf9\u7684\u4e2a\u6570&#043;\u6392\u5e8f&#043;\u53f3\u8fb9\u7684\u9006\u5e8f\u5bf9\u7684\u4e2a\u6570&#043;\u6392\u5e8f<br \/>\n        ret&#043;&#061;mergeSort(nums,left,mid);<br \/>\n        ret&#043;&#061;mergeSort(nums,mid&#043;1,right);<\/p>\n<p>        \/\/3.\u4e00\u5de6\u4e00\u53f3\u7684\u60c5\u51b5<br \/>\n        int cur1&#061;left,cur2&#061;mid&#043;1,i&#061;0;<br \/>\n        while(cur1&lt;&#061;mid&amp;&amp;cur2&lt;&#061;right)<br \/>\n        {<br \/>\n            if(nums[cur1]&lt;&#061;nums[cur2]) tmp[i&#043;&#043;]&#061;nums[cur2&#043;&#043;];<br \/>\n            else<br \/>\n            {<br \/>\n                ret&#043;&#061;right-cur2&#043;1;<br \/>\n                tmp[i&#043;&#043;]&#061;nums[cur1&#043;&#043;];<br \/>\n            }<br \/>\n        }<br \/>\n        \/\/4.\u5904\u7406\u4e0b\u6392\u5e8f,\u5c06\u5269\u4e0b\u7684\u5143\u7d20\u653e\u8fdb\u53bb<br \/>\n        while(cur1&lt;&#061;mid)tmp[i&#043;&#043;]&#061;nums[cur1&#043;&#043;];<br \/>\n        while(cur2&lt;&#061;right)tmp[i&#043;&#043;]&#061;nums[cur2&#043;&#043;];<br \/>\n        for(int j&#061;left;j&lt;&#061;right;j&#043;&#043;)<br \/>\n        {<br \/>\n            nums[j]&#061;tmp[j-left];<br \/>\n        }<br \/>\n        return ret;<br \/>\n    }<br \/>\n};<\/p>\n<p>\u6539\u52a8\u7684\u4ee3\u7801\u5728\u8fd9\u91cc <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011342-681027c64c62d.png\" alt=\"image.png\" \/><\/p>\n<h3>50.\u8ba1\u7b97\u53f3\u4fa7\u2f29\u4e8e\u5f53\u524d\u5143\u7d20\u7684\u4e2a\u6570<\/h3>\n<p>\u9898\u76ee\u94fe\u63a5 \u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4\u00a0nums\u00a0&#xff0c;\u6309\u8981\u6c42\u8fd4\u56de\u4e00\u4e2a\u65b0\u6570\u7ec4\u00a0counts\u00a0\u3002\u6570\u7ec4\u00a0counts\u00a0\u6709\u8be5\u6027\u8d28&#xff1a;\u00a0counts[i]\u00a0\u7684\u503c\u662f\u00a0\u00a0nums[i]\u00a0\u53f3\u4fa7\u5c0f\u4e8e\u00a0nums[i]\u00a0\u7684\u5143\u7d20\u7684\u6570\u91cf\u3002<\/p>\n<p>\u793a\u4f8b 1&#xff1a;<\/p>\n<p>\u8f93\u5165&#xff1a; nums &#061; [5,2,6,1] \u8f93\u51fa&#xff1a; [2,1,1,0] \u89e3\u91ca 5 \u7684\u53f3\u4fa7\u6709 2 \u4e2a\u66f4\u5c0f\u7684\u5143\u7d20 (2 \u548c 1) 2 \u7684\u53f3\u4fa7\u4ec5\u6709 1 \u4e2a\u66f4\u5c0f\u7684\u5143\u7d20 (1) 6 \u7684\u53f3\u4fa7\u6709 1 \u4e2a\u66f4\u5c0f\u7684\u5143\u7d20 (1) 1 \u7684\u53f3\u4fa7\u6709 0 \u4e2a\u66f4\u5c0f\u7684\u5143\u7d20<\/p>\n<p>\u793a\u4f8b 2&#xff1a;<\/p>\n<p>\u8f93\u5165&#xff1a; nums &#061; [-1] \u8f93\u51fa&#xff1a;[0]<\/p>\n<p>\u793a\u4f8b 3&#xff1a;<\/p>\n<p>\u8f93\u5165&#xff1a; nums &#061; [-1,-1] \u8f93\u51fa&#xff1a;[0,0]<\/p>\n<p>\u6709\u70b9\u50cf\u6211\u4eec\u7684\u9006\u5e8f\u5bf9 \u4f7f\u7528\u5f52\u5e76\u6392\u5e8f<\/p>\n<p>\u6211\u4eec\u9700\u8981\u5feb\u901f\u6c42\u51fa\u5f53\u524d\u5143\u7d20\u53f3\u8fb9\u6709\u591a\u5c11\u4e2a\u5143\u7d20\u6bd4\u5f53\u524d\u5143\u7d20\u5c0f \u6211\u4eec\u8fd9\u91cc\u4f7f\u7528\u7b56\u7565\u4e8c&#xff1a;\u5f53\u524d\u5143\u7d20\u53f3\u8fb9\u5143\u7d20\u6709\u591a\u5c11\u4e2a\u6bd4\u6211\u5c0f<\/p>\n<p>\u5982\u679cnums[cur1]&lt;&#061;nums[cur2]\u7684\u8bdd&#xff0c;\u90a3\u4e48\u6211\u4eec\u7684cur2\u5f97\u5f80\u53f3\u8fb9\u8fdb\u884c\u632a\u52a8\u4e86 \u4f46\u662f\u5982\u679cnums[cur1]&gt;nums[cur2]\u7684\u8bdd&#xff0c;\u90a3\u4e48\u6211\u4eec\u5c31\u5f97\u5c06nums[cur1]\u5728\u7edf\u8ba1\u6570\u7684\u90a3\u4e2a\u6570\u7ec4\u4e2d\u7684\u5bf9\u5e94\u7684\u4f4d\u7f6e\u52a0\u4e0a\u6211\u4eec\u6709\u591a\u5c11\u4e2a\u5c0f\u4e8ecur2\u7684\u4f4d\u7f6e\u7684\u6570\u4e86&#xff0c;\u6240\u4ee5\u6211\u4eec\u5f97\u627e\u5230cur1\u7684\u539f\u59cb\u4e0b\u6807\u4e86&#xff0c;\u6211\u7684\u601d\u8def\u662f\u4f7f\u7528hash&#xff0c;\u4f46\u662f\u5982\u679c\u51fa\u73b0\u4e86\u91cd\u590d\u5143\u7d20\u7684\u8bdd\u5c31\u4e0d\u597d\u641e\u4e86 \u6211\u4eec\u518d\u521b\u5efa\u4e00\u4e2a\u6570\u7ec4&#xff0c;\u5b58\u7684\u662f\u6211\u4eec\u539f\u59cb\u7684\u4e0b\u6807&#xff0c;\u4e00\u8d77\u8fdb\u884c\u7ed1\u5b9a\u79fb\u52a8\u5c31\u884c\u4e86<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011342-681027c679f51.png\" alt=\"image.png\" \/><\/p>\n<p>\u6211\u4eec\u8fd9\u91cc\u662f\u9700\u8981\u521b\u5efa\u4e24\u4e2a\u8f85\u52a9\u6570\u7ec4\u7684&#xff0c;\u4e00\u4e2a\u662fnums\u5408\u5e76\u7684\u8f85\u52a9\u6570\u7ec4 \u4e00\u4e2a\u662f\u539f\u59cb\u4e0b\u6807\u7684\u8f85\u52a9\u6570\u7ec4<\/p>\n<p>class Solution<\/p>\n<p>{<\/p>\n<p>\u00a0 \u00a0 vector&lt;int&gt;ret;<\/p>\n<p>\u00a0 \u00a0 vector&lt;int&gt;index;\/\/\u8bb0\u5f55\u5f53\u524d\u5143\u7d20\u7684\u539f\u59cb\u4e0b\u6807<\/p>\n<p>\u00a0 \u00a0 int tmpNums[500010];\/\/nums\u7684\u8f85\u52a9\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 int tmpIndex[500010];\/\/index\u7684\u8f85\u52a9\u6570\u7ec4<\/p>\n<p>public:<\/p>\n<p>\u00a0 \u00a0 vector&lt;int&gt; countSmaller(vector&lt;int&gt;&amp; nums)<\/p>\n<p>\u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int n&#061;nums.size();<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 ret.resize(n);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 index.resize(n);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/\u521d\u59cb\u5316index\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 for(int i&#061;0;i&lt;n;i&#043;&#043;)<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 index[i]&#061;i;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 mergerSort(nums,0,n-1);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 return ret;<\/p>\n<p>\u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 void mergerSort(vector&lt;int&gt;&amp;nums,int left,int right)<\/p>\n<p>\u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/\u5148\u5904\u7406\u8fb9\u754c\u60c5\u51b5<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 if(left&gt;&#061;right) return ;\/\/\u8981\u4e48\u8fd9\u4e2a\u6570\u7ec4\u53ea\u6709\u4e00\u4e2a\u5143\u7d20&#xff0c;\u8981\u4e48\u5c31\u662f\u6ca1\u6709\u5143\u7d20<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/1.\u6839\u636e\u4e2d\u95f4\u5143\u7d20\u5212\u5206\u533a\u95f4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int mid&#061;(right&#043;left)&gt;&gt;1;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/[left,mid][mid&#043;1,right]<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/2.\u5148\u5904\u7406\u5de6\u53f3\u4e24\u90e8\u5206<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 mergerSort(nums,left,mid);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 mergerSort(nums,mid&#043;1,right);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/3.\u5904\u7406\u4e00\u5de6\u4e00\u53f3\u7684\u60c5\u51b5<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int cur1&#061;left,cur2&#061;mid&#043;1,i&#061;0;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid&amp;&amp;cur2&lt;&#061;right)\/\/\u964d\u5e8f\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if(nums[cur1]&lt;&#061;nums[cur2])<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/\u964d\u5e8f\u6570\u7ec4&#xff0c;\u8c01\u5927\u5c31\u79fb\u52a8\u8c01<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmpNums[i]&#061;nums[cur2];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmpIndex[i&#043;&#043;]&#061;index[cur2&#043;&#043;];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 else\/\/nums[cur1]&gt;nums[cur2]<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/index[cur2]\u5c31\u662fcur2\u5f53\u524d\u7684\u4e0b\u6807<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ret[index[cur1]]&#043;&#061;right-cur2&#043;1;\/\/\u91cd\u70b9&#xff0c;\u5148\u627e\u5230\u539f\u59cb\u4f4d\u7f6e\u7684\u4e0b\u6807,\u6211\u4eec\u8fd9\u91cc\u7edf\u8ba1\u7684\u662fcur1\u4f4d\u7f6e\u540e\u9762\u7684\u6570\u6709\u591a\u5c11\u4e2a\u6bd4cur1\u5c0f<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmpNums[i]&#061;nums[cur1];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmpIndex[i&#043;&#043;]&#061;index[cur1&#043;&#043;];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/3.\u5904\u7406\u6392\u5e8f\u5269\u4e0b\u7684\u6392\u5e8f\u8fc7\u7a0b<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid) \/\/\u8bf4\u660e\u6211\u4eec\u7684cur1\u8fd8\u6709\u9884\u7559\u7684\u6570\u636e&#xff0c;\u90a3\u4e48\u6211\u4eec\u5c06\u5269\u4e0b\u7684\u6570\u636e\u5168\u90e8\u653e\u5230\u6211\u4eec\u7684\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmpNums[i]&#061;nums[cur1];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmpIndex[i&#043;&#043;]&#061;index[cur1&#043;&#043;];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur2&lt;&#061;right) \/\/\u8bf4\u660e\u6211\u4eec\u7684cur1\u8fd8\u6709\u9884\u7559\u7684\u6570\u636e&#xff0c;\u90a3\u4e48\u6211\u4eec\u5c06\u5269\u4e0b\u7684\u6570\u636e\u5168\u90e8\u653e\u5230\u6211\u4eec\u7684\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmpNums[i]&#061;nums[cur2];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmpIndex[i&#043;&#043;]&#061;index[cur2&#043;&#043;];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/\u8fd8\u539f<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 for(int j&#061;left;j&lt;&#061;right;j&#043;&#043; )<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 nums[j]&#061;tmpNums[j-left];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 index[j]&#061;tmpIndex[j-left];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 }<\/p>\n<p>};<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011342-681027c61d97d.png\" alt=\"image.png\" \/> \u6c42\u5f53\u524d\u4f4d\u7f6e\u7684\u53f3\u8fb9\u6709\u591a\u5c11\u4e2a\u6570\u6bd4cur1\u5c0f\u7684\u3002\u6240\u4ee5\u6211\u4eec\u8fd9\u91cc\u662f\u964d\u5e8f\u7684&#xff0c;\u5c06\u5927\u7684\u5143\u7d20\u5148\u8fdb\u884c\u79fb\u52a8\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb<\/p>\n<h3>51.\u7ffb\u8f6c\u5bf9<\/h3>\n<p>\u9898\u76ee\u94fe\u63a5 \u7ed9\u5b9a\u4e00\u4e2a\u6570\u7ec4\u00a0nums\u00a0&#xff0c;\u5982\u679c\u00a0i &lt; j\u00a0\u4e14\u00a0nums[i] &gt; 2*nums[j]\u00a0\u6211\u4eec\u5c31\u5c06\u00a0(i, j)\u00a0\u79f0\u4f5c\u4e00\u4e2a \u91cd\u8981\u7ffb\u8f6c\u5bf9\u3002<\/p>\n<p>\u4f60\u9700\u8981\u8fd4\u56de\u7ed9\u5b9a\u6570\u7ec4\u4e2d\u7684\u91cd\u8981\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf\u3002<\/p>\n<p>\u793a\u4f8b 1:<\/p>\n<p>\u8f93\u5165: [1,3,2,3,1] \u8f93\u51fa: 2<\/p>\n<p>\u793a\u4f8b 2:<\/p>\n<p>\u8f93\u5165: [2,4,3,5,1] \u8f93\u51fa: 3<\/p>\n<p>\u627e\u4e24\u4e2a\u6570&#xff0c;\u524d\u9762\u7684\u6570\u662f\u5927\u4e8e\u540e\u9762\u7684\u90a3\u4e2a\u6570\u7684\u4e24\u500d\u7684<\/p>\n<p>\u7b56\u7565\u4e00&#xff1a;\u8ba1\u7b97\u5f53\u524d\u5143\u7d20\u540e\u9762&#xff0c;\u6709\u591a\u5c11\u5143\u7d20\u7684\u4e24\u500d\u6bd4\u6211\u5c0f \u964d\u5e8f \u6211\u4eec\u53d1\u73b0cur2\u4f4d\u7f6e\u7684\u4e24\u500d\u7684\u5927\u5c0f\u6bd4cur1\u5c0f&#xff0c;\u90a3\u4e48cur2\u540e\u9762\u7684\u6570\u5b57\u7684\u4e24\u522b\u90fd\u6bd4cur1\u5c0f <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011342-681027c6af00c.png\" alt=\"image.png\" \/><\/p>\n<p>\u8ba1\u7b97\u7ffb\u8f6c\u5bf9-&gt;\u540c\u5411\u53cc\u6307\u9488 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011342-681027c6d99eb.png\" alt=\"image.png\" \/><\/p>\n<p>\u7b56\u7565\u4e8c&#xff1a;\u8ba1\u7b97\u5f53\u524d\u5143\u7d20\u4e4b\u524d&#xff0c;\u6709\u591a\u5c11\u5143\u7d20\u7684\u4e00\u534a\u6bd4\u6211\u5927 \u5347\u5e8f \u6211\u4eec\u8fd9\u91cc\u79fb\u52a8cur1&#xff0c;\u5982\u679ccur1\u7684\u4e00\u534a\u6bd4cur2\u5c0f\u7684\u8bdd&#xff0c;\u90a3\u4e48cur1\u53f3\u79fb \u5f53\u6211\u4eec\u53d1\u73b0cur1\u7684\u4e00\u534a\u6bd4cur2\u5927\u7684\u8bdd&#xff0c;\u90a3\u4e48cur1\u540e\u9762\u7684\u4e00\u534a\u90fd\u6bd4cur2\u5927<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/04\/20250429011343-681027c72b44a.png\" alt=\"image.png\" \/> \u4e0b\u9762\u662f\u964d\u5e8f\u7684\u4ee3\u7801<\/p>\n<p>class Solution<\/p>\n<p>{<\/p>\n<p>\u00a0 \u00a0 int tmp[50010];\/\/\u8f85\u52a9\u6570\u7ec4&#xff0c;\u5e2e\u52a9\u6211\u4eec\u5408\u5e76\u6392\u5e8f<\/p>\n<p>public:<\/p>\n<p>\u00a0 \u00a0 int reversePairs(vector&lt;int&gt;&amp; nums)<\/p>\n<p>\u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 return mergeSort(nums,0,nums.size()-1);<\/p>\n<p>\u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 int mergeSort(vector&lt;int&gt;&amp;nums,int left,int right)<\/p>\n<p>\u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 if(left&gt;&#061;right) return 0;\/\/\u5904\u7406\u5f02\u5e38\u60c5\u51b5<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int ret&#061;0; \u00a0<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/1.\u5148\u6839\u636e\u4e2d\u95f4\u5143\u7d20\u5212\u5206\u533a\u95f4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int mid&#061;(right&#043;left)&gt;&gt;1;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/[left,mid][mid&#043;1,right]<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/2.\u5148\u8ba1\u7b97\u5de6\u53f3\u4e24\u4fa7\u7684\u7ffb\u8f6c\u5bf9<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 ret&#043;&#061;mergeSort(nums,left,mid);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 ret&#043;&#061;mergeSort(nums,mid&#043;1,right);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/3.\u5148\u8ba1\u7b97\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int cur1&#061;left,cur2&#061;mid&#043;1,i&#061;left;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid)\/\/\u964d\u5e8f<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 while(cur2&lt;&#061;right &amp;&amp;nums[cur2]&gt;&#061;nums[cur1]\/2.0) cur2&#043;&#043;;\/\/\u5411\u540e\u8fdb\u884c\u79fb\u52a8&#xff0c;\u76f4\u5230\u627e\u5230\u5408\u9002\u7684\u4f4d\u7f6e<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if(cur2&gt;right) break;\/\/\u5982\u679c\u6ee1\u8db3\u4e86\u8d8a\u754c\u7684\u60c5\u51b5\u4e86&#xff0c;\u90a3\u4e48\u6211\u4eec\u76f4\u63a5break\u5c31\u884c\u4e86<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/\u51fa\u4e86\u5faa\u73af\u5c31\u8bf4\u660e\u6211\u4eec\u627e\u5230\u5bf9\u5e94\u7684\u4f4d\u7f6e\u4e86<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ret&#043;&#061;right-cur2&#043;1;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 cur1&#043;&#043;;\/\/cur1\u5411\u540e\u79fb\u52a8<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/4.\u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 cur1&#061;left,cur2&#061;mid&#043;1;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid&amp;&amp;cur2&lt;&#061;right)<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmp[i&#043;&#043;]&#061;nums[cur1]&lt;&#061;nums[cur2]?nums[cur2&#043;&#043;]:nums[cur1&#043;&#043;];\/\/\u56e0\u4e3a\u8fd9\u91cc\u662f\u4e00\u4e2a\u964d\u5e8f\u7684\u6570\u7ec4&#xff0c;\u8c01\u5927\u8c01\u5c31\u79fb\u52a8\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid)tmp[i&#043;&#043;]&#061;nums[cur1&#043;&#043;];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur2&lt;&#061;right)tmp[i&#043;&#043;]&#061;nums[cur2&#043;&#043;];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/5.\u8fd8\u539f<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 for(int j&#061;left;j&lt;&#061;right;j&#043;&#043;)<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 nums[j]&#061;tmp[j];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 return ret;<\/p>\n<p>\u00a0 \u00a0 }<\/p>\n<p>};<\/p>\n<p>\u6211\u4eec\u5148\u6839\u636e\u4e2d\u95f4\u5143\u7d20\u5212\u5206\u533a\u95f4&#xff0c;\u7136\u540e\u8ba1\u7b97\u5de6\u53f3\u4e24\u4fa7\u7684\u7ffb\u8f6c\u5bf9&#xff0c;\u8fd9\u4e2a\u5c31\u662f\u9012\u5f52\u8c03\u7528\u51fd\u6570 \u7136\u540e\u8ba1\u7b97\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf&#xff0c;\u7136\u540e\u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4&#xff0c;\u6700\u540e\u5c31\u662f\u8fd8\u539f\u4e86 \u3002<\/p>\n<p>\u8fd9\u91cc\u8ba1\u7b97\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf&#xff0c;\u6211\u4eec\u8ba9\u6211\u4eec\u7684cur1\u4e0d\u52a8&#xff0c;cur\u4e00\u76f4\u5f80\u540e\u79fb\u52a8&#xff0c;\u76f4\u5230\u9047\u5230\u4e86\u6ee1\u8db3\u6761\u4ef6\u7684&#xff0c;\u5c31\u662fnums[cur2]&gt;&#061;nums[cur1]\/2.0\u7684\u8bdd&#xff0c;\u90a3\u4e48\u6211\u4eec\u5c31\u5c06cur2\u540e\u9762\u8fd9\u6bb5\u533a\u95f4\u8fdb\u884c\u7d2f\u52a0\u5230ret\u4e2d\u53bb&#xff0c;\u7136\u540e\u518d\u53bb\u79fb\u52a8cur1\u8fdb\u884c\u4e0b\u4e00\u7ec4\u7684\u5224\u65ad&#xff0c;\u5faa\u73af\u7ed3\u675f\u4e4b\u540e&#xff0c;\u6211\u4eec\u7684\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf\u5c31\u8ba1\u7b97\u51fa\u6765\u4e86<\/p>\n<p>\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u5f97\u5c06\u5f53\u524d\u7684\u8fd9\u6bb5\u548c\u522b\u7684\u6bb5\u8fdb\u884c\u5408\u5e76&#xff0c;\u5c31\u662f\u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4\u7684\u64cd\u4f5c&#xff0c;\u76f4\u63a5\u5408\u5e76\u5728tmp\u8fd9\u4e2a\u8f85\u52a9\u6570\u7ec4\u4e2d&#xff0c;\u5408\u5e76\u5b8c\u6210\u4e4b\u540e\u53ef\u80fd\u4f1a\u6709\u4e00\u7ec4\u6570\u7ec4\u8fd8\u6709\u5269\u4f59\u7684\u6570\u636e&#xff0c;\u6211\u4eec\u5c06\u8fd9\u4e9b\u6570\u636e\u653e\u5230\u6211\u4eec\u7684tmp\u4e2d\u53bb \u6700\u540e\u6211\u4eec\u9700\u8981\u5c06\u539f\u5148\u7684\u6570\u7ec4\u8fdb\u884c\u8fd8\u539f\u64cd\u4f5c \u4e3a\u4ec0\u4e48\u9700\u8981\u8fdb\u884c\u8fd8\u539f\u64cd\u4f5c&#xff1f; \u5728\u9012\u5f52\u8fc7\u7a0b\u4e2d&#xff0c;\u539f\u59cb\u6570\u7ec4 nums \u7684\u6570\u636e\u4f1a\u88ab\u62c6\u5206\u6210\u8bb8\u591a\u5b50\u6570\u7ec4&#xff0c;\u4e14\u6bcf\u4e2a\u5b50\u6570\u7ec4\u90fd\u5728\u9012\u5f52\u8fc7\u7a0b\u4e2d\u7ecf\u8fc7\u5408\u5e76\u64cd\u4f5c\u3002\u5728\u5408\u5e76\u8fc7\u7a0b\u4e2d&#xff0c;\u6211\u4eec\u5c06\u6392\u597d\u5e8f\u7684\u5b50\u6570\u7ec4\u7684\u5143\u7d20\u5408\u5e76\u5230\u8f85\u52a9\u6570\u7ec4 tmp \u4e2d\u3002\u5982\u679c\u4e0d\u8fd8\u539f\u56de\u6765&#xff0c;nums \u6570\u7ec4\u5c31\u65e0\u6cd5\u4fdd\u6301\u6b63\u786e\u7684\u6392\u5e8f\u987a\u5e8f&#xff0c;\u4e5f\u65e0\u6cd5\u51c6\u786e\u5730\u53cd\u6620\u6700\u7ec8\u7684\u6392\u5e8f\u7ed3\u679c<\/p>\n<p>\u6211\u4eec\u4f7f\u7528\u5347\u5e8f\u7684\u4ee3\u7801\u8fdb\u884c\u89e3\u51b3\u95ee\u9898 \u5347\u5e8f\u5c31\u662f\u627e\u5f53\u524d\u5143\u7d20\u4e4b\u524d\u6709\u591a\u5c11\u4e2a\u6570\u6bd4\u6211\u5927&#xff0c; \u6240\u4ee5\u6b64\u65f6\u56fa\u5b9a\u7684\u5c31\u662fcur2\u4e86<\/p>\n<p>class Solution<\/p>\n<p>{<\/p>\n<p>\u00a0 \u00a0 int tmp[50010];\/\/\u8f85\u52a9\u6570\u7ec4&#xff0c;\u5e2e\u52a9\u6211\u4eec\u5408\u5e76\u6392\u5e8f<\/p>\n<p>public:<\/p>\n<p>\u00a0 \u00a0 int reversePairs(vector&lt;int&gt;&amp; nums)<\/p>\n<p>\u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 return mergeSort(nums,0,nums.size()-1);<\/p>\n<p>\u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 int mergeSort(vector&lt;int&gt;&amp;nums,int left,int right)<\/p>\n<p>\u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 if(left&gt;&#061;right) return 0;\/\/\u5904\u7406\u5f02\u5e38\u60c5\u51b5<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int ret&#061;0; \u00a0<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/1.\u5148\u6839\u636e\u4e2d\u95f4\u5143\u7d20\u5212\u5206\u533a\u95f4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int mid&#061;(right&#043;left)&gt;&gt;1;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/[left,mid][mid&#043;1,right]<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/2.\u5148\u8ba1\u7b97\u5de6\u53f3\u4e24\u4fa7\u7684\u7ffb\u8f6c\u5bf9&#xff08;\u9012\u5f52\u8c03\u7528\u64cd\u4f5c&#xff09;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 ret&#043;&#061;mergeSort(nums,left,mid);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 ret&#043;&#061;mergeSort(nums,mid&#043;1,right);<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/3.\u5148\u8ba1\u7b97\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 int cur1&#061;left,cur2&#061;mid&#043;1,i&#061;left;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur2&lt;&#061;right)\/\/\u5347\u5e8f<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid &amp;&amp;nums[cur2]&gt;&#061;nums[cur1]\/2.0) cur1&#043;&#043;;\/\/\u5411\u540e\u8fdb\u884c\u79fb\u52a8&#xff0c;\u76f4\u5230\u627e\u5230\u5408\u9002\u7684\u4f4d\u7f6e<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if(cur1&gt;mid) break;\/\/\u5982\u679c\u6ee1\u8db3\u4e86\u8d8a\u754c\u7684\u60c5\u51b5\u4e86&#xff0c;\u90a3\u4e48\u6211\u4eec\u76f4\u63a5break\u5c31\u884c\u4e86<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/\u51fa\u4e86\u5faa\u73af\u5c31\u8bf4\u660e\u6211\u4eec\u627e\u5230\u5bf9\u5e94\u7684\u4f4d\u7f6e\u4e86<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ret&#043;&#061;mid-cur1&#043;1;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 cur2&#043;&#043;;\/\/cur1\u5411\u540e\u79fb\u52a8<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/4.\u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 cur1&#061;left,cur2&#061;mid&#043;1;<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid&amp;&amp;cur2&lt;&#061;right)<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 tmp[i&#043;&#043;]&#061;nums[cur1]&lt;&#061;nums[cur2]?nums[cur1&#043;&#043;]:nums[cur2&#043;&#043;];\/\/\u56e0\u4e3a\u8fd9\u91cc\u662f\u4e00\u4e2a\u964d\u5e8f\u7684\u6570\u7ec4&#xff0c;\u8c01\u5927\u8c01\u5c31\u79fb\u52a8\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur1&lt;&#061;mid)tmp[i&#043;&#043;]&#061;nums[cur1&#043;&#043;];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 while(cur2&lt;&#061;right)tmp[i&#043;&#043;]&#061;nums[cur2&#043;&#043;];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \/\/5.\u8fd8\u539f<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 for(int j&#061;left;j&lt;&#061;right;j&#043;&#043;)<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 {<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 nums[j]&#061;tmp[j];<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 }<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 return ret;<\/p>\n<p>\u00a0 \u00a0 }<\/p>\n<p>};<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb1k\u6b21\uff0c\u70b9\u8d5e88\u6b21\uff0c\u6536\u85cf72\u6b21\u3002\u4f46\u662f\u5982\u679cnums[cur1]&gt;nums[cur2]\u7684\u8bdd\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u5f97\u5c06nums[cur1]\u5728\u7edf\u8ba1\u6570\u7684\u90a3\u4e2a\u6570\u7ec4\u4e2d\u7684\u5bf9\u5e94\u7684\u4f4d\u7f6e\u52a0\u4e0a\u6211\u4eec\u6709\u591a\u5c11\u4e2a\u5c0f\u4e8ecur2\u7684\u4f4d\u7f6e\u7684\u6570\u4e86\uff0c\u6240\u4ee5\u6211\u4eec\u5f97\u627e\u5230cur1\u7684\u539f\u59cb\u4e0b\u6807\u4e86\uff0c\u6211\u7684\u601d\u8def\u662f\u4f7f\u7528hash\uff0c\u4f46\u662f\u5982\u679c\u51fa\u73b0\u4e86\u91cd\u590d\u5143\u7d20\u7684\u8bdd\u5c31\u4e0d\u597d\u641e\u4e86\u3002\u5982\u679c\u6211\u4eec\u5f53\u524dcur1\u5927\u4e8ecur2\u7684\u8bdd\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u662f\u964d\u5e8f\u7684\uff0c\u6240\u4ee5cur2\u540e\u9762\u7684\u90fd\u6bd4cur2\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u627e\u5230\u6bd4cur1\u5c0f\u7684\u6570\u5c31\u884c\u4e86\uff0c\u90a3\u4e48cur2\u540e\u9762\u4e00\u5927\u5806\u6bd4cur1\u5c0f\u7684\uff0c\u7edf\u8ba1\u5b8c\u5f53\u524d\u6570\u4e2d\u6709\u591a\u5c11\u4e2a\u6570\u6bd4cur1\u5c0f\u7684\uff0c\u7136\u540e\u6211\u4eec\u7684cur1\u8fdb\u884c\u53f3\u79fb\u64cd\u4f5c\u3002<\/p>\n","protected":false},"author":2,"featured_media":34175,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[2692,427,925],"topic":[],"class_list":["post-34191","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-leetcode","tag-427","tag-925"],"yoast_head":"<!-- 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content=\"\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb1k\u6b21\uff0c\u70b9\u8d5e88\u6b21\uff0c\u6536\u85cf72\u6b21\u3002\u4f46\u662f\u5982\u679cnums[cur1]&gt;nums[cur2]\u7684\u8bdd\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u5f97\u5c06nums[cur1]\u5728\u7edf\u8ba1\u6570\u7684\u90a3\u4e2a\u6570\u7ec4\u4e2d\u7684\u5bf9\u5e94\u7684\u4f4d\u7f6e\u52a0\u4e0a\u6211\u4eec\u6709\u591a\u5c11\u4e2a\u5c0f\u4e8ecur2\u7684\u4f4d\u7f6e\u7684\u6570\u4e86\uff0c\u6240\u4ee5\u6211\u4eec\u5f97\u627e\u5230cur1\u7684\u539f\u59cb\u4e0b\u6807\u4e86\uff0c\u6211\u7684\u601d\u8def\u662f\u4f7f\u7528hash\uff0c\u4f46\u662f\u5982\u679c\u51fa\u73b0\u4e86\u91cd\u590d\u5143\u7d20\u7684\u8bdd\u5c31\u4e0d\u597d\u641e\u4e86\u3002\u5982\u679c\u6211\u4eec\u5f53\u524dcur1\u5927\u4e8ecur2\u7684\u8bdd\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u662f\u964d\u5e8f\u7684\uff0c\u6240\u4ee5cur2\u540e\u9762\u7684\u90fd\u6bd4cur2\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u627e\u5230\u6bd4cur1\u5c0f\u7684\u6570\u5c31\u884c\u4e86\uff0c\u90a3\u4e48cur2\u540e\u9762\u4e00\u5927\u5806\u6bd4cur1\u5c0f\u7684\uff0c\u7edf\u8ba1\u5b8c\u5f53\u524d\u6570\u4e2d\u6709\u591a\u5c11\u4e2a\u6570\u6bd4cur1\u5c0f\u7684\uff0c\u7136\u540e\u6211\u4eec\u7684cur1\u8fdb\u884c\u53f3\u79fb\u64cd\u4f5c\u3002\" 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