{"id":57991,"date":"2025-08-15T23:42:43","date_gmt":"2025-08-15T15:42:43","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/57991.html"},"modified":"2025-08-15T23:42:43","modified_gmt":"2025-08-15T15:42:43","slug":"%e3%80%90%e4%bc%98%e5%85%88%e7%ae%97%e6%b3%95%e3%80%91%e5%88%86%e6%b2%bb","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/57991.html","title":{"rendered":"\u3010\u4f18\u5148\u7b97\u6cd5\u3011\u5206\u6cbb"},"content":{"rendered":"<\/p>\n<h4>\u5206\u6cbb<\/h4>\n<ul>\n<li>\u5feb\u901f\u6392\u5e8f<\/li>\n<li>\n<ul>\n<li>1.\u989c\u2f8a\u5206\u7c7b&#xff08;medium&#xff09;<\/li>\n<li>2.\u5feb\u901f\u6392\u5e8f&#xff08;medium&#xff09;<\/li>\n<li>3.\u6570\u7ec4\u4e2d\u7684\u7b2cK\u4e2a\u6700\u2f24\u5143\u7d20&#xff08;medium&#xff09;<\/li>\n<\/ul>\n<\/li>\n<li>\u5f52\u5e76\u6392\u5e8f<\/li>\n<li>\n<ul>\n<li>1.\u6392\u5e8f\u6570\u7ec4&#xff08;medium&#xff09;<\/li>\n<li>2.\u6570\u7ec4\u4e2d\u7684\u9006\u5e8f\u5bf9&#xff08;hard&#xff09;<\/li>\n<li>3.\u8ba1\u7b97\u53f3\u4fa7\u2f29\u4e8e\u5f53\u524d\u5143\u7d20\u7684\u4e2a\u6570&#xff08;hard&#xff09;<\/li>\n<li>4.\u7ffb\u8f6c\u5bf9&#xff08;hard&#xff09;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>\u5feb\u901f\u6392\u5e8f<\/h2>\n<h3>1.\u989c\u2f8a\u5206\u7c7b&#xff08;medium&#xff09;<\/h3>\n<p>\u9898\u2f6c\u94fe\u63a5&#xff1a;75. \u989c\u2f8a\u5206\u7c7b \u9898\u2f6c\u63cf\u8ff0&#xff1a; \u7ed9\u5b9a\u2f00\u4e2a\u5305\u542b\u7ea2\u2f8a\u3001\u2f69\u2f8a\u548c\u84dd\u2f8a\u3001\u5171 n \u4e2a\u5143\u7d20\u7684\u6570\u7ec4 nums &#xff0c;\u539f\u5730\u5bf9\u5b83\u4eec\u8fdb\u2f8f\u6392\u5e8f&#xff0c;\u4f7f\u5f97\u76f8\u540c\u989c\u2f8a\u7684\u5143\u7d20\u76f8\u90bb&#xff0c;\u5e76\u6309\u7167\u7ea2\u2f8a\u3001\u2f69\u2f8a\u3001\u84dd\u2f8a\u987a\u5e8f\u6392\u5217\u3002 \u6211\u4eec\u4f7f\u2f64\u6574\u6570 0\u3001 1 \u548c 2 \u5206\u522b\u8868\u2f70\u7ea2\u2f8a\u3001\u2f69\u2f8a\u548c\u84dd\u2f8a\u3002 \u5fc5\u987b\u5728\u4e0d\u4f7f\u2f64\u5e93\u7684 sort \u51fd\u6570\u7684\u60c5\u51b5\u4e0b\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002 \u2f70\u4f8b 1&#xff1a; \u8f93\u2f0a&#xff1a;nums &#061; [2,0,2,1,1,0] \u8f93\u51fa&#xff1a;[0,0,1,1,2,2]<\/p>\n<p>\u89e3\u6cd5&#xff08;\u5feb\u6392\u601d\u60f3 &#8211; \u4e09\u6307\u9488\u6cd5\u4f7f\u6570\u7ec4\u5206\u4e09\u5757&#xff09;&#xff1a;<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815154121-689f5521eb283.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u7b97\u6cd5\u601d\u8def&#xff1a; \u7c7b\u2f50\u6570\u7ec4\u5206\u4e24\u5757\u7684\u7b97\u6cd5\u601d\u60f3&#xff0c;\u8fd9\u2fa5\u662f\u5c06\u6570\u7ec4\u5206\u6210\u4e09\u5757&#xff0c;\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u518d\u6dfb\u52a0\u2f00\u4e2a\u6307\u9488&#xff0c;\u5b9e\u73b0\u6570\u7ec4\u5206\u4e09\u5757\u3002 \u8bbe\u6570\u7ec4\u2f24\u2f29\u4e3a n &#xff0c;\u5b9a\u4e49\u4e09\u4e2a\u6307\u9488 left, cur, right : \u25e6 left &#xff1a;\u2f64\u6765\u6807\u8bb0 0 \u5e8f\u5217\u7684\u672b\u5c3e&#xff0c;\u56e0\u6b64\u521d\u59cb\u5316\u4e3a -1 &#xff1b; \u25e6 cur &#xff1a;\u2f64\u6765\u626b\u63cf\u6570\u7ec4&#xff0c;\u521d\u59cb\u5316\u4e3a 0 &#xff1b; \u25e6 right &#xff1a;\u2f64\u6765\u6807\u8bb0 2 \u5e8f\u5217\u7684\u8d77\u59cb\u4f4d\u7f6e&#xff0c;\u56e0\u6b64\u521d\u59cb\u5316\u4e3a n \u3002 \u5728 cur \u5f80\u540e\u626b\u63cf\u7684\u8fc7\u7a0b\u4e2d&#xff0c;\u4fdd\u8bc1&#xff1a; \u25e6 [0, left] \u5185\u7684\u5143\u7d20\u90fd\u662f 0 &#xff1b; \u25e6 [left &#043; 1, cur &#8211; 1] \u5185\u7684\u5143\u7d20\u90fd\u662f 1 &#xff1b; \u25e6 [cur, right &#8211; 1] \u5185\u7684\u5143\u7d20\u662f\u5f85\u5b9a\u5143\u7d20&#xff1b; \u25e6 [right, n] \u5185\u7684\u5143\u7d20\u90fd\u662f 2 \u3002 \u7b97\u6cd5\u6d41\u7a0b&#xff1a; a. \u521d\u59cb\u5316 cur &#061; 0&#xff0c;left &#061; -1&#xff0c; right &#061; numsSize &#xff1b; b. \u5f53 cur &lt; right \u7684\u65f6\u5019&#xff08;\u56e0\u4e3a right \u8868\u2f70\u7684\u662f 2 \u5e8f\u5217\u7684\u5de6\u8fb9\u754c&#xff0c;\u56e0\u6b64\u5f53 cur \u78b0\u5230right \u7684\u65f6\u5019&#xff0c;\u8bf4\u660e\u5df2\u7ecf\u5c06\u6240\u6709\u6570\u636e\u626b\u63cf\u5b8c\u6bd5\u4e86&#xff09;&#xff0c;\u2f00\u76f4\u8fdb\u2f8f\u4e0b\u2faf\u5faa\u73af&#xff1a; \u6839\u636e nums[cur] \u7684\u503c&#xff0c;\u53ef\u4ee5\u5206\u4e3a\u4e0b\u2faf\u4e09\u79cd\u60c5\u51b5&#xff1a;<\/p>\n<ul>\n<li>i. nums[cur] &#061; &#061; 0 &#xff1b;\u8bf4\u660e\u6b64\u65f6\u8fd9\u4e2a\u4f4d\u7f6e\u7684\u5143\u7d20\u9700\u8981\u5728 left &#043; 1 \u7684\u4f4d\u7f6e\u4e0a&#xff0c;\u56e0\u6b64\u4ea4\u6362 left &#043; 1 \u4e0e cur \u4f4d\u7f6e\u7684\u5143\u7d20&#xff0c;\u5e76\u4e14\u8ba9 left&#043;&#043; &#xff08;\u6307\u5411 0 \u5e8f\u5217\u7684\u53f3\u8fb9\u754c&#xff09;&#xff0c;cur&#043;&#043; &#xff08;\u4e3a\u4ec0\u4e48\u53ef\u4ee5 &#043;&#043; \u5462&#xff0c;\u662f\u56e0\u4e3a left &#043; 1 \u4f4d\u7f6e\u8981\u4e48\u662f 0 &#xff0c;\u8981\u4e48\u662f cur &#xff0c;\u4ea4\u6362\u5b8c\u6bd5\u4e4b\u540e&#xff0c;\u8fd9\u4e2a\u4f4d\u7f6e\u7684\u503c\u5df2\u7ecf\u7b26\u5408\u6211\u4eec\u7684\u8981\u6c42&#xff0c;\u56e0\u6b64 cur&#043;&#043; &#xff09;&#xff1b;<\/li>\n<li>ii. nums[cur] &#061;&#061; 1 &#xff1b;\u8bf4\u660e\u8fd9\u4e2a\u4f4d\u7f6e\u5e94\u8be5\u5728 left \u548c cur \u4e4b\u95f4&#xff0c;\u6b64\u65f6\u2f46\u9700\u4ea4\u6362&#xff0c;\u76f4\u63a5\u8ba9 cur&#043;&#043; &#xff0c;\u5224\u65ad\u4e0b\u2f00\u4e2a\u5143\u7d20\u5373\u53ef&#xff1b;<\/li>\n<li>iii. nums[cur] &#061; &#061; 2 &#xff1b;\u8bf4\u660e\u8fd9\u4e2a\u4f4d\u7f6e\u7684\u5143\u7d20\u5e94\u8be5\u5728 right &#8211; 1 \u7684\u4f4d\u7f6e&#xff0c;\u56e0\u6b64\u4ea4\u6362right &#8211; 1 \u4e0e cur \u4f4d\u7f6e\u7684\u5143\u7d20&#xff0c;\u5e76\u4e14\u8ba9 right&#8211; &#xff08;\u6307\u5411 2 \u5e8f\u5217\u7684\u5de6\u8fb9\u754c&#xff09;&#xff0c;cur \u4e0d\u53d8&#xff08;\u56e0\u4e3a\u4ea4\u6362\u8fc7\u6765\u7684\u6570\u662f\u6ca1\u6709\u88ab\u5224\u65ad\u8fc7\u7684&#xff0c;\u56e0\u6b64\u9700\u8981\u5728\u4e0b\u8f6e\u5faa\u73af\u4e2d\u5224\u65ad&#xff09;<\/li>\n<\/ul>\n<p>c. \u5f53\u5faa\u73af\u7ed3\u675f\u4e4b\u540e&#xff1a; [0, left] \u8868\u2f70 0 \u5e8f\u5217&#xff1b; [left &#043; 1, right &#8211; 1] \u8868\u2f70 1 \u5e8f\u5217&#xff1b; [right, numsSize &#8211; 1] \u8868\u2f70 2 \u5e8f\u5217\u3002<\/p>\n<p>\u7b97\u6cd5\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Solution<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">void<\/span> <span class=\"token function\">swap<\/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> i<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> j<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span> t <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> t<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">void<\/span> <span class=\"token function\">sortColors<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span> left <span class=\"token operator\">&#061;<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> right <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">,<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>i <span class=\"token operator\">&lt;<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token function\">swap<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#043;&#043;<\/span>left<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\">else<\/span> <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">else<\/span> <span class=\"token function\">swap<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8212;<\/span>right<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 punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h3>2.\u5feb\u901f\u6392\u5e8f&#xff08;medium&#xff09;<\/h3>\n<p>\u9898\u2f6c\u94fe\u63a5&#xff1a;912. \u6392\u5e8f\u6570\u7ec4 \u7531\u4e8e\u2f12\u6263\u7684\u6d4b\u8bd5\u2f64\u4f8b\u5728\u4e0d\u65ad\u52a0\u5f3a&#xff0c;\u6240\u4ee5\u8fd9\u2fa5\u7684\u6570\u7ec4\u5212\u5206\u4e09\u5757\u7684\u601d\u60f3\u642d\u914d\u968f\u673a\u9009\u62e9\u57fa\u51c6\u5143\u7d20\u7684\u2f45\u6cd5\u662f\u2f50\u8f83\u4f18\u79c0\u7684\u3002 \u987a\u4fbf\u8bf4\u4e2a\u6709\u8da3\u7684\u4e8b&#xff1a;\u5b98\u2f45\u9898\u89e3\u7684\u5feb\u6392\u4ee3\u7801\u63d0\u4ea4\u540e\u4f1a\u8d85\u65f6~~~ 2022\/12\/07 \u9898\u2f6c\u63cf\u8ff0&#xff1a;<\/p>\n<p>\u7ed9\u4f60\u2f00\u4e2a\u6574\u6570\u6570\u7ec4 nums&#xff0c;\u8bf7\u4f60\u5c06\u8be5\u6570\u7ec4\u5347\u5e8f\u6392\u5217\u3002 \u2f70\u4f8b 1&#xff1a; \u8f93\u2f0a&#xff1a;nums &#061; [5,2,3,1] \u8f93\u51fa&#xff1a;[1,2,3,5] \u2f70\u4f8b 2&#xff1a; \u8f93\u2f0a&#xff1a;nums &#061; [5,1,1,2,0,0] \u8f93\u51fa&#xff1a;[0,0,1,1,2,5]<\/p>\n<p>\u89e3\u6cd5&#xff08;\u6570\u7ec4\u5206\u4e09\u5757\u601d\u60f3 &#043; \u968f\u673a\u9009\u62e9\u57fa\u51c6\u5143\u7d20\u7684\u5feb\u901f\u6392\u5e8f&#xff09;&#xff1a; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815154136-689f55302f046.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815154140-689f5534241d1.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u7b97\u6cd5\u601d\u8def&#xff1a; \u6211\u4eec\u5728\u6570\u636e\u7ed3\u6784\u9636\u6bb5\u5b66\u4e60\u7684\u5feb\u901f\u6392\u5e8f\u7684\u601d\u60f3\u53ef\u4ee5\u77e5\u9053&#xff0c;\u5feb\u6392\u6700\u6838\u2f3c\u7684\u2f00\u6b65\u5c31\u662f Partition (\u5206\u5272\u6570\u636e)&#xff1a;\u5c06\u6570\u636e\u6309\u7167\u2f00\u4e2a\u6807\u51c6&#xff0c;\u5206\u6210\u5de6\u53f3\u4e24\u90e8\u5206\u3002 \u5982\u679c\u6211\u4eec\u4f7f\u2f64\u8377\u5170\u56fd\u65d7\u95ee\u9898\u7684\u601d\u60f3&#xff0c;\u5c06\u6570\u7ec4\u5212\u5206\u4e3a \u5de6 \u4e2d \u53f3 \u4e09\u90e8\u5206&#xff1a;\u5de6\u8fb9\u662f\u2f50\u57fa\u51c6\u5143\u7d20\u2f29\u7684\u6570\u636e&#xff0c;\u4e2d\u95f4\u662f\u4e0e\u57fa\u51c6\u5143\u7d20\u76f8\u540c\u7684\u6570\u636e&#xff0c;\u53f3\u8fb9\u662f\u2f50\u57fa\u51c6\u5143\u7d20\u2f24\u7684\u6570\u636e\u3002\u7136\u540e\u518d\u53bb\u9012\u5f52\u7684\u6392\u5e8f\u5de6\u8fb9\u90e8\u5206\u548c\u53f3\u8fb9\u90e8\u5206\u5373\u53ef&#xff08;\u53ef\u4ee5\u820d\u53bb\u2f24\u91cf\u7684\u4e2d\u95f4\u90e8\u5206&#xff09;\u3002 \u5728\u5904\u7406\u6570\u636e\u91cf\u6709\u5f88\u591a\u91cd\u590d\u7684\u60c5\u51b5\u4e0b&#xff0c;\u6548\u7387\u4f1a\u2f24\u2f24\u63d0\u5347\u3002 \u7b97\u6cd5\u6d41\u7a0b&#xff1a; \u968f\u673a\u9009\u62e9\u57fa\u51c6\u7b97\u6cd5\u6d41\u7a0b&#xff1a; \u51fd\u6570\u8bbe\u8ba1&#xff1a;int randomKey(vector&amp; nums, int left, int right) a. \u5728\u4e3b\u51fd\u6570\u90a3\u2fa5\u79cd\u2f00\u9897\u968f\u673a\u6570\u79cd\u2f26&#xff1b; b. \u5728\u968f\u673a\u9009\u62e9\u57fa\u51c6\u51fd\u6570\u8fd9\u2fa5\u2f63\u6210\u2f00\u4e2a\u968f\u673a\u6570&#xff1b; c. \u7531\u4e8e\u6211\u4eec\u8981\u968f\u673a\u4ea7\u2f63\u2f00\u4e2a\u57fa\u51c6&#xff0c;\u56e0\u6b64\u53ef\u4ee5\u5c06\u968f\u673a\u6570\u8f6c\u6362\u6210\u968f\u673a\u4e0b\u6807&#xff1a;\u8ba9\u968f\u673a\u6570 % \u4e0a\u533a\u95f4\u2f24\u2f29&#xff0c;\u7136\u540e\u52a0\u4e0a\u533a\u95f4\u7684\u5de6\u8fb9\u754c\u5373\u53ef\u3002 \u5feb\u901f\u6392\u5e8f\u7b97\u6cd5\u4e3b\u8981\u6d41\u7a0b&#xff1a; a. \u5b9a\u4e49\u9012\u5f52\u51fa\u2f1d&#xff1b; b. \u5229\u2f64\u968f\u673a\u9009\u62e9\u57fa\u51c6\u51fd\u6570\u2f63\u6210\u2f00\u4e2a\u57fa\u51c6\u5143\u7d20&#xff1b; c. \u5229\u2f64\u8377\u5170\u56fd\u65d7\u601d\u60f3\u5c06\u6570\u7ec4\u5212\u5206\u6210\u4e09\u4e2a\u533a\u57df&#xff1b; d. \u9012\u5f52\u5904\u7406\u5de6\u8fb9\u533a\u57df\u548c\u53f3\u8fb9\u533a\u57df\u3002 \u7b97\u6cd5\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Solution<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">sortArray<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token function\">qsort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">return<\/span> nums<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">void<\/span> <span class=\"token function\">qsort<\/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> l<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> r<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>l <span class=\"token operator\">&gt;&#061;<\/span> r<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ \u6570\u7ec4\u5206\u4e09\u5757<\/span><br \/>\n <span class=\"token keyword\">int<\/span> key <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token keyword\">new<\/span> <span class=\"token class-name\">Random<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">nextInt<\/span><span class=\"token punctuation\">(<\/span>r <span class=\"token operator\">&#8211;<\/span> l <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#043;<\/span> l<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">int<\/span> left <span class=\"token operator\">&#061;<\/span> l <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> right <span class=\"token operator\">&#061;<\/span> r <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> i <span class=\"token operator\">&#061;<\/span> l<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>i <span class=\"token operator\">&lt;<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;<\/span> key<span class=\"token punctuation\">)<\/span> <span class=\"token function\">swap<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#043;&#043;<\/span>left<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\">else<\/span> <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> key<span class=\"token punctuation\">)<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">else<\/span> <span class=\"token function\">swap<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8212;<\/span>right<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 comment\">\/\/ [l, left] [left &#043; 1, right &#8211; 1] [rigth, r]<\/span><br \/>\n <span class=\"token function\">qsort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> l<span class=\"token punctuation\">,<\/span> left<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token function\">qsort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> right<span class=\"token punctuation\">,<\/span> r<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">void<\/span> <span class=\"token function\">swap<\/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> i<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> j<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span> t <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> t<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h3>3.\u6570\u7ec4\u4e2d\u7684\u7b2cK\u4e2a\u6700\u2f24\u5143\u7d20&#xff08;medium&#xff09;<\/h3>\n<p>\u9898\u2f6c\u94fe\u63a5&#xff1a;215. \u6570\u7ec4\u4e2d\u7684\u7b2cK\u4e2a\u6700\u2f24\u5143\u7d20 \u9898\u2f6c\u63cf\u8ff0&#xff1a;<\/p>\n<p>\u7ed9\u5b9a\u6574\u6570\u6570\u7ec4 nums \u548c\u6574\u6570 k&#xff0c;\u8bf7\u8fd4\u56de\u6570\u7ec4\u4e2d\u7b2c k \u4e2a\u6700\u2f24\u7684\u5143\u7d20\u3002 \u8bf7\u6ce8\u610f&#xff0c;\u4f60\u9700\u8981\u627e\u7684\u662f\u6570\u7ec4\u6392\u5e8f\u540e\u7684\u7b2c k \u4e2a\u6700\u2f24\u7684\u5143\u7d20&#xff0c;\u2f7d\u4e0d\u662f\u7b2c k \u4e2a\u4e0d\u540c\u7684\u5143\u7d20\u3002 \u4f60\u5fc5\u987b\u8bbe\u8ba1\u5e76\u5b9e\u73b0\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n) \u7684\u7b97\u6cd5\u89e3\u51b3\u6b64\u95ee\u9898\u3002 \u2f70\u4f8b 1: \u8f93\u2f0a: [3,2,1,5,6,4], k &#061; 2 \u8f93\u51fa: 5 \u2f70\u4f8b 2: \u8f93\u2f0a: [3,2,3,1,2,4,5,5,6], k &#061; 4 \u8f93\u51fa: 4 \u63d0\u2f70&#xff1a; 1 &lt;&#061; k &lt;&#061; nums.length &lt;&#061; 10^5 -10^4 &lt;&#061; nums[i] &lt;&#061; 10^4<\/p>\n<p>\u89e3\u6cd5&#xff08;\u5feb\u901f\u9009\u62e9\u7b97\u6cd5&#xff09;&#xff1a; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815154152-689f5540d89f4.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815154154-689f5542db626.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u7b97\u6cd5\u601d\u8def&#xff1a; \u5728\u5feb\u6392\u4e2d&#xff0c;\u5f53\u6211\u4eec\u628a\u6570\u7ec4\u300c\u5206\u6210\u4e09\u5757\u300d\u4e4b\u540e&#xff1a; [l, left] [left &#043; 1, right &#8211; 1] [right, r] &#xff0c;\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u6bcf\u2f00\u4e2a\u533a\u95f4\u5185\u5143\u7d20\u7684\u300c\u4e2a\u6570\u300d&#xff0c;\u8fdb\u2f7d\u63a8\u65ad\u51fa\u6211\u4eec\u8981\u627e\u7684\u5143\u7d20\u662f\u5728\u300c\u54ea\u2f00\u4e2a\u533a\u95f4\u300d\u2fa5\u2faf\u3002 \u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u53bb\u300c\u76f8\u5e94\u7684\u533a\u95f4\u300d\u53bb\u5bfb\u627e\u6700\u7ec8\u7ed3\u679c\u5c31\u597d\u4e86\u3002 \u7b97\u6cd5\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Solution<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">findKthLargest<\/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\">return<\/span> <span class=\"token function\">qsort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> k<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">qsort<\/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> l<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> r<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> k<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>l <span class=\"token operator\">&#061;&#061;<\/span> r<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">return<\/span> nums<span class=\"token punctuation\">[<\/span>l<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token comment\">\/\/ 1. \u6309\u7167\u968f\u673a\u9009\u62e9\u7684\u57fa\u51c6\u5143\u7d20&#xff0c;\u5c06\u6570\u7ec4\u5206\u4e09\u5757<\/span><br \/>\n <span class=\"token keyword\">int<\/span> key <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span><span class=\"token keyword\">new<\/span> <span class=\"token class-name\">Random<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">nextInt<\/span><span class=\"token punctuation\">(<\/span>r <span class=\"token operator\">&#8211;<\/span> l <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#043;<\/span> l<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">int<\/span> left <span class=\"token operator\">&#061;<\/span> l <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> right <span class=\"token operator\">&#061;<\/span> r <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> i <span class=\"token operator\">&#061;<\/span> l<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>i <span class=\"token operator\">&lt;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;<\/span> key<span class=\"token punctuation\">)<\/span> <span class=\"token function\">swap<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#043;&#043;<\/span>left<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\">else<\/span> <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> key<span class=\"token punctuation\">)<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">else<\/span> <span class=\"token function\">swap<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8212;<\/span>right<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 comment\">\/\/ 2. \u5206\u60c5\u51b5\u8ba8\u8bba<\/span><br \/>\n <span class=\"token keyword\">int<\/span> c <span class=\"token operator\">&#061;<\/span> r <span class=\"token operator\">&#8211;<\/span> right <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> b <span class=\"token operator\">&#061;<\/span> right <span class=\"token operator\">&#8211;<\/span> left <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>c <span class=\"token operator\">&gt;&#061;<\/span> k<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token function\">qsort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> right<span class=\"token punctuation\">,<\/span> r<span class=\"token punctuation\">,<\/span> k<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">else<\/span> <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>c <span class=\"token operator\">&#043;<\/span> b <span class=\"token operator\">&gt;&#061;<\/span> k<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> key<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">else<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token function\">qsort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> l<span class=\"token punctuation\">,<\/span> left<span class=\"token punctuation\">,<\/span> k <span class=\"token operator\">&#8211;<\/span> b <span class=\"token operator\">&#8211;<\/span> c<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">void<\/span> <span class=\"token function\">swap<\/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> i<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> j<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span> t <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n nums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> t<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h2>\u5f52\u5e76\u6392\u5e8f<\/h2>\n<h3>1.\u6392\u5e8f\u6570\u7ec4&#xff08;medium&#xff09;<\/h3>\n<p>\u9898\u2f6c\u94fe\u63a5&#xff1a;912. \u6392\u5e8f\u6570\u7ec4 \u9898\u2f6c\u63cf\u8ff0&#xff1a;<\/p>\n<p>\u7ed9\u4f60\u2f00\u4e2a\u6574\u6570\u6570\u7ec4 nums&#xff0c;\u8bf7\u4f60\u5c06\u8be5\u6570\u7ec4\u5347\u5e8f\u6392\u5217\u3002 \u2f70\u4f8b 1&#xff1a; \u8f93\u2f0a&#xff1a;nums &#061; [5,2,3,1] \u8f93\u51fa&#xff1a;[1,2,3,5] \u2f70\u4f8b 2&#xff1a; \u8f93\u2f0a&#xff1a;nums &#061; [5,1,1,2,0,0] \u8f93\u51fa&#xff1a;[0,0,1,1,2,5]<\/p>\n<p>\u89e3\u6cd5&#xff08;\u5f52\u5e76\u6392\u5e8f&#xff09;&#xff1a; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815154203-689f554b6da61.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u7b97\u6cd5\u601d\u8def&#xff1a; \u5f52\u5e76\u6392\u5e8f\u7684\u6d41\u7a0b\u5145\u5206\u7684\u4f53\u73b0\u4e86\u300c\u5206\u2f7d\u6cbb\u4e4b\u300d\u7684\u601d\u60f3&#xff0c;\u2f24\u4f53\u8fc7\u7a0b\u5206\u4e3a\u4e24\u6b65&#xff1a; \u25e6 \u5206&#xff1a;\u5c06\u6570\u7ec4\u2f00\u5206\u4e3a\u2f06\u4e3a\u4e24\u90e8\u5206&#xff0c;\u2f00\u76f4\u5206\u89e3\u5230\u6570\u7ec4\u7684\u2ed3\u5ea6\u4e3a 1 &#xff0c;\u4f7f\u6574\u4e2a\u6570\u7ec4\u7684\u6392\u5e8f\u8fc7\u7a0b\u88ab\u5206\u4e3a\u300c\u5de6\u534a\u90e8\u5206\u6392\u5e8f\u300d &#043; \u300c\u53f3\u534a\u90e8\u5206\u6392\u5e8f\u300d&#xff1b; \u25e6 \u6cbb&#xff1a;\u5c06\u4e24\u4e2a\u8f83\u77ed\u7684\u300c\u6709\u5e8f\u6570\u7ec4\u5408\u5e76\u6210\u2f00\u4e2a\u2ed3\u7684\u6709\u5e8f\u6570\u7ec4\u300d&#xff0c;\u2f00\u76f4\u5408\u5e76\u5230\u6700\u521d\u7684\u2ed3\u5ea6\u3002 \u7b97\u6cd5\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Solution<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> tmp<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token function\">sortArray<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n tmp <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> nums<span class=\"token punctuation\">.<\/span>length <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">return<\/span> nums<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">void<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> left<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&gt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p> <span class=\"token comment\">\/\/ 1. \u6839\u636e\u4e2d\u95f4\u70b9\u5212\u5206\u533a\u95f4<\/span><br \/>\n <span class=\"token keyword\">int<\/span> mid <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&#043;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ [left, mid] [mid &#043; 1, right]<\/span><\/p>\n<p> <span class=\"token comment\">\/\/ 2. \u5148\u628a\u5de6\u53f3\u533a\u95f4\u6392\u4e2a\u5e8f<\/span><br \/>\n <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> left<span class=\"token punctuation\">,<\/span> mid<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p> <span class=\"token comment\">\/\/ 3. \u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4<\/span><br \/>\n <span class=\"token keyword\">int<\/span> cur1 <span class=\"token operator\">&#061;<\/span> left<span class=\"token punctuation\">,<\/span> cur2 <span class=\"token operator\">&#061;<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid <span class=\"token operator\">&amp;&amp;<\/span> cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span><br \/>\n tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">?<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">:<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ \u5904\u7406\u6ca1\u6709\u904d\u5386\u5b8c\u7684\u6570\u7ec4<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid<span class=\"token punctuation\">)<\/span> tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ 4. \u8fd8\u539f<\/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> left<span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> tmp<span class=\"token punctuation\">[<\/span>j <span class=\"token operator\">&#8211;<\/span> left<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h3>2.\u6570\u7ec4\u4e2d\u7684\u9006\u5e8f\u5bf9&#xff08;hard&#xff09;<\/h3>\n<p>\u9898\u2f6c\u94fe\u63a5&#xff1a;\u5251\u6307 Offer 51. \u6570\u7ec4\u4e2d\u7684\u9006\u5e8f\u5bf9 \u9898\u2f6c\u63cf\u8ff0&#xff1a;<\/p>\n<p>\u5728\u6570\u7ec4\u4e2d\u7684\u4e24\u4e2a\u6570\u5b57&#xff0c;\u5982\u679c\u524d\u2faf\u2f00\u4e2a\u6570\u5b57\u2f24\u4e8e\u540e\u2faf\u7684\u6570\u5b57&#xff0c;\u5219\u8fd9\u4e24\u4e2a\u6570\u5b57\u7ec4\u6210\u2f00\u4e2a\u9006\u5e8f\u5bf9\u3002\u8f93\u2f0a\u2f00\u4e2a\u6570\u7ec4&#xff0c;\u6c42\u51fa\u8fd9\u4e2a\u6570\u7ec4\u4e2d\u7684\u9006\u5e8f\u5bf9\u7684\u603b\u6570\u3002 \u2f70\u4f8b 1: \u8f93\u2f0a: [7,5,6,4] \u8f93\u51fa: 5\u00b7\u00b7<\/p>\n<p>\u89e3\u6cd5&#xff08;\u5229\u2f64\u5f52\u5e76\u6392\u5e8f\u7684\u8fc7\u7a0b \u2014 \u5206\u6cbb&#xff09;&#xff1a;<img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815154211-689f555383c32.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u7b97\u6cd5\u601d\u8def&#xff1a; \u2f64\u5f52\u5e76\u6392\u5e8f\u6c42\u9006\u5e8f\u6570\u662f\u5f88\u7ecf\u5178\u7684\u2f45\u6cd5&#xff0c;\u4e3b\u8981\u5c31\u662f\u5728\u5f52\u5e76\u6392\u5e8f\u7684\u5408\u5e76\u8fc7\u7a0b\u4e2d\u7edf\u8ba1\u51fa\u9006\u5e8f\u5bf9\u7684\u6570\u91cf&#xff0c;\u4e5f\u5c31\u662f\u5728\u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u5e8f\u5217\u7684\u8fc7\u7a0b\u4e2d&#xff0c;\u80fd\u591f\u5feb\u901f\u6c42\u51fa\u9006\u5e8f\u5bf9\u7684\u6570\u91cf\u3002 \u6211\u4eec\u5c06\u8fd9\u4e2a\u95ee\u9898\u5206\u89e3\u6210\u2f0f\u4e2a\u2f29\u95ee\u9898&#xff0c;\u9010\u2f00\u7834\u89e3\u8fd9\u9053\u9898\u3002 \u6ce8\u610f&#xff1a;\u9ed8\u8ba4\u90fd\u662f\u5347\u5e8f&#xff0c;\u5982\u679c\u638c\u63e1\u5347\u5e8f\u7684\u8bdd&#xff0c;\u964d\u5e8f\u7684\u5f52\u5e76\u8fc7\u7a0b\u4e5f\u662f\u53ef\u4ee5\u89e3\u51b3\u95ee\u9898\u7684\u3002<\/p>\n<ul>\n<li>\n<p>\u5148\u89e3\u51b3\u7b2c\u2f00\u4e2a\u95ee\u9898&#xff0c;\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u5229\u2f64\u5f52\u5e76\u6392\u5e8f&#xff1f; \u5982\u679c\u6211\u4eec\u5c06\u6570\u7ec4\u4ece\u4e2d\u95f4\u5212\u5206\u6210\u4e24\u4e2a\u90e8\u5206&#xff0c;\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5c06\u9006\u5e8f\u5bf9\u4ea7\u2f63\u7684\u2f45\u5f0f\u5212\u5206\u6210\u4e09\u7ec4&#xff1a; \u2022 \u9006\u5e8f\u5bf9\u4e2d\u4e24\u4e2a\u5143\u7d20&#xff1a;\u5168\u90e8\u4ece\u5de6\u6570\u7ec4\u4e2d\u9009\u62e9 \u2022 \u9006\u5e8f\u5bf9\u4e2d\u4e24\u4e2a\u5143\u7d20&#xff1a;\u5168\u90e8\u4ece\u53f3\u6570\u7ec4\u4e2d\u9009\u62e9 \u2022 \u9006\u5e8f\u5bf9\u4e2d\u4e24\u4e2a\u5143\u7d20&#xff1a;\u2f00\u4e2a\u9009\u5de6\u6570\u7ec4\u53e6\u2f00\u4e2a\u9009\u53f3\u6570\u7ec4 \u6839\u636e\u6392\u5217\u7ec4\u5408\u7684\u5206\u7c7b\u76f8\u52a0\u539f\u7406&#xff0c;\u4e09\u79cd\u79cd\u60c5\u51b5\u4e0b\u4ea7\u2f63\u7684\u9006\u5e8f\u5bf9\u7684\u603b\u548c&#xff0c;\u6b63\u597d\u7b49\u4e8e\u603b\u7684\u9006\u5e8f\u5bf9\u6570\u91cf\u3002\u2f7d\u8fd9\u4e2a\u601d\u8def\u6b63\u597d\u5339\u914d\u5f52\u5e76\u6392\u5e8f\u7684\u8fc7\u7a0b&#xff1a; \u2022 \u5148\u6392\u5e8f\u5de6\u6570\u7ec4&#xff1b; \u2022 \u518d\u6392\u5e8f\u53f3\u6570\u7ec4&#xff1b; \u2022 \u5de6\u6570\u7ec4\u548c\u53f3\u6570\u7ec4\u5408\u2f06\u4e3a\u2f00\u3002 \u56e0\u6b64&#xff0c;\u6211\u4eec\u53ef\u4ee5\u5229\u2f64\u5f52\u5e76\u6392\u5e8f\u7684\u8fc7\u7a0b&#xff0c;\u5148\u6c42\u51fa\u5de6\u534a\u6570\u7ec4\u4e2d\u9006\u5e8f\u5bf9\u7684\u6570\u91cf&#xff0c;\u518d\u6c42\u51fa\u53f3\u534a\u6570\u7ec4\u4e2d\u9006\u5e8f\u5bf9\u7684\u6570\u91cf&#xff0c;\u6700\u540e\u6c42\u51fa\u2f00\u4e2a\u9009\u62e9\u5de6\u8fb9&#xff0c;\u53e6\u2f00\u4e2a\u9009\u62e9\u53f3\u8fb9\u60c5\u51b5\u4e0b\u9006\u5e8f\u5bf9\u7684\u6570\u91cf&#xff0c;\u4e09\u8005\u76f8\u52a0\u5373\u53ef\u3002<\/p>\n<\/li>\n<li>\n<p>\u89e3\u51b3\u7b2c\u2f06\u4e2a\u95ee\u9898&#xff0c;\u4e3a\u4ec0\u4e48\u8981\u8fd9\u4e48\u505a&#xff1f; 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right[cur2]&#xff0c;\u7531\u4e8e\u4e24\u4e2a\u6570\u7ec4\u90fd\u662f\u5347\u5e8f\u7684&#xff0c;\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u65ad\u5b9a&#xff0c;\u6b64\u523b left \u6570\u7ec4\u4e2d[cur1, 2] \u533a\u95f4\u5185\u7684 3 \u4e2a\u5143\u7d20\u5747\u53ef\u4e0e right[cur2] \u7684\u5143\u7d20\u6784\u6210\u9006\u5e8f\u5bf9&#xff0c;\u56e0\u6b64\u53ef\u4ee5\u7d2f\u52a0\u9006\u5e8f\u5bf9\u7684\u6570\u91cf ret&#043;&#061; 3&#xff0c;\u5e76\u4e14\u5c06 right[cur2] \u52a0\u2f0a\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d&#xff0c;cur2&#043;&#043; \u904d\u5386\u4e0b\u2f00\u4e2a\u5143\u7d20\u3002\u7b2c\u2f00\u8f6e\u5faa\u73af\u7ed3\u675f\u540e&#xff1a;left &#061; [5, 7, 9] right &#061; [x, 5, 8] help &#061; [4] ret &#061; 3 cur1 &#061; 0 cur2 &#061; 1 \u7b2c\u2f06\u8f6e\u5faa\u73af&#xff1a; left[cur1] &#061;&#061; right[cur2]&#xff0c;\u56e0\u4e3a right[cur2] \u53ef\u80fd\u4e0e left \u6570\u7ec4\u4e2d\u5f80\u540e\u7684\u5143\u7d20\u6784\u6210\u9006\u5e8f\u5bf9&#xff0c;\u56e0\u6b64\u6211\u4eec\u9700\u8981\u5c06 left[cur1] \u52a0\u2f0a\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb&#xff0c;\u6b64\u65f6\u6ca1\u6709\u4ea7\u2f63\u9006\u5e8f\u5bf9&#xff0c;\u4e0d\u66f4\u65b0 ret\u3002\u7b2c\u2f06\u8f6e\u5faa\u73af\u7ed3\u675f\u540e&#xff1a;left &#061; [x, 7, 9] right &#061; [x, 5, 8] help &#061; [4, 5] ret &#061; 3 cur1 &#061; 1 cur2 &#061; 1 \u7b2c\u4e09\u8f6e\u5faa\u73af&#xff1a; left[cur1] &gt; right[cur2]&#xff0c;\u4e0e\u7b2c\u2f00\u8f6e\u5faa\u73af\u76f8\u540c&#xff0c;\u6b64\u523b left \u6570\u7ec4\u4e2d[cur1, 2] \u533a\u95f4\u5185\u7684 2 \u4e2a\u5143\u7d20\u5747\u53ef\u4e0e right[cur2] \u7684\u5143\u7d20\u6784\u6210\u9006\u5e8f\u5bf9&#xff0c;\u66f4\u65b0 ret \u7684\u503c\u4e3a ret &#043;&#061; 2&#xff0c;\u5e76\u4e14\u5c06 right[cur2] \u52a0\u2f0a\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb&#xff0c;cur2&#043;&#043; \u904d\u5386\u4e0b\u2f00\u4e2a\u5143\u7d20\u3002 \u7b2c\u4e09\u8f6e\u5faa\u73af\u7ed3\u675f\u540e&#xff1a;left &#061; [x, 7, 9] right &#061; [x, x, 8] help &#061; [4, 5, 5] ret &#061; 5 cur1 &#061; 1 cur2 &#061; 2 \u7b2c\u56db\u8f6e\u5faa\u73af&#xff1a; left[cur1] &lt; right[cur2]&#xff0c;\u7531\u4e8e\u4e24\u4e2a\u6570\u7ec4\u90fd\u662f\u5347\u5e8f\u7684&#xff0c;\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a left[cur1] \u2f50 right \u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u90fd\u8981\u2f29\u3002left[cur1] \u8fd9\u4e2a\u5143\u7d20\u662f\u4e0d\u53ef\u80fd\u4e0e right \u6570\u7ec4\u4e2d\u7684\u5143\u7d20\u6784\u6210\u9006\u5e8f\u5bf9\u3002\u56e0\u6b64&#xff0c;\u2f24\u80c6\u7684\u5c06 left[cur1] \u8fd9\u4e2a\u5143\u7d20\u52a0\u2f0a\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb&#xff0c;\u4e0d\u66f4\u7ec6 ret \u7684\u503c\u3002\u7b2c\u56db\u8f6e\u5faa\u73af\u7ed3\u675f\u540e&#xff1a;left &#061; [x, x, 9] right &#061; [x, x, 8] help &#061; [4, 5, 5, 7] ret &#061; 5 cur1 &#061; 2 cur2 &#061; 2 \u7b2c\u4e94\u8f6e\u5faa\u73af&#xff1a; left[cur1] &gt; right[cur2]&#xff0c;\u4e0e\u7b2c\u2f00\u3001\u7b2c\u4e09\u8f6e\u5faa\u73af\u76f8\u540c\u3002\u6b64\u65f6 left \u6570\u7ec4\u5185\u7684 1 \u4e2a\u5143\u7d20\u80fd\u4e0eright[cur2] \u6784\u6210\u9006\u5e8f\u5bf9&#xff0c;\u66f4\u65b0 ret \u7684\u503c&#xff0c;\u5e76\u4e14\u5c06 right[cur2] \u52a0\u2f0a\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb\u3002\u7b2c\u4e94\u8f6e\u5faa\u73af\u7ed3\u675f\u540e&#xff1a;left &#061; [x, x, 9] right &#061; [x, x, x] help &#061; [4, 5, 5, 7, 8] ret &#061; 6 cur1 &#061; 2 cur2 &#061; 2 \u5904\u7406\u5269\u4f59\u5143\u7d20&#xff1a; \u2022 \u5982\u679c\u662f\u5de6\u8fb9\u51fa\u73b0\u5269\u4f59&#xff0c;\u8bf4\u660e\u5de6\u8fb9\u5269\u4e0b\u7684\u6240\u6709\u5143\u7d20\u90fd\u662f\u2f50\u53f3\u8fb9\u5143\u7d20\u2f24\u7684&#xff0c;\u4f46\u662f\u5b83\u4eec\u90fd\u662f\u5df2\u7ecf\u88ab\u8ba1\u7b97\u8fc7\u7684&#xff08;\u6211\u4eec\u4ee5\u53f3\u8fb9\u7684\u5143\u7d20\u4e3a\u57fa\u51c6\u7684&#xff09;&#xff0c;\u56e0\u6b64\u4e0d\u4f1a\u4ea7\u2f63\u9006\u5e8f\u5bf9&#xff0c;\u4ec5\u9700\u5f52\u5e76\u6392\u5e8f\u5373\u53ef\u3002 \u2022 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]&#xff0c;\u901a\u8fc7\u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4\u7684\u8fc7\u7a0b&#xff0c;\u6765\u6c42\u5f97\u9006\u5e8f\u5bf9\u7684\u6570\u91cf&#xff1a;\u89c4\u5b9a\u5982\u4e0b\u5b9a\u4e49\u6765\u53d9\u8ff0\u8fc7\u7a0b: cur1 \u904d\u5386 left \u6570\u7ec4&#xff0c;cur2 \u904d\u5386 right \u6570\u7ec4&#xff0c;ret \u8bb0\u5f55\u9006\u5e8f\u5bf9\u7684\u6570\u91cf \u7b2c\u2f00\u8f6e\u5faa\u73af&#xff1a; left[cur1] &gt; right[cur2]&#xff0c;\u5148\u4e0d\u8981\u7740\u6025\u7edf\u8ba1&#xff0c;\u56e0\u4e3a\u6211\u4eec\u8981\u627e\u7684\u662f\u5f53\u524d\u5143\u7d20\u540e\u2faf\u6709\u591a\u5c11\u2f50\u5b83\u2f29\u7684&#xff0c;\u8fd9\u2fa5\u867d\u7136\u51fa\u73b0\u4e86\u2f00\u4e2a&#xff0c;\u4f46\u662f right \u6570\u7ec4\u4e2d\u4f9d\u65e7\u8fd8\u53ef\u80fd\u6709\u5176\u4f59\u2f50\u5b83\u2f29\u7684\u3002\u56e0\u6b64\u6b64\u65f6\u4ec5\u5c06 right[cur2] \u52a0\u2f0a\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb&#xff0c;\u5e76\u4e14\u5c06 cur2&#043;&#043;\u3002\u7b2c\u2f00\u8f6e\u5faa\u73af\u7ed3\u675f\u540e&#xff1a;left &#061; [5, 7, 9] right &#061; [x, 5, 8] help &#061; [4] ret &#061; 0 cur1 &#061; 0 cur2 &#061; 1 \u7b2c\u2f06\u8f6e\u5faa\u73af&#xff1a; left[cur1] &#061; &#061; right[cur2]&#xff0c;\u7531\u4e8e\u4e24\u4e2a\u6570\u7ec4\u90fd\u662f\u5347\u5e8f&#xff0c;\u8fd9\u4e2a\u65f6\u5019\u5bf9\u4e8e\u5143\u7d20 left[cur1] \u6765\u8bf4&#xff0c;\u6211\u4eec\u5df2\u7ecf\u53ef\u4ee5\u65ad\u5b9a right \u6570\u7ec4\u4e2d [0, cur2) \u5de6\u95ed\u53f3\u5f00\u533a\u95f4\u4e0a\u7684\u5143\u7d20\u90fd\u662f\u2f50\u5b83\u2f29\u7684\u3002\u56e0\u6b64\u6b64\u65f6\u53ef\u4ee5\u7edf\u8ba1\u9006\u5e8f\u5bf9\u7684\u6570\u91cf ret &#043;&#061; cur2 &#8211; 0&#xff0c;\u5e76\u4e14\u5c06 left[cur1] \u653e\u2f0a\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb&#xff0c;cur1&#043;&#043; \u904d\u5386\u4e0b\u2f00\u4e2a\u5143\u7d20\u3002\u7b2c\u2f06\u8f6e\u5faa\u73af\u7ed3\u675f\u540e&#xff1a;left &#061; [x, 7, 9] right &#061; [x, 5, 8] help &#061; [4, 5] ret &#061; 1 cur1 &#061; 1 cur2 &#061; 1 \u7b2c\u4e09\u8f6e\u5faa\u73af&#xff1a; left[cur1] &gt; right[cur2]&#xff0c;\u4e0e\u7b2c\u2f00\u8f6e\u5faa\u73af\u76f8\u540c&#xff0c;\u76f4\u63a5\u5c06 right[cur2] \u52a0\u2f0a\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb&#xff0c;cur2&#043;&#043; \u904d\u5386\u4e0b\u2f00\u4e2a\u5143\u7d20\u3002\u7b2c\u4e09\u8f6e\u5faa\u73af\u7ed3\u675f\u540e&#xff1a;left &#061; [x, 7, 9] right &#061; [x, x, 8] help &#061; [4, 5, 5] ret &#061; 1 cur1 &#061; 1 cur2 &#061; 2 \u7b2c\u56db\u8f6e\u5faa\u73af&#xff1a; left[cur1] &lt; right[cur2]&#xff0c;\u7531\u4e8e\u4e24\u4e2a\u6570\u7ec4\u90fd\u662f\u5347\u5e8f\u7684&#xff0c;\u8fd9\u4e2a\u65f6\u5019\u5bf9\u4e8e\u5143\u7d20 left[cur1] \u6765\u8bf4&#xff0c;\u6211\u4eec\u4f9d\u65e7\u5df2\u7ecf\u53ef\u4ee5\u65ad\u5b9a right \u6570\u7ec4\u4e2d [0, cur2) \u5de6\u95ed\u53f3\u5f00\u533a\u95f4\u4e0a\u7684\u5143\u7d20\u90fd\u662f\u2f50\u5b83\u2f29\u7684\u3002\u56e0\u6b64\u6b64\u65f6\u53ef\u4ee5\u7edf\u8ba1\u9006\u5e8f\u5bf9\u7684\u6570\u91cf ret &#043;&#061; cur2 &#8211; 0&#xff0c;\u5e76\u4e14\u5c06 left[cur1] \u653e\u2f0a\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb&#xff0c;cur1&#043;&#043; \u904d\u5386\u4e0b\u2f00\u4e2a\u5143\u7d20\u3002\u7b2c\u56db\u8f6e\u5faa\u73af\u7ed3\u675f\u540e&#xff1a;left &#061; [9] right &#061; [8] help &#061; [4, 5, 5, 7] ret &#061; 3 cur1 &#061; 2 cur2 &#061; 2 \u7b2c\u4e94\u8f6e\u5faa\u73af&#xff1a; left[cur1] &gt; right[cur2]&#xff0c;\u4e0e\u7b2c\u2f00\u3001\u7b2c\u4e09\u8f6e\u5faa\u73af\u76f8\u540c\u3002\u76f4\u63a5\u5c06 right[cur2] \u52a0\u2f0a\u5230\u8f85\u52a9\u6570\u7ec4\u4e2d\u53bb&#xff0c;cur2&#043;&#043; \u904d\u5386\u4e0b\u2f00\u4e2a\u5143\u7d20\u3002\u7b2c\u4e94\u8f6e\u5faa\u73af\u7ed3\u675f\u540e&#xff1a;left &#061; [x, x, 9] right &#061; [x, x, x] help &#061; [4, 5, 5, 7, 8] ret &#061; 3 cur1 &#061; 2 cur2 &#061; 2 \u5904\u7406\u5269\u4f59\u5143\u7d20&#xff1a; \u2022 \u5982\u679c\u662f\u5de6\u8fb9\u51fa\u73b0\u5269\u4f59&#xff0c;\u8bf4\u660e\u5de6\u8fb9\u5269\u4e0b\u7684\u6240\u6709\u5143\u7d20\u90fd\u662f\u2f50\u53f3\u8fb9\u5143\u7d20\u2f24\u7684&#xff0c;\u4f46\u662f\u76f8\u2f50\u8f83\u4e8e\u2f45\u6cd5\u2f00&#xff0c;\u9006\u5e8f\u5bf9\u7684\u6570\u91cf\u662f\u6ca1\u6709\u7edf\u8ba1\u8fc7\u7684\u3002\u56e0\u6b64&#xff0c;\u6211\u4eec\u9700\u8981\u7edf\u8ba1 ret \u7684\u503c&#xff1a; \u25e6 \u8bbe\u5de6\u8fb9\u6570\u7ec4\u5269\u4f59\u5143\u7d20\u7684\u4e2a\u6570\u4e3a leave \u25e6 ret &#043;&#061; leave * &#xff08;cur2 &#8211; 0&#xff09; \u5bf9\u4e8e\u672c\u9898\u6765\u8bf4&#xff0c;\u5904\u7406\u5269\u4f59\u5143\u7d20\u7684\u65f6\u5019&#xff0c; left \u6570\u7ec4\u5269\u4f59 1 \u4e2a\u5143\u7d20&#xff0c;cur2 &#8211; 0 &#061; 3&#xff0c;\u56e0\u6b64 ret \u9700\u8981\u7c7b\u52a0\u4e0a 3&#xff0c;\u7ed3\u679c\u4e3a 6\u3002\u4e0e\u2f45\u6cd5\u2f00\u6c42\u5f97\u7684\u7ed3\u679c\u76f8\u540c\u3002 \u2022 \u5982\u679c\u662f\u53f3\u8fb9\u51fa\u73b0\u5269\u4f59&#xff0c;\u8bf4\u660e\u53f3\u8fb9\u5269\u4e0b\u7684\u5143\u7d20\u90fd\u662f\u2f50\u5de6\u8fb9\u2f24\u7684&#xff0c;\u4e0d\u7b26\u5408\u9006\u5e8f\u5bf9\u7684\u5b9a\u4e49&#xff0c;\u56e0\u6b64\u4e5f\u4e0d\u9700\u8981\u5904\u7406&#xff0c;\u4ec5\u9700\u5f52\u5e76\u6392\u5e8f\u5373\u53ef\u3002 \u6574\u4e2a\u8fc7\u7a0b\u53ea\u9700\u5c06\u4e24\u4e2a\u6570\u7ec4\u904d\u5386\u2f00\u904d\u5373\u53ef&#xff0c;\u65f6\u95f4\u590d\u6742\u5ea6\u4f9d\u65e7\u4e3a O(N)\u3002 \u7531\u4e0a\u8ff0\u8fc7\u7a0b\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u2f45\u6cd5\u2f06\u7edf\u8ba1\u9006\u5e8f\u5bf9\u7684\u5173\u952e\u70b9&#xff1a; \u5728\u5408\u5e76\u6709\u5e8f\u6570\u7ec4\u7684\u65f6\u5019&#xff0c;\u9047\u5230\u5de6\u6570\u7ec4\u5f53\u524d\u5143\u7d20 &lt;&#061; \u53f3\u6570\u7ec4\u5f53\u524d\u5143\u7d20\u65f6&#xff0c;\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u53f3\u6570\u7ec4\u5df2\u7ecf\u904d\u5386\u8fc7\u7684\u5143\u7d20\u7684\u2ed3\u5ea6&#xff0c;\u5feb\u901f\u6c42\u51fa\u5de6\u6570\u7ec4\u5f53\u524d\u5143\u7d20\u540e\u2faf\u6709\u591a\u5c11\u4e2a\u6570\u2f50\u5b83\u2f24\u3002\u4f46\u662f\u9700\u8981\u6ce8\u610f\u7684\u662f&#xff0c;\u5728\u5904\u7406\u5269\u4f59\u5143\u7d20\u7684\u65f6\u5019&#xff0c;\u2f45\u6cd5\u2f06\u8fd8\u9700\u8981\u7edf\u8ba1\u9006\u5e8f\u5bf9\u7684\u6570\u91cf\u3002<\/p>\n<p>\u5347\u5e8f\u7684\u7248\u672c\u7b97\u6cd5\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Solution<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> tmp<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">reversePairs<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n tmp <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">return<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> n <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> left<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&gt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">int<\/span> ret <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ 1. \u9009\u62e9\u2f00\u4e2a\u4e2d\u95f4\u70b9&#xff0c;\u5c06\u6570\u7ec4\u5212\u5206\u6210\u4e24\u90e8\u5206<\/span><br \/>\n <span class=\"token keyword\">int<\/span> mid <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&#043;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ [left, mid] [mid &#043; 1, right]<\/span><br \/>\n <span class=\"token comment\">\/\/ 2. \u5de6\u534a\u90e8\u5206\u7684\u4e2a\u6570 &#043; \u6392\u5e8f &#043; \u53f3\u534a\u90e8\u5206\u7684\u4e2a\u6570 &#043; \u6392\u5e8f<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> left<span class=\"token punctuation\">,<\/span> mid<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ 3. \u2f00\u5de6\u2f00\u53f3\u7684\u4e2a\u6570<\/span><br \/>\n <span class=\"token keyword\">int<\/span> cur1 <span class=\"token operator\">&#061;<\/span> left<span class=\"token punctuation\">,<\/span> cur2 <span class=\"token operator\">&#061;<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid <span class=\"token operator\">&amp;&amp;<\/span> cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> <span class=\"token comment\">\/\/ \u5347\u5e8f\u7248\u672c<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">else<\/span><span class=\"token punctuation\">{<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> mid <span class=\"token operator\">&#8211;<\/span> cur1 <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token operator\">&#043;&#043;<\/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><br \/>\n <span class=\"token comment\">\/\/ 4. \u5904\u7406\u2f00\u4e0b\u6392\u5e8f<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid<span class=\"token punctuation\">)<\/span> tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<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> left<span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> tmp<span class=\"token punctuation\">[<\/span>j <span class=\"token operator\">&#8211;<\/span> left<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p> <span class=\"token keyword\">return<\/span> ret<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>\u964d\u5e8f\u7684\u7248\u672c\u7b97\u6cd5\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Solution<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> tmp<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">reversePairs<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n tmp <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">return<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> n <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> left<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&gt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">int<\/span> ret <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ 1. \u9009\u62e9\u2f00\u4e2a\u4e2d\u95f4\u70b9&#xff0c;\u5c06\u6570\u7ec4\u5212\u5206\u6210\u4e24\u90e8\u5206<\/span><br \/>\n <span class=\"token keyword\">int<\/span> mid <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&#043;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ [left, mid] [mid &#043; 1, right]<\/span><br \/>\n <span class=\"token comment\">\/\/ 2. \u5de6\u534a\u90e8\u5206\u7684\u4e2a\u6570 &#043; \u6392\u5e8f &#043; \u53f3\u534a\u90e8\u5206\u7684\u4e2a\u6570 &#043; \u6392\u5e8f<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> left<span class=\"token punctuation\">,<\/span> mid<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ 3. \u2f00\u5de6\u2f00\u53f3\u7684\u4e2a\u6570<\/span><br \/>\n <span class=\"token keyword\">int<\/span> cur1 <span class=\"token operator\">&#061;<\/span> left<span class=\"token punctuation\">,<\/span> cur2 <span class=\"token operator\">&#061;<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid <span class=\"token operator\">&amp;&amp;<\/span> cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> <span class=\"token comment\">\/\/ \u964d\u5e8f\u7684\u7248\u672c<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><span class=\"token keyword\">else<\/span><span class=\"token punctuation\">{<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> right <span class=\"token operator\">&#8211;<\/span> cur2 <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/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><br \/>\n <span class=\"token comment\">\/\/ 4. \u5904\u7406\u2f00\u4e0b\u6392\u5e8f<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid<span class=\"token punctuation\">)<\/span> tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<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> left<span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> tmp<span class=\"token punctuation\">[<\/span>j <span class=\"token operator\">&#8211;<\/span> left<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p> <span class=\"token keyword\">return<\/span> ret<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h3>3.\u8ba1\u7b97\u53f3\u4fa7\u2f29\u4e8e\u5f53\u524d\u5143\u7d20\u7684\u4e2a\u6570&#xff08;hard&#xff09;<\/h3>\n<p>\u9898\u2f6c\u94fe\u63a5&#xff1a;315. \u8ba1\u7b97\u53f3\u4fa7\u2f29\u4e8e\u5f53\u524d\u5143\u7d20\u7684\u4e2a\u6570 \u9898\u2f6c\u63cf\u8ff0&#xff1a;<\/p>\n<p>\u7ed9\u4f60\u2f00\u4e2a\u6574\u6570\u6570\u7ec4 nums &#xff0c;\u6309\u8981\u6c42\u8fd4\u56de\u2f00\u4e2a\u65b0\u6570\u7ec4 counts \u3002\u6570\u7ec4 counts \u6709\u8be5\u6027\u8d28&#xff1a; counts[i] \u7684\u503c\u662f nums[i] \u53f3\u4fa7\u2f29\u4e8e nums[i] \u7684\u5143\u7d20\u7684\u6570\u91cf\u3002 \u2f70\u4f8b 1&#xff1a; \u8f93\u2f0a&#xff1a;nums &#061; [5,2,6,1] \u8f93\u51fa&#xff1a;[2,1,1,0] \u89e3\u91ca&#xff1a; 5 \u7684\u53f3\u4fa7\u6709 2 \u4e2a\u66f4\u2f29\u7684\u5143\u7d20 (2 \u548c 1) 2 \u7684\u53f3\u4fa7\u4ec5\u6709 1 \u4e2a\u66f4\u2f29\u7684\u5143\u7d20 (1) 6 \u7684\u53f3\u4fa7\u6709 1 \u4e2a\u66f4\u2f29\u7684\u5143\u7d20 (1) 1 \u7684\u53f3\u4fa7\u6709 0 \u4e2a\u66f4\u2f29\u7684\u5143\u7d20<\/p>\n<p>\u89e3\u6cd5&#xff08;\u5f52\u5e76\u6392\u5e8f&#xff09;&#xff1a; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815154218-689f555a7b5d6.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u7b97\u6cd5\u601d\u8def&#xff1a; \u8fd9\u2f00\u9053\u9898\u7684\u89e3\u6cd5\u4e0e \u6c42\u6570\u7ec4\u4e2d\u7684\u9006\u5e8f\u5bf9 \u7684\u89e3\u6cd5\u662f\u7c7b\u4f3c\u7684&#xff0c;\u4f46\u662f\u8fd9\u2f00\u9053\u9898\u8981\u6c42\u7684\u4e0d\u662f\u6c42\u603b\u7684\u4e2a\u6570&#xff0c;\u2f7d\u662f\u8981\u8fd4\u56de\u2f00\u4e2a\u6570\u7ec4&#xff0c;\u8bb0\u5f55\u6bcf\u2f00\u4e2a\u5143\u7d20\u7684\u53f3\u8fb9\u6709\u591a\u5c11\u4e2a\u5143\u7d20\u2f50\u2f83\u2f30\u2f29\u3002\u4f46\u662f\u5728\u6211\u4eec\u5f52\u5e76\u6392\u5e8f\u7684\u8fc7\u7a0b\u4e2d&#xff0c;\u5143\u7d20\u7684\u4e0b\u6807\u662f\u4f1a\u8ddf\u7740\u53d8\u5316\u7684&#xff0c;\u56e0\u6b64\u6211\u4eec\u9700\u8981\u2f00\u4e2a\u8f85\u52a9\u6570\u7ec4&#xff0c;\u6765\u5c06\u6570\u7ec4\u5143\u7d20\u548c\u5bf9\u5e94\u7684\u4e0b\u6807\u7ed1\u5b9a\u5728\u2f00\u8d77\u5f52\u5e76&#xff0c;\u4e5f\u5c31\u662f\u518d\u5f52\u5e76\u5143\u7d20\u7684\u65f6\u5019&#xff0c;\u987a\u52bf\u5c06\u4e0b\u6807\u4e5f\u8f6c\u79fb\u5230\u5bf9\u5e94\u7684\u4f4d\u7f6e\u4e0a\u3002 \u7531\u4e8e\u6211\u4eec\u8981\u5feb\u901f\u7edf\u8ba1\u51fa\u67d0\u2f00\u4e2a\u5143\u7d20\u540e\u2faf\u6709\u591a\u5c11\u4e2a\u2f50\u5b83\u2f29\u7684&#xff0c;\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5229\u2f64\u6c42\u9006\u5e8f\u5bf9\u7684\u7b2c\u2f06\u79cd\u2f45\u6cd5\u3002 \u7b97\u6cd5\u6d41\u7a0b&#xff1a;<\/p>\n<ul>\n<li>\u521b\u5efa\u4e24\u4e2a\u5168\u5c40\u7684\u6570\u7ec4&#xff1a; vector index&#xff1a;\u8bb0\u5f55\u4e0b\u6807 vector ret&#xff1a;\u8bb0\u5f55\u7ed3\u679c index \u2f64\u6765\u4e0e\u539f\u6570\u7ec4\u4e2d\u5bf9\u5e94\u4f4d\u7f6e\u7684\u5143\u7d20\u7ed1\u5b9a&#xff0c;ret \u2f64\u6765\u8bb0\u5f55\u6bcf\u4e2a\u4f4d\u7f6e\u7edf\u8ba1\u51fa\u6765\u7684\u9006\u5e8f\u5bf9\u7684\u4e2a\u6570\u3002<\/li>\n<li>countSmaller() \u4e3b\u51fd\u6570&#xff1a; a. \u8ba1\u7b97 nums \u6570\u7ec4\u7684\u2f24\u2f29\u4e3a n&#xff1b; b. \u521d\u59cb\u5316\u5b9a\u4e49\u7684\u4e24\u4e2a\u5168\u5c40\u7684\u6570\u7ec4&#xff1b; i. \u4e3a\u4e24\u4e2a\u6570\u7ec4\u5f00\u8f9f\u2f24\u2f29\u4e3a n \u7684\u7a7a\u95f4 ii. index \u521d\u59cb\u5316\u4e3a\u6570\u7ec4\u4e0b\u6807&#xff1b; iii. ret \u521d\u59cb\u5316\u4e3a 0 c. \u8c03\u2f64 mergeSort() \u51fd\u6570&#xff0c;\u5e76\u4e14\u8fd4\u56de ret \u7ed3\u679c\u6570\u7ec4\u3002<\/li>\n<li>void mergeSort( vector&amp; nums, int left, int right ) \u51fd\u6570&#xff1a; \u51fd\u6570\u8bbe\u8ba1&#xff1a;\u901a\u8fc7\u4fee\u6539\u5168\u5c40\u7684\u6570\u7ec4 ret&#xff0c; \u7edf\u8ba1\u51fa\u6bcf\u2f00\u4e2a\u4f4d\u7f6e\u5bf9\u5e94\u7684\u9006\u5e8f\u5bf9\u7684\u6570\u91cf&#xff0c;\u5e76\u4e14\u6392\u5e8f&#xff1b; \u2f46\u9700\u8fd4\u56de\u503c&#xff0c;\u56e0\u4e3a\u76f4\u63a5\u5bf9\u5168\u5c40\u53d8\u91cf\u4fee\u6539&#xff0c;\u5f53\u51fd\u6570\u7ed3\u675f\u7684\u65f6\u5019&#xff0c;\u5168\u5c40\u53d8\u91cf\u5df2\u7ecf\u88ab\u4fee\u6539\u6210\u6700\u540e\u7684\u7ed3\u679c\u3002<\/li>\n<li>mergeSort() \u51fd\u6570\u6d41\u7a0b&#xff1a; a. \u5b9a\u4e49\u9012\u5f52\u51fa\u2f1d&#xff1a;left &gt;&#061; right \u65f6&#xff0c;\u76f4\u63a5\u8fd4\u56de&#xff1b; b. \u5212\u5206\u533a\u95f4&#xff1a;\u6839\u636e\u4e2d\u70b9 mid&#xff0c;\u5c06\u533a\u95f4\u5212\u5206\u4e3a [left, mid] \u548c [mid &#043; 1, right]&#xff1b; c. \u7edf\u8ba1\u5de6\u53f3\u4e24\u4e2a\u533a\u95f4\u9006\u5e8f\u5bf9\u7684\u6570\u91cf&#xff1a; &#xff08;1&#xff09;i. \u7edf\u8ba1\u5de6\u8fb9\u533a\u95f4 [left, mid] \u4e2d\u6bcf\u4e2a\u5143\u7d20\u5bf9\u5e94\u7684\u9006\u5e8f\u5bf9\u7684\u6570\u91cf\u5230 ret \u6570\u7ec4\u4e2d&#xff0c;\u5e76\u6392\u5e8f&#xff1b; &#xff08;2&#xff09;ii. \u7edf\u8ba1\u53f3\u8fb9\u533a\u95f4 [mid &#043; 1, right] \u4e2d\u6bcf\u4e2a\u5143\u7d20\u5bf9\u5e94\u7684\u9006\u5e8f\u5bf9\u7684\u6570\u91cf\u5230 ret \u6570\u7ec4\u4e2d&#xff0c;\u5e76\u6392\u5e8f\u3002 d. \u5408\u5e76\u5de6\u53f3\u4e24\u4e2a\u6709\u5e8f\u533a\u95f4&#xff0c;\u5e76\u4e14\u7edf\u8ba1\u51fa\u9006\u5e8f\u5bf9\u7684\u6570\u91cf&#xff1a; &#xff08;1&#xff09;i. \u521b\u5efa\u4e24\u4e2a\u2f24\u2f29\u4e3a right &#8211; left &#043; 1 \u2f24\u2f29\u7684\u8f85\u52a9\u6570\u7ec4&#xff1a; \u2022 numsTmp&#xff1a; \u6392\u5e8f\u2f64\u7684\u8f85\u52a9\u6570\u7ec4&#xff1b; \u2022 indexTmp&#xff1a;\u5904\u7406\u4e0b\u6807\u2f64\u7684\u8f85\u52a9\u6570\u7ec4\u3002 &#xff08;2&#xff09;ii. \u521d\u59cb\u5316\u904d\u5386\u6570\u7ec4\u7684\u6307\u9488&#xff1a;cur1 &#061; left&#xff08;\u904d\u5386\u5de6\u534a\u90e8\u5206\u6570\u7ec4&#xff09;cur2 &#061; mid &#043; 1&#xff08;\u904d\u5386\u53f3\u534a\u8fb9\u6570\u7ec4&#xff09;dest &#061; 0&#xff08;\u904d\u5386\u8f85\u52a9\u6570\u7ec4&#xff09;curRet&#xff08;\u8bb0\u5f55\u5408\u5e76\u65f6\u4ea7\u2f63\u7684\u9006\u5e8f\u5bf9\u7684\u6570\u91cf&#xff09;&#xff1b; &#xff08;3&#xff09;iii. \u5faa\u73af\u5408\u5e76\u533a\u95f4&#xff1a; \u2022 \u5f53 nums[cur1] &lt;&#061; nums[cur2] \u65f6&#xff1a; \u25e6 \u8bf4\u660e\u6b64\u65f6 [mid &#043; 1, cur2) \u4e4b\u95f4\u7684\u5143\u7d20\u90fd\u662f\u2f29\u4e8e nums[cur1] \u7684&#xff0c;\u9700\u8981\u7d2f\u52a0\u5230 ret \u6570\u7ec4\u7684 indext[cur1] \u4f4d\u7f6e\u4e0a&#xff08;\u56e0\u4e3a index \u5b58\u50a8\u7684\u662f\u5143\u7d20\u5bf9\u5e94\u4f4d\u7f6e\u5728\u539f\u6570\u7ec4\u4e2d\u7684\u4e0b\u6807&#xff09; \u25e6 \u5f52\u5e76\u6392\u5e8f&#xff1a;\u4e0d\u4ec5\u8981\u5c06\u6570\u636e\u653e\u5728\u5bf9\u5e94\u7684\u4f4d\u7f6e\u4e0a&#xff0c;\u4e5f\u8981\u5c06\u6570\u636e\u5bf9\u5e94\u7684\u5750\u6807\u4e5f\u653e\u5728\u5bf9\u5e94\u7684\u4f4d\u7f6e\u4e0a&#xff0c;\u4f7f\u6570\u636e\u4e0e\u539f\u59cb\u7684\u4e0b\u6807\u7ed1\u5b9a\u5728\u2f00\u8d77\u79fb\u52a8\u3002 \u2022 \u5f53 nums[cur1] &gt; nums[cur2] \u65f6&#xff0c;\u2f46\u9700\u7edf\u8ba1&#xff0c;\u76f4\u63a5\u5f52\u5e76&#xff0c;\u6ce8\u610f index \u4e5f\u8981\u8ddf\u7740\u5f52\u5e76\u3002 &#xff08;4&#xff09;iv. \u5904\u7406\u5f52\u5e76\u6392\u5e8f\u4e2d\u5269\u4f59\u7684\u5143\u7d20&#xff1b; \u2022 \u5f53\u5de6\u8fb9\u6709\u5269\u4f59\u7684\u65f6\u5019&#xff0c;\u8fd8\u9700\u8981\u7edf\u8ba1\u9006\u5e8f\u5bf9\u7684\u6570\u91cf&#xff1b; \u2022 \u5f53\u53f3\u8fb9\u8fd8\u6709\u5269\u4f59\u7684\u65f6\u5019&#xff0c;\u2f46\u9700\u7edf\u8ba1&#xff0c;\u76f4\u63a5\u5f52\u5e76\u3002 &#xff08;5&#xff09;v. \u5c06\u8f85\u52a9\u6570\u7ec4\u7684\u5185\u5bb9\u66ff\u6362\u5230\u539f\u6570\u7ec4\u4e2d\u53bb&#xff1b;<\/li>\n<\/ul>\n<p>Java \u7b97\u6cd5\u4ee3\u7801&#xff1a;<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Solution<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> ret<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> index<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u6807\u8bb0 nums \u4e2d\u5f53\u524d\u5143\u7d20\u7684\u539f\u59cb\u4e0b\u6807<\/span><br \/>\n <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> tmpIndex<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> tmpNums<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token class-name\">List<\/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> <span class=\"token function\">countSmaller<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n ret <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n index <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n tmpIndex <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n tmpNums <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ \u521d\u59cb\u5316 index \u6570\u7ec4<\/span><br \/>\n <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n index<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> n <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token class-name\">List<\/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> l <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token class-name\">ArrayList<\/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><span class=\"token punctuation\">(<\/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> x <span class=\"token operator\">:<\/span> ret<span class=\"token punctuation\">)<\/span><br \/>\n l<span class=\"token punctuation\">.<\/span><span class=\"token function\">add<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">return<\/span> l<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">void<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> left<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&gt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ 1. \u6839\u636e\u4e2d\u95f4\u5143\u7d20\u5212\u5206\u533a\u95f4<\/span><br \/>\n <span class=\"token keyword\">int<\/span> mid <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&#043;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ [left, mid] [mid &#043; 1, right]<\/span><br \/>\n <span class=\"token comment\">\/\/ 2. \u5904\u7406\u5de6\u53f3\u4e24\u4e2a\u533a\u95f4<\/span><br \/>\n <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> left<span class=\"token punctuation\">,<\/span> mid<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ 3. \u5904\u7406\u2f00\u5de6\u2f00\u53f3\u7684\u60c5\u51b5<\/span><br \/>\n <span class=\"token keyword\">int<\/span> cur1 <span class=\"token operator\">&#061;<\/span> left<span class=\"token punctuation\">,<\/span> cur2 <span class=\"token operator\">&#061;<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid <span class=\"token operator\">&amp;&amp;<\/span> cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> <span class=\"token comment\">\/\/ \u964d\u5e8f\u6392\u5e8f<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n tmpNums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n tmpIndex<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> index<span class=\"token punctuation\">[<\/span>cur2<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><span class=\"token keyword\">else<\/span><span class=\"token punctuation\">{<\/span><br \/>\n ret<span class=\"token punctuation\">[<\/span>index<span class=\"token punctuation\">[<\/span>cur1<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;&#061;<\/span> right <span class=\"token operator\">&#8211;<\/span> cur2 <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u91cd\u70b9<\/span><br \/>\n tmpNums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n tmpIndex<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> index<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/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><br \/>\n <span class=\"token comment\">\/\/ 4. \u5904\u7406\u5269\u4f59\u7684\u6392\u5e8f\u2f2f\u4f5c<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n tmpNums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n tmpIndex<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> index<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n tmpNums<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n tmpIndex<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> index<span class=\"token punctuation\">[<\/span>cur2<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <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> left<span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;&#061;<\/span> right<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 nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> tmpNums<span class=\"token punctuation\">[<\/span>j <span class=\"token operator\">&#8211;<\/span> left<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n index<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> tmpIndex<span class=\"token punctuation\">[<\/span>j <span class=\"token operator\">&#8211;<\/span> left<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h3>4.\u7ffb\u8f6c\u5bf9&#xff08;hard&#xff09;<\/h3>\n<p>\u9898\u2f6c\u94fe\u63a5&#xff1a;493. \u7ffb\u8f6c\u5bf9 \u9898\u2f6c\u63cf\u8ff0&#xff1a;<\/p>\n<p>\u7ed9\u5b9a\u2f00\u4e2a\u6570\u7ec4 nums &#xff0c;\u5982\u679c i &lt; j \u4e14 nums[i] &gt; 2*nums[j] \u6211\u4eec\u5c31\u5c06 (i, j) \u79f0\u4f5c\u2f00\u4e2a\u91cd\u8981\u7ffb\u8f6c\u5bf9\u3002\u4f60\u9700\u8981 \u8fd4\u56de\u7ed9\u5b9a\u6570\u7ec4\u4e2d\u7684\u91cd\u8981\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf\u3002 \u2f70\u4f8b 1: \u8f93\u2f0a: [1,3,2,3,1] \u8f93\u51fa: 2<\/p>\n<p>\u9898\u2f6c\u89e3\u6790&#xff1a; \u7ffb\u8f6c\u5bf9\u548c\u9006\u5e8f\u5bf9\u7684\u5b9a\u4e49\u2f24\u540c\u2f29\u5f02&#xff0c;\u9006\u5e8f\u5bf9\u662f\u524d\u2faf\u7684\u6570\u8981\u2f24\u4e8e\u540e\u2faf\u7684\u6570\u3002\u2f7d\u7ffb\u8f6c\u5bf9\u662f\u524d\u2faf\u7684\u2f00\u4e2a\u6570\u8981 \u2f24\u4e8e\u540e\u2faf\u67d0\u4e2a\u6570\u7684\u4e24\u500d\u3002\u56e0\u6b64&#xff0c;\u6211\u4eec\u4f9d\u65e7\u53ef\u4ee5\u2f64\u5f52\u5e76\u6392\u5e8f\u7684\u601d\u60f3\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002<\/p>\n<p>\u89e3\u6cd5&#xff08;\u5f52\u5e76\u6392\u5e8f&#xff09;&#xff1a; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250815154229-689f55657db73.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u7b97\u6cd5\u601d\u8def&#xff1a; \u2f24\u601d\u8def\u4e0e\u6c42\u9006\u5e8f\u5bf9\u7684\u601d\u8def\u2f00\u6837&#xff0c;\u5c31\u662f\u5229\u2f64\u5f52\u5e76\u6392\u5e8f\u7684\u601d\u60f3&#xff0c;\u5c06\u6c42\u6574\u4e2a\u6570\u7ec4\u7684\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf&#xff0c;\u8f6c\u6362\u6210\u4e09\u90e8\u5206&#xff1a;\u5de6\u534a\u533a\u95f4\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf&#xff0c;\u53f3\u534a\u533a\u95f4\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf&#xff0c;\u2f00\u5de6\u2f00\u53f3\u9009\u62e9\u65f6\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf\u3002\u91cd\u70b9\u5c31\u662f\u5728\u5408\u5e76\u533a\u95f4\u8fc7\u7a0b\u4e2d&#xff0c;\u5982\u4f55\u8ba1\u7b97\u51fa\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf\u3002 \u4e0e\u4e0a\u4e2a\u95ee\u9898\u4e0d\u540c\u7684\u662f&#xff0c;\u4e0a\u2f00\u9053\u9898\u6211\u4eec\u53ef\u4ee5\u2f00\u8fb9\u5408\u5e76\u2f00\u904d\u8ba1\u7b97&#xff0c;\u4f46\u662f\u8fd9\u9053\u9898\u8981\u6c42\u7684\u662f\u5de6\u8fb9\u5143\u7d20\u2f24\u4e8e\u53f3\u8fb9\u5143\u7d20\u7684\u4e24\u500d&#xff0c;\u5982\u679c\u6211\u4eec\u76f4\u63a5\u5408\u5e76\u7684\u8bdd&#xff0c;\u662f\u2f46\u6cd5\u5feb\u901f\u8ba1\u7b97\u51fa\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf\u7684\u3002 \u4f8b\u5982 left &#061; [4, 5, 6] right &#061; [3, 4, 5] \u65f6&#xff0c;\u5982\u679c\u662f\u5f52\u5e76\u6392\u5e8f\u7684\u8bdd&#xff0c;\u6211\u4eec\u9700\u8981\u8ba1\u7b97 left \u6570\u7ec4\u4e2d\u6709\u591a\u5c11\u4e2a\u80fd\u4e0e 3 \u7ec4\u6210\u7ffb\u8f6c\u5bf9\u3002\u4f46\u662f\u6211\u4eec\u8981\u904d\u5386\u5230\u6700\u540e\u2f00\u4e2a\u5143\u7d20 6 \u624d\u80fd\u786e\u5b9a&#xff0c;\u65f6\u95f4\u590d\u6742\u5ea6\u8f83\u2fbc\u3002 \u56e0\u6b64\u6211\u4eec\u9700\u8981\u5728\u5f52\u5e76\u6392\u5e8f\u4e4b\u524d\u5b8c\u6210\u7ffb\u8f6c\u5bf9\u7684\u7edf\u8ba1\u3002 \u4e0b\u2faf\u4f9d\u65e7\u4ee5\u2f00\u4e2a\u2f70\u4f8b\u6765\u6a21\u4eff\u4e24\u4e2a\u6709\u5e8f\u5e8f\u5217\u5982\u4f55\u5feb\u901f\u6c42\u51fa\u7ffb\u8f6c\u5bf9\u7684\u8fc7\u7a0b&#xff1a; \u5047\u5b9a\u5df2\u7ecf\u6709\u4e24\u4e2a\u5df2\u7ecf\u6709\u5e8f\u7684\u5e8f\u5217 left &#061; [4, 5, 6] right &#061; [1, 2, 3] \u3002 \u2f64\u4e24\u4e2a\u6307\u9488 cur1 cur2 \u904d\u5386\u4e24\u4e2a\u6570\u7ec4\u3002 \u25e6 \u5bf9\u4e8e\u4efb\u610f\u7ed9\u5b9a\u7684 left[cur1] \u2f7d\u2f94&#xff0c;\u6211\u4eec\u4e0d\u65ad\u5730\u5411\u53f3\u79fb\u52a8 cur2&#xff0c;\u76f4\u5230 left[cur1] &lt;&#061; 2 *right[cur2]\u3002\u6b64\u65f6\u5bf9\u4e8e right \u6570\u7ec4\u2f7d\u2f94&#xff0c;cur2 \u4e4b\u524d\u7684\u5143\u7d20\u5168\u90e8\u90fd\u53ef\u4ee5\u4e0e left[cur1] \u6784\u6210\u7ffb\u8f6c\u5bf9\u3002 \u25e6 \u968f\u540e&#xff0c;\u6211\u4eec\u518d\u5c06 cur1 \u5411\u53f3\u79fb\u52a8\u2f00\u4e2a\u5355\u4f4d&#xff0c;\u6b64\u65f6 cur2 \u6307\u9488\u5e76\u4e0d\u9700\u8981\u56de\u9000&#xff08;\u56e0\u4e3a left \u6570\u7ec4\u662f\u5347\u5e8f\u7684&#xff09;\u4f9d\u65e7\u5f80\u53f3\u79fb\u52a8\u76f4\u5230 left[cur1] &lt;&#061; 2 * right[cur2]\u3002\u4e0d\u65ad\u91cd\u590d\u8fd9\u6837\u7684\u8fc7\u7a0b&#xff0c;\u5c31\u80fd\u591f\u6c42\u51fa\u6240\u6709\u5de6\u53f3\u7aef\u70b9\u5206\u522b\u4f4d\u4e8e\u4e24\u4e2a\u2f26\u6570\u7ec4\u7684\u7ffb\u8f6c\u5bf9\u6570\u2f6c\u3002<\/p>\n<p>\u7531\u4e8e\u4e24\u4e2a\u6307\u9488\u6700\u540e\u90fd\u662f\u4e0d\u56de\u9000\u7684\u7684\u626b\u63cf\u5230\u6570\u7ec4\u7684\u7ed3\u5c3e&#xff0c;\u56e0\u6b64\u4e24\u4e2a\u6709\u5e8f\u5e8f\u5217\u6c42\u51fa\u7ffb\u8f6c\u5bf9\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f O(N)\u3002 \u7efc\u4e0a\u6240\u8ff0&#xff0c;\u6211\u4eec\u53ef\u4ee5\u5229\u2f64\u5f52\u5e76\u6392\u5e8f\u7684\u8fc7\u7a0b&#xff0c;\u5c06\u6c42\u2f00\u4e2a\u6570\u7ec4\u7684\u7ffb\u8f6c\u5bf9\u8f6c\u6362\u6210\u6c42 \u5de6\u6570\u7ec4\u7684\u7ffb\u8f6c\u5bf9\u6570\u91cf &#043;\u53f3\u6570\u7ec4\u4e2d\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf &#043; \u5de6\u53f3\u6570\u7ec4\u5408\u5e76\u65f6\u7ffb\u8f6c\u5bf9\u7684\u6570\u91cf\u3002<\/p>\n<p>\u7b97\u6cd5\u4ee3\u7801&#xff1a; \u964d\u5e8f\u7248\u672c<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Solution<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> tmp<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">reversePairs<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n tmp <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">return<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> n <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> left<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&gt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">int<\/span> ret <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ 1. \u6839\u636e\u4e2d\u95f4\u5143\u7d20&#xff0c;\u5c06\u533a\u95f4\u5206\u6210\u4e24\u90e8\u5206<\/span><br \/>\n <span class=\"token keyword\">int<\/span> mid <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&#043;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ [left, mid] [mid &#043; 1, right]<\/span><\/p>\n<p> <span class=\"token comment\">\/\/ 2. \u6c42\u51fa\u5de6\u53f3\u4e24\u4e2a\u533a\u95f4\u7684\u7ffb\u8f6c\u5bf9<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> left<span class=\"token punctuation\">,<\/span> mid<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p> <span class=\"token comment\">\/\/ 3. \u5904\u7406\u2f00\u5de6\u2f00\u53f3 &#8211; \u5148\u8ba1\u7b97\u7ffb\u8f6c\u5bf9<\/span><br \/>\n <span class=\"token keyword\">int<\/span> cur1 <span class=\"token operator\">&#061;<\/span> left<span class=\"token punctuation\">,<\/span> cur2 <span class=\"token operator\">&#061;<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> i <span class=\"token operator\">&#061;<\/span> left<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ \u964d\u5e8f\u7248\u672c<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur2 <span class=\"token operator\">&lt;&#061;<\/span> right <span class=\"token operator\">&amp;&amp;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&gt;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">)<\/span> cur2<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>cur2 <span class=\"token operator\">&gt;<\/span> right<span class=\"token punctuation\">)<\/span><br \/>\n <span class=\"token keyword\">break<\/span><span class=\"token punctuation\">;<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> right <span class=\"token operator\">&#8211;<\/span> cur2 <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><\/p>\n<p> <span class=\"token comment\">\/\/ 4. \u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4<\/span><br \/>\n cur1 <span class=\"token operator\">&#061;<\/span> left<span class=\"token punctuation\">;<\/span> cur2 <span class=\"token operator\">&#061;<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid <span class=\"token operator\">&amp;&amp;<\/span> cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span><br \/>\n tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">?<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">:<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid<span class=\"token punctuation\">)<\/span> tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<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> left<span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n nums<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> tmp<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p> <span class=\"token keyword\">return<\/span> ret<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>\u5347\u5e8f\u7248\u672c<\/p>\n<p><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Solution<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> tmp<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">reversePairs<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">.<\/span>length<span class=\"token punctuation\">;<\/span><br \/>\n tmp <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">return<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> n <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><br \/>\n <span class=\"token keyword\">public<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> nums<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> left<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&gt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">int<\/span> ret <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p> <span class=\"token comment\">\/\/ 1. \u6839\u636e\u4e2d\u95f4\u5143\u7d20&#xff0c;\u5c06\u533a\u95f4\u5206\u6210\u4e24\u90e8\u5206<\/span><br \/>\n <span class=\"token keyword\">int<\/span> mid <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>left <span class=\"token operator\">&#043;<\/span> right<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ [left, mid] [mid &#043; 1, right]<\/span><\/p>\n<p> <span class=\"token comment\">\/\/ 2. \u6c42\u51fa\u5de6\u53f3\u4e24\u4e2a\u533a\u95f4\u7684\u7ffb\u8f6c\u5bf9<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> left<span class=\"token punctuation\">,<\/span> mid<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> <span class=\"token function\">mergeSort<\/span><span class=\"token punctuation\">(<\/span>nums<span class=\"token punctuation\">,<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p> <span class=\"token comment\">\/\/ 3. \u5904\u7406\u2f00\u5de6\u2f00\u53f3 &#8211; \u5148\u8ba1\u7b97\u7ffb\u8f6c\u5bf9<\/span><br \/>\n <span class=\"token keyword\">int<\/span> cur1 <span class=\"token operator\">&#061;<\/span> left<span class=\"token punctuation\">,<\/span> cur2 <span class=\"token operator\">&#061;<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> i <span class=\"token operator\">&#061;<\/span> left<span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token comment\">\/\/ \u5347\u5e8f\u7248\u672c<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span><br \/>\n <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid <span class=\"token operator\">&amp;&amp;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&gt;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">)<\/span> cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&gt;<\/span> mid<span class=\"token punctuation\">)<\/span><br \/>\n <span class=\"token keyword\">break<\/span><span class=\"token punctuation\">;<\/span><br \/>\n ret <span class=\"token operator\">&#043;&#061;<\/span> mid <span class=\"token operator\">&#8211;<\/span> cur1 <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n cur2<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n <span class=\"token punctuation\">}<\/span><\/p>\n<p> <span class=\"token comment\">\/\/ 4. \u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4 &#8211; \u5347\u5e8f<\/span><br \/>\ncur1 <span class=\"token operator\">&#061;<\/span> left<span class=\"token punctuation\">;<\/span> cur2 <span class=\"token operator\">&#061;<\/span> mid <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid <span class=\"token operator\">&amp;&amp;<\/span> cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span><br \/>\ntmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">?<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">:<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur1 <span class=\"token operator\">&lt;&#061;<\/span> mid<span class=\"token punctuation\">)<\/span> tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur1<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>cur2 <span class=\"token operator\">&lt;&#061;<\/span> right<span class=\"token punctuation\">)<\/span> tmp<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> nums<span class=\"token punctuation\">[<\/span>cur2<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span 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