{"id":249,"date":"2020-02-01T04:53:12","date_gmt":"2020-01-31T20:53:12","guid":{"rendered":"https:\/\/twocups.cn\/?p=249"},"modified":"2021-03-21T18:17:49","modified_gmt":"2021-03-21T10:17:49","slug":"17","status":"publish","type":"post","link":"https:\/\/twocups.cn\/index.php\/2020\/02\/01\/17\/","title":{"rendered":"\u3010\u7b97\u6cd5\u3011\u5341\u5927\u6392\u5e8f\u7b97\u6cd5\u603b\u7ed3\uff08Java\u4ee3\u7801\u5b9e\u73b0\uff09"},"content":{"rendered":"\n<h4><img width=\"80\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2019\/12\/logo\u6a2a.png\" alt=\"\" class=\"wp-image-152\" srcset=\"https:\/\/twocups.cn\/wp-content\/uploads\/2019\/12\/logo\u6a2a.png 3337w, https:\/\/twocups.cn\/wp-content\/uploads\/2019\/12\/logo\u6a2a-300x125.png 300w, https:\/\/twocups.cn\/wp-content\/uploads\/2019\/12\/logo\u6a2a-1024x426.png 1024w, https:\/\/twocups.cn\/wp-content\/uploads\/2019\/12\/logo\u6a2a-768x320.png 768w, https:\/\/twocups.cn\/wp-content\/uploads\/2019\/12\/logo\u6a2a-1536x639.png 1536w, https:\/\/twocups.cn\/wp-content\/uploads\/2019\/12\/logo\u6a2a-2048x852.png 2048w\" sizes=\"(max-width: 3337px) 100vw, 3337px\" \/>\u7248\u6743\u58f0\u660e\uff1a\u672c\u6587\u4e3a\u535a\u4e3b\u539f\u521b\u6587\u7ae0\uff0c\u8f6c\u8f7d\u8bf7\u6ce8\u660e\u51fa\u5904\uff1a<a href=\"https:\/\/twocups.cn\/index.php\/2020\/02\/01\/17\/\">https:\/\/twocups.cn\/index.php\/2020\/02\/01\/17\/<\/a><\/h4>\n\n\n\n<p>\u6700\u8fd1\u9047\u5230\u4e86\u4e00\u4e2a\u6392\u5e8f\u95ee\u9898\uff0c\u5374\u53d1\u73b0\u81ea\u5df1\u5341\u5927\u7ecf\u5178\u6392\u5e8f\u7b97\u6cd5\u8bb0\u4e0d\u6e05\u4e86\u3002\u6211\u672c\u6765\u4ee5\u4e3a\u5341\u5927\u6392\u5e8f\u7b97\u6cd5\u8fd9\u4e48\u7ecf\u5178\u7684\u4e1c\u897f\uff0c\u7f51\u4e0a\u80af\u5b9a\u4f1a\u6709\u542b\u6709\u6d4b\u8bd5\u7684 Java \u4ee3\u7801\u5b9e\u73b0\uff0c\u5e94\u8be5\u5f88\u5bb9\u6613\u5c31\u80fd\u627e\u5230\u3002\u4e0d\u8fc7\u51fa\u4e4e\u610f\u6599\u7684\u662f\uff0c\u73b0\u5728\u7684\u8fd9\u4e9b\u80fd\u6c47\u96c6\u5168\u90e8\u6392\u5e8f\u7b97\u6cd5\u7684\u603b\u7ed3\u7bc7\u90fd\u6216\u591a\u6216\u5c11\u7684\u6709\u70b9\u95ee\u9898\u3002\u6240\u4ee5\u6211\u8fd8\u662f\u81ea\u5df1\u5168\u90e8\u5199\u4e00\u904d\uff0c\u6b63\u597d\u590d\u4e60\u4e00\u4e0b\u3002\u4ee3\u7801\u5728\u7ed3\u5c3e\uff0c\u5e76\u4e14\u5305\u542b\u6d4b\u8bd5\u7528\u4f8b\u3002<\/p>\n\n\n\n<p>\u8fd9\u7bc7\u535a\u5ba2\u4e2d\u6240\u63d0\u5230\u7684\u6240\u6709\u6392\u5e8f\u7b97\u6cd5\u5747\u4ee5\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\u4e3a\u4f8b\uff0c\u5176\u4ed6\u60c5\u51b5\u8bf7\u81ea\u884c\u7c7b\u6bd4\u3002\u672c\u6587\u53ea\u9002\u5408\u5df2\u7ecf\u5b66\u8fc7\u6392\u5e8f\u5e76\u60f3\u518d\u56de\u987e\u4e00\u904d\u7684\u4eba\uff0c\u5f88\u591a\u5730\u65b9\u53ea\u662f\u63d0\u4e00\u4e0b\u6392\u5e8f\u7684\u601d\u8def\u3002\u5982\u679c\u5b8c\u5168\u6ca1\u6709\u5b66\u8fc7\uff0c\u5efa\u8bae\u8fd8\u662f\u5148\u53bb\u7cfb\u7edf\u5730\u5b66\u4e60\u4e00\u4e0b\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"966\" height=\"588\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u603b\u7ed3.png\" alt=\"\" class=\"wp-image-250\" srcset=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u603b\u7ed3.png 966w, https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u603b\u7ed3-300x183.png 300w, https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u603b\u7ed3-768x467.png 768w\" sizes=\"(max-width: 966px) 100vw, 966px\" \/><\/figure><\/div>\n\n\n\n<h2>1. \u76f4\u63a5\u63d2\u5165\u6392\u5e8f\uff08Insertion Sort\uff09<\/h2>\n\n\n\n<p><strong>\u76f4\u63a5\u63d2\u5165\u6392\u5e8f<\/strong>\u662f\u4e00\u79cd\u7b80\u5355\u76f4\u89c2\u7684\u6392\u5e8f\u65b9\u6cd5\u3002\u4e3b\u8981\u601d\u60f3\u662f\u5bf9\u4e8e\u672a\u6392\u5e8f\u7684\u5143\u7d20\uff0c\u5728\u5df2\u6392\u5e8f\u7684\u5143\u7d20\u4e2d\u4ece\u540e\u5411\u524d\u626b\u63cf\uff0c\u627e\u5230\u5408\u9002\u7684\u4f4d\u7f6e\u540e\u63d2\u5165\u3002<\/p>\n\n\n\n<p>\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u662f<strong>\u7a33\u5b9a<\/strong>\u7684\u3002\u56e0\u4e3a\u672a\u6392\u5e8f\u7684\u5143\u7d20\u5728\u5411\u524d\u626b\u63cf\u7684\u8fc7\u7a0b\u4e2d\u9047\u5230\u76f8\u540c\u7684\u5143\u7d20\u5c31\u4e0d\u4f1a\u7ee7\u7eed\u5411\u524d\u626b\u63cf\u4e86\uff0c\u66f4\u4e0d\u4f1a\u63d2\u5728\u5b83\u7684\u524d\u9762\u3002<\/p>\n\n\n\n<p>\u5e73\u5747\u548c\u6700\u5dee\u60c5\u51b5 <strong>T(n) = O(n<sup>2<\/sup>)<\/strong>\uff0c\u6700\u4f73\u60c5\u51b5  <strong>T(n) = O(n)<\/strong>\u3002\u5982\u679c\u8fd9\u4e2a\u6570\u7ec4\u539f\u6765\u5c31\u662f\u6709\u5e8f\u7684\uff0c\u90a3\u4e48\u53ea\u9700\u8981\u6bd4\u8f83 <strong>n-1<\/strong> \u6b21\uff0c\u4e0d\u9700\u8981\u79fb\u52a8\uff0c\u6240\u4ee5\u6700\u597d\u60c5\u51b5\u4e0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f <strong>n<\/strong>\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"811\" height=\"505\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u76f4\u63a5\u63d2\u5165\u6392\u5e8f.gif\" alt=\"\" class=\"wp-image-260\"\/><\/figure><\/div>\n\n\n\n<h2>2. \u5e0c\u5c14\u6392\u5e8f\uff08Shell Sort\uff09<\/h2>\n\n\n\n<p><strong>\u5e0c\u5c14\u6392\u5e8f<\/strong>\u662f\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u7684\u5347\u7ea7\u7248\u3002\u4e3b\u8981\u601d\u60f3\u662f\u628a\u4e00\u7ec4\u6570\u7ec4\u5206\u6210\u4e86\u4e0d\u540c\u7684\u201c\u7ec4\u201d\uff0c\u53ea\u6709\u540c\u7ec4\u5143\u7d20\u624d\u80fd\u6bd4\u8f83\u548c\u6392\u5e8f\u3002\u968f\u7740\u6392\u5e8f\u7684\u8fdb\u884c\uff0c\u201c\u7ec4\u201d\u4f1a\u6162\u6162\u51cf\u5c11\uff0c\u201c\u7ec4\u201d\u4e2d\u7684\u5143\u7d20\u4e5f\u4f1a\u6162\u6162\u589e\u591a\uff0c\u6570\u7ec4\u6574\u4f53\u4e5f\u4f1a\u6162\u6162\u6709\u5e8f\u3002<\/p>\n\n\n\n<p>\u5e0c\u5c14\u6392\u5e8f\u662f<strong>\u4e0d\u7a33\u5b9a<\/strong>\u7684\u3002\u867d\u7136\u662f\u5426\u7a33\u5b9a\u662f\u7531\u8be5\u7b97\u6cd5\u4ee3\u7801\u7684\u5177\u4f53\u5b9e\u73b0\u51b3\u5b9a\u7684\uff0c\u4f46\u8fd9\u79cd\u5143\u7d20\u95f4\u8fdc\u8ddd\u79bb\u7684\u4ea4\u6362\u4e00\u822c\u90fd\u5f88\u96be\u4fdd\u8bc1\u76f8\u540c\u5143\u7d20\u7684\u76f8\u5bf9\u4f4d\u7f6e\u3002<\/p>\n\n\n\n<p>\u6700\u5dee\u60c5\u51b5 <strong>T(n) = O(n<sup>2<\/sup>)<\/strong>\uff0c\u5e73\u5747\u60c5\u51b5 <strong>T(n) = O(n<sup>1.3<\/sup>)<\/strong>\uff0c\u6700\u4f73\u60c5\u51b5 <strong>T(n) = O(n)<\/strong>\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"1494\" height=\"1558\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u5e0c\u5c14\u6392\u5e8f.png\" alt=\"\" class=\"wp-image-259\" srcset=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u5e0c\u5c14\u6392\u5e8f.png 1494w, https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u5e0c\u5c14\u6392\u5e8f-288x300.png 288w, https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u5e0c\u5c14\u6392\u5e8f-982x1024.png 982w, https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u5e0c\u5c14\u6392\u5e8f-768x801.png 768w, https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u5e0c\u5c14\u6392\u5e8f-1473x1536.png 1473w\" sizes=\"(max-width: 1494px) 100vw, 1494px\" \/><\/figure><\/div>\n\n\n\n<h2>3. \u7b80\u5355\u9009\u62e9\u6392\u5e8f\uff08Selection Sort\uff09<\/h2>\n\n\n\n<p><strong>\u7b80\u5355\u9009\u62e9\u6392\u5e8f<\/strong>\u662f\u65f6\u95f4\u590d\u6742\u5ea6\u4e0a\u6700\u7a33\u5b9a\u7684\u6392\u5e8f\u7b97\u6cd5\u4e4b\u4e00\u3002\u6392\u5e8f\u65b9\u6cd5\u5f88\u7b80\u5355\uff0c\u6bcf\u6b21\u90fd\u4ece\u672a\u6392\u5e8f\u7684\u6570\u7ec4\u4e2d\u627e\u5230\u6700\u5c0f\u7684\u5143\u7d20\uff0c\u7136\u540e\u653e\u5728\u6700\u524d\u7aef\u3002<\/p>\n\n\n\n<p>\u7b80\u5355\u9009\u62e9\u6392\u5e8f\u662f<strong>\u4e0d\u7a33\u5b9a<\/strong>\u7684\u3002\u6bd5\u7adf\u5b83\u6bcf\u8d9f\u53ea\u662f\u9009\u62e9\u6700\u5c0f\u7684\u5143\u7d20\uff0c\u9009\u54ea\u4e2a\u53ef\u4e0d\u4e00\u5b9a\uff0c\u6ca1\u529e\u6cd5\u4fdd\u8bc1\u4e24\u4e2a\u76f8\u540c\u5143\u7d20\u7684\u76f8\u5bf9\u4f4d\u7f6e\u3002<\/p>\n\n\n\n<p>\u4efb\u4f55\u60c5\u51b5\u4e0b <strong>T(n) = O(n<sup>2<\/sup>)<\/strong>\uff0c\u6240\u4ee5\u8bf4\u5b83\u5728\u65f6\u95f4\u590d\u6742\u5ea6\u4e0a\u7a33\u5b9a\u561b\u3002\u56e0\u4e3a\u65e0\u8bba\u6570\u7ec4\u6709\u5e8f\u6216\u662f\u65e0\u5e8f\uff0c\u7b80\u5355\u9009\u62e9\u6392\u5e8f\u90fd\u4f1a\u904d\u5386 <strong>n<\/strong> \u904d\u8fd9\u4e2a\u6570\u7ec4\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"811\" height=\"248\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u7b80\u5355\u9009\u62e9\u6392\u5e8f.gif\" alt=\"\" class=\"wp-image-255\"\/><\/figure><\/div>\n\n\n\n<h2>4. \u5806\u6392\u5e8f\uff08Heap Sort\uff09<\/h2>\n\n\n\n<p><strong>\u5806\u6392\u5e8f<\/strong>\u662f\u5229\u7528\u4e86\u6700\u5927\u5806\u8fd9\u79cd\u6570\u636e\u7ed3\u6784\u7684\u6392\u5e8f\u65b9\u6cd5\u3002\u56e0\u4e3a\u6bcf\u6b21\u5c06\u5806\u8c03\u6574\u4e3a\u6700\u5927\u5806\u540e\uff0c\u5806\u7684\u6839\u7ed3\u70b9\u4e00\u5b9a\u662f\u5806\u4e2d\u6700\u5927\u7684\u5143\u7d20\u3002\u6211\u4eec\u901a\u8fc7\u4e0d\u505c\u7684\u53d6\u51fa\u6700\u5927\u5806\u7684\u6839\u8282\u70b9\u548c\u91cd\u65b0\u8c03\u6574\u4e3a\u6700\u5927\u5806\uff0c\u5c31\u53ef\u4ee5\u4e00\u76f4\u5f97\u5230\u672a\u6392\u5e8f\u6570\u7ec4\u7684\u6700\u5927\u503c\u3002<\/p>\n\n\n\n<p>\u5806\u6392\u5e8f\u662f<strong>\u4e0d\u7a33\u5b9a<\/strong>\u7684\u3002\u6bd5\u7adf\u8fdc\u8ddd\u79bb\u5143\u7d20\u4ea4\u6362\uff0c\u4e0d\u597d\u4fdd\u8bc1\u76f8\u540c\u5143\u7d20\u7684\u76f8\u5bf9\u4f4d\u7f6e\u3002<\/p>\n\n\n\n<p>\u4efb\u4f55\u60c5\u51b5\u4e0b <strong>T(n) = O(nlogn)<\/strong>\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"547\" height=\"364\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u5806\u6392\u5e8f.gif\" alt=\"\" class=\"wp-image-251\"\/><\/figure><\/div>\n\n\n\n<h2>5. \u5192\u6ce1\u6392\u5e8f\uff08Bubble Sort\uff09<\/h2>\n\n\n\n<p><strong>\u5192\u6ce1\u6392\u5e8f<\/strong>\u662f\u5f88\u7b80\u7b54\u7684\u4e00\u79cd\u6392\u5e8f\u65b9\u6cd5\u3002\u987e\u540d\u601d\u4e49\uff0c\u6570\u7ec4\u4e2d\u6700\u5927\u7684\u5143\u7d20\u4f1a\u50cf\u6ce1\u6ce1\u4e00\u6837\u201c\u6d6e\u201d\u5230\u961f\u5217\u7684\u672b\u7aef\u3002\u4e3b\u8981\u7684\u601d\u60f3\u662f\u901a\u8fc7\u5143\u7d20\u7684\u4e24\u4e24\u4ea4\u6362\uff0c\u5c06\u961f\u5217\u4e2d\u6700\u5927\u7684\u5143\u7d20\u79fb\u52a8\u5230\u961f\u5217\u7684\u672b\u5c3e\u3002<\/p>\n\n\n\n<p>\u5192\u6ce1\u6392\u5e8f\u662f<strong>\u7a33\u5b9a<\/strong>\u7684\u3002\u56e0\u4e3a\u5b83\u662f\u5143\u7d20\u4e24\u4e24\u4ea4\u6362\uff0c\u5982\u679c\u4e24\u4e2a\u5143\u7d20\u76f8\u7b49\uff0c\u5c31\u4e0d\u4f1a\u4ea4\u6362\u3002\u8fd9\u6837\u5c31\u4fdd\u8bc1\u4e86\u76f8\u540c\u5143\u7d20\u7684\u76f8\u5bf9\u4f4d\u7f6e\u4e0d\u53d8\u3002<\/p>\n\n\n\n<p>\u5e73\u5747\u548c\u6700\u5dee\u60c5\u51b5 <strong>T(n) = O(n<sup>2<\/sup>)<\/strong>\uff0c\u6700\u4f73\u60c5\u51b5  <strong>T(n) = O(n)<\/strong>\u3002\u56e0\u4e3a\u5e73\u5747\u548c\u6700\u5dee\u60c5\u51b5\u4e0b\u6bcf\u6b21\u904d\u5386\u8fd9\u4e2a\u957f\u5ea6\u4e3a <strong>n<\/strong> \u6570\u7ec4\u90fd\u53ea\u80fd\u786e\u5b9a\u4e00\u4e2a\u5143\u7d20\uff0c\u6240\u4ee5\u60f3\u8981\u786e\u5b9a\u5168\u90e8 <strong>n<\/strong> \u4e2a\u5143\u7d20\u7684\u4f4d\u7f6e\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5c31\u4e3a <strong>n\u00d7n<\/strong>\u3002\u4f46\u6700\u4f73\u60c5\u51b5\u4e0b\uff0c\u5982\u679c\u6570\u7ec4\u662f\u6709\u5e8f\u7684\uff0c\u90a3\u4e48\u53ea\u8981\u904d\u5386\u4e00\u6b21\u5c31\u591f\u4e86\uff0c\u6240\u4ee5\u65f6\u95f4\u590d\u6742\u5ea6\u662f <strong>n<\/strong>\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"826\" height=\"257\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u5192\u6ce1\u6392\u5e8f.gif\" alt=\"\" class=\"wp-image-257\"\/><\/figure><\/div>\n\n\n\n<h2>6. \u5feb\u901f\u6392\u5e8f\uff08Quick Sort\uff09<\/h2>\n\n\n\n<p><strong>\u5feb\u901f\u6392\u5e8f<\/strong>\u662f\u5341\u5927\u6392\u5e8f\u7b97\u6cd5\u4e2d\u6700\u7ecf\u5178\u7684\u4e00\u4e2a\u3002\u4e3b\u8981\u601d\u60f3\u662f\u901a\u8fc7\u4e00\u8d9f\u6392\u5e8f\u5c06\u5f85\u6392\u5e8f\u7684\u6570\u7ec4\u5206\u4e3a\u72ec\u7acb\u7684\u4e24\u4e2a\u90e8\u5206\uff0c\u524d\u534a\u90e8\u5206\u90fd\u6bd4\u4e2d\u95f4\u7684\u5173\u952e\u5143\u7d20\u5c0f\uff0c\u540e\u534a\u90e8\u5206\u90fd\u6bd4\u4e2d\u95f4\u7684\u5173\u952e\u5143\u7d20\u5927\uff0c\u4ece\u800c\u786e\u5b9a\u4e86\u4e2d\u95f4\u7684\u5173\u952e\u5143\u7d20\u7684\u4f4d\u7f6e\u3002<\/p>\n\n\n\n<p>\u5feb\u901f\u6392\u5e8f\u662f<strong>\u4e0d\u7a33\u5b9a<\/strong>\u7684\uff0c\u6bd5\u7adf\u8981\u8fdc\u8ddd\u79bb\u7684\u8c03\u6362\u5143\u7d20\u3002<\/p>\n\n\n\n<p>\u6700\u4f73\u548c\u5e73\u5747\u60c5\u51b5\u4e0b <strong>T(n) = O(nlogn)<\/strong>\uff0c\u6700\u5dee\u60c5\u51b5\u4e0b <strong>T(n) = O(n<sup>2<\/sup>)<\/strong>\u3002\u5feb\u901f\u6392\u5e8f\u7684\u5b9e\u73b0\u4f9d\u8d56\u7684\u662f\u9012\u5f52\u52a0\u4e8c\u5206\u6cd5\uff0c\u4f46\u8fd9\u4e2a\u4e8c\u5206\u6cd5\u5e76\u4e0d\u662f\u5b8c\u7f8e\u7684\u4e8c\u5206\u6cd5\u3002\u5982\u679c\u4e8c\u5206\u6cd5\u6bcf\u6b21\u6b63\u597d\u53ea\u5206\u5230\u4e00\u8fb9\uff0c\u90a3\u4e48\u4e00\u5171\u5c31\u6709 <strong>n-1<\/strong> \u5c42\uff0c\u6240\u4ee5\u65f6\u95f4\u590d\u6742\u5ea6\u662f  <strong>n<sup>2<\/sup><\/strong>\uff1b\u5176\u4ed6\u60c5\u51b5\u4e0b\u4e00\u5171\u6709<strong>logn<\/strong> \u5c42\uff0c\u6240\u4ee5\u65f6\u95f4\u590d\u6742\u5ea6\u662f <strong>n*logn<\/strong>\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"811\" height=\"252\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u5feb\u901f\u6392\u5e8f.gif\" alt=\"\" class=\"wp-image-256\"\/><\/figure><\/div>\n\n\n\n<h2>7. \u5f52\u5e76\u6392\u5e8f\uff08Merge Sort\uff09<\/h2>\n\n\n\n<p><strong>\u5f52\u5e76\u6392\u5e8f<\/strong>\u4ee5\u9700\u8981\u989d\u5916\u7a7a\u95f4\u4f5c\u4e3a\u4ee3\u4ef7\uff0c\u8868\u73b0\u6bd4\u7b80\u5355\u9009\u62e9\u6392\u5e8f\u597d\u5f97\u591a\u3002\u4e8c\u8def\u5f52\u5e76\u6392\u5e8f\u5c31\u662f\u4e24\u4e24\u6392\u5e8f\uff0c\u7136\u540e\u4e24\u4e2a\u533a\u57df\u4e00\u8d77\u6392\u5e8f\uff0c\u4ee5\u6b64\u7c7b\u63a8\u3002<\/p>\n\n\n\n<p>\u5f52\u5e76\u6392\u5e8f\u662f<strong>\u7a33\u5b9a<\/strong>\u7684\u3002\u56e0\u4e3a\u5728\u4f7f\u7528\u989d\u5916\u7a7a\u95f4\u7684\u65f6\u5019\uff0c\u9760\u524d\u533a\u57df\u7684\u5143\u7d20\u53ea\u8981\u5c0f\u4e8e\u7b49\u4e8e\u9760\u540e\u533a\u57df\u7684\u5143\u7d20\u5c31\u80fd\u88ab\u653e\u8fdb\u989d\u5916\u7a7a\u95f4\u3002<\/p>\n\n\n\n<p>\u4efb\u4f55\u60c5\u51b5\u4e0b <strong>T(n) = O(nlogn)<\/strong>\u3002\u5f52\u5e76\u6392\u5e8f\u4e3b\u8981\u662f\u9760\u9012\u5f52\u52a0\u4e8c\u5206\u6cd5\uff0c\u6bcf\u4e00\u5c42\u7684\u65f6\u95f4\u4ee3\u4ef7\u90fd\u662f <strong>n<\/strong> \u76f8\u5173\uff0c\u4e00\u5171\u6709 <strong>logn<\/strong> \u5c42\uff0c\u6240\u4ee5\u65f6\u95f4\u590d\u6742\u5ea6\u662f <strong>n*logn<\/strong>\u3002\u6240\u4ee5\u65e0\u8bba\u6570\u7ec4\u662f\u4e0d\u662f\u6709\u5e8f\u7684\uff0c\u90fd\u4f1a\u88ab\u4e8c\u5206\u6cd5\u5206\u4e3a\u524d\u540e\u4e24\u4e2a\u90e8\u5206\uff0c\u7136\u540e\u9012\u5f52\u4e0b\u53bb\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"811\" height=\"505\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u5f52\u5e76\u6392\u5e8f.gif\" alt=\"\" class=\"wp-image-252\"\/><\/figure><\/div>\n\n\n\n<h2>8. \u57fa\u6570\u6392\u5e8f\uff08Radix Sort\uff09<\/h2>\n\n\n\n<p><strong>\u57fa\u6570\u6392\u5e8f<\/strong>\u662f\u975e\u6bd4\u8f83\u6392\u5e8f\u3002\u4e3b\u8981\u601d\u60f3\u662f\u5bf9\u6570\u7ec4\u4e2d\u6240\u6709\u5143\u7d20\u5148\u6839\u636e\u5176\u4e2a\u4f4d\u8fdb\u884c\u6392\u5e8f\uff0c\u518d\u6839\u636e\u5176\u5341\u4f4d\u8fdb\u884c\u6392\u5e8f\uff0c\u4e4b\u540e\u662f\u767e\u4f4d\u3001\u5343\u4f4d\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u5230\u6700\u9ad8\u4f4d\u3002<\/p>\n\n\n\n<p>\u57fa\u6570\u6392\u5e8f\u662f<strong>\u7a33\u5b9a<\/strong>\u7684\u3002\u56e0\u4e3a\u5b83\u662f\u975e\u6bd4\u8f83\u6392\u5e8f\uff0c\u5143\u7d20\u4e4b\u95f4\u7684\u987a\u5e8f\u4e0d\u4f9d\u8d56\u5143\u7d20\u4e4b\u95f4\u7684\u6bd4\u8f83\u3002<\/p>\n\n\n\n<p>\u4efb\u4f55\u60c5\u51b5\u4e0b  <strong>T(n) = O(n * k)<\/strong>\uff0c\u5176\u4e2d <strong>k<\/strong> \u662f\u6876\u7684\u4e2a\u6570\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"1012\" height=\"574\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u57fa\u6570\u6392\u5e8f.gif\" alt=\"\" class=\"wp-image-253\"\/><\/figure><\/div>\n\n\n\n<h2>9. \u8ba1\u6570\u6392\u5e8f\uff08Counting Sort\uff09<\/h2>\n\n\n\n<p><strong>\u8ba1\u6570\u6392\u5e8f<\/strong>\u662f\u975e\u6bd4\u8f83\u6392\u5e8f\u3002\u5b83\u7684\u6838\u5fc3\u662f\u5c06\u6570\u7ec4\u4e2d\u7684\u5143\u7d20\u503c\u8f6c\u6362\u4e3a\u952e\u5b58\u50a8\u5728\u989d\u5916\u7a7a\u95f4\u4e2d\u3002\u4e3b\u8981\u601d\u60f3\u662f\u989d\u5916\u521b\u5efa\u4e00\u4e2a\u6570\u7ec4\uff0c\u989d\u5916\u6570\u7ec4\u4e2d\u5143\u7d20\u4e0b\u6807\u662f\u5f85\u6392\u5e8f\u6570\u7ec4\u4e2d\u5143\u7d20\u7684\u503c\uff0c\u800c\u989d\u5916\u6570\u7ec4\u4e2d\u7684\u503c\u662f\u5176\u4e0b\u6807\u7684\u503c\u5728\u5f85\u6392\u5e8f\u6570\u7ec4\u4e2d\u4f5c\u4e3a\u5143\u7d20\u7684\u503c\u51fa\u73b0\u7684\u6b21\u6570\u3002<\/p>\n\n\n\n<p>\u8ba1\u6570\u6392\u5e8f\u662f<strong>\u7a33\u5b9a<\/strong>\u7684\u3002\u56e0\u4e3a\u5b83\u662f\u975e\u6bd4\u8f83\u6392\u5e8f\uff0c\u5143\u7d20\u4e4b\u95f4\u7684\u987a\u5e8f\u4e0d\u4f9d\u8d56\u5143\u7d20\u4e4b\u95f4\u7684\u6bd4\u8f83\u3002<\/p>\n\n\n\n<p>\u4efb\u4f55\u60c5\u51b5\u4e0b <strong>T(n) = O(n+k)<\/strong>\uff0c\u5176\u4e2d <strong>k<\/strong> \u662f\u6876\u7684\u4e2a\u6570\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"1012\" height=\"557\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u8ba1\u6570\u6392\u5e8f.gif\" alt=\"\" class=\"wp-image-254\"\/><\/figure><\/div>\n\n\n\n<h2>10. \u6876\u6392\u5e8f\uff08Bucket Sort\uff09<\/h2>\n\n\n\n<p><strong>\u6876\u6392\u5e8f<\/strong>\u662f\u8ba1\u6570\u6392\u5e8f\u7684\u5347\u7ea7\u7248\uff0c\u4e5f\u662f\u975e\u6bd4\u8f83\u6392\u5e8f\u3002\u4e3b\u8981\u601d\u60f3\u662f\u5bf9\u6570\u7ec4\u4e2d\u6570\u503c\u8303\u56f4\u8fdb\u884c\u5212\u5206\uff0c\u6570\u7ec4\u4e2d\u7684\u6bcf\u4e2a\u5143\u7d20\u6839\u636e\u5176\u6570\u503c\u7684\u6240\u5728\u8303\u56f4\uff0c\u8fdb\u5165\u4e0d\u540c\u7684\u201c\u6876\u201d\u3002\u7136\u540e\u5728\u4e0d\u540c\u7684\u6876\u4e2d\u5206\u522b\u5bf9\u8fd9\u4e9b\u5143\u7d20\u8fdb\u884c\u6392\u5e8f\uff08\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\uff09\uff0c\u518d\u4f9d\u6b21\u8f93\u51fa\u3002<\/p>\n\n\n\n<p>\u6876\u6392\u5e8f\u662f<strong>\u7a33\u5b9a<\/strong>\u7684\u3002\u56e0\u4e3a\u5b83\u662f\u975e\u6bd4\u8f83\u6392\u5e8f\uff0c\u5143\u7d20\u4e4b\u95f4\u7684\u987a\u5e8f\u4e0d\u4f9d\u8d56\u5143\u7d20\u4e4b\u95f4\u7684\u6bd4\u8f83\u3002<\/p>\n\n\n\n<p>\u6700\u597d\u548c\u5e73\u5747\u60c5\u51b5\u4e0b <strong>T(n) = O(n+k)<\/strong>\uff0c\u6700\u5dee\u60c5\u51b5\u4e0b <strong>T(n) = O(n<sup>2<\/sup>)<\/strong>\uff0c\u5176\u4e2d <strong>k<\/strong> \u662f\u6876\u7684\u4e2a\u6570\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" width=\"1050\" height=\"580\" src=\"https:\/\/twocups.cn\/wp-content\/uploads\/2020\/02\/\u6392\u5e8f_\u6876\u6392\u5e8f.gif\" alt=\"\" class=\"wp-image-261\"\/><\/figure><\/div>\n\n\n\n<h2>Java \u4ee3\u7801\u5b9e\u73b0\uff08\u542b\u6d4b\u8bd5\uff09<\/h2>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"java\" data-enlighter-theme=\"classic\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import java.util.ArrayList;\nimport java.util.Arrays;\n\npublic class Sort {\n    public static void main(String[] args) {\n        int[] arr = new int[20];\n        int index = 0;\n        for(int i = 20;i > 0;i--)\n            arr[index++] = i;\n        System.out.println(\"\u539f\u6570\u7ec4\uff1a\");\n        System.out.println(Arrays.toString(arr));\n        System.out.println(\"\u5f00\u59cb\u6392\u5e8f\");\n        arr = MergeSort(arr);\n        System.out.println(\"\u6392\u5e8f\u540e\u4e3a\uff1a\");\n        System.out.println(Arrays.toString(arr));\n    }\n\n    \/\/ \u5de5\u5177\uff1a\u4ea4\u6362\u6570\u7ec4\u4e2d\u5143\u7d20\u7684\u4f4d\u7f6e\n    public static int[] swap(int[] arr, int i, int j){\n        int temp = arr[i];\n        arr[i] = arr[j];\n        arr[j] = temp;\n        return arr;\n    }\n\n    \/\/ ****** 1.\u76f4\u63a5\u63d2\u5165\u6392\u5e8f ******\n    public static int[] InsertionSort(int[] arr){\n        if(arr.length == 0 || arr.length == 1)\n            return arr;\n        for(int i = 0;i &lt; arr.length - 1;i++){\n            \/\/ \u5c06 i+1 \u4f4d\u7f6e\u7684\u6570\u63d2\u5165 0 \u5230 i \u4e4b\u95f4\u7684\u6570\u7ec4\uff0c\u4ece\u540e\u5f80\u524d\u904d\u5386\n            \/\/ current \u6307 i+1 \u7684\u4f4d\u7f6e\u5143\u7d20\uff0cpre \u6307 0 \u5230 i \u4e2d\u4f9d\u6b21\u5411\u524d\u904d\u5386\u7684\u6307\u9488\n            int current = arr[i+1];\n            int pre = i;\n            while(pre >= 0 &amp;&amp; current &lt; arr[pre]){\n                arr[pre+1] = arr[pre];\n                pre--;\n            }\n            \/\/ \u6700\u540e\u5c06\u539f\u6765 i+1 \u4f4d\u7f6e\u7684\u5143\u7d20\u653e\u5165\u73b0\u5728 0 \u5230 i+1 \u4e4b\u95f4\u6570\u7ec4\u4e2d\u6b63\u786e\u7684\u4f4d\u7f6e\u4e0a\n            \/\/ pre+1 \u662f\u56e0\u4e3a\u521a\u624d\u5faa\u73af\u7ed3\u675f\u65f6\u53c8\u81ea\u51cf\u4e86\u4e00\u6b21\n            arr[pre+1] = current;\n            \/\/ \u6253\u5370\u8fd9\u4e00\u8f6e\u7684\u6392\u5e8f\u7ed3\u679c\n            System.out.println(Arrays.toString(arr));\n        }\n        return arr;\n    }\n\n    \/\/ ****** 2.\u5e0c\u5c14\u6392\u5e8f ******\n    \/\/ \u5e0c\u5c14\u6392\u5e8f\u6700\u91cd\u8981\u7684\u53d8\u91cf\u5c31\u662f gap\uff0c\u6240\u6709\u9700\u8981+1\u6216\u8005\u81ea\u52a01\u7684\u5730\u65b9\u90fd\u8981\u6ce8\u610f\n    public static int[] ShellSort(int[] arr){\n        if(arr.length == 0 || arr.length == 1)\n            return arr;\n        int current, gap = arr.length \/ 2;\n        while(gap > 0){\n            for(int  i = gap;i &lt; arr.length;i++){\n                \/\/ \u5c06 pre+gap \u4f4d\u7f6e\u7684\u6570\u63d2\u5165 0 \u5230 pre \u4e4b\u95f4\u201c\u540c\u7ec4\u201d\u7684\u6570\u7ec4\uff0c\u4ece\u540e\u5f80\u524d\u904d\u5386\n                \/\/ current \u6307 pre+gap \u7684\u4f4d\u7f6e\u5143\u7d20\n                current = arr[i];\n                int pre = i - gap;\n                while(pre >= 0 &amp;&amp; arr[pre] > current){\n                    arr[pre+gap] = arr[pre];\n                    pre -= gap;\n                }\n                arr[pre+gap] = current;\n                \/\/ \u6253\u5370\u8fd9\u4e00\u8f6e\u7684\u6392\u5e8f\u7ed3\u679c\n                System.out.println(Arrays.toString(arr));\n            }\n            gap \/= 2;\n        }\n        return arr;\n    }\n\n    \/\/ ****** 3.\u7b80\u5355\u9009\u62e9\u6392\u5e8f ******\n    public static int[] SelectionSort(int[] arr){\n        if(arr.length == 0 || arr.length == 1)\n            return arr;\n        for(int i = 0;i &lt; arr.length - 1;i++){\n            \/\/ \u6bcf\u4e00\u8f6e\u6311\u51fa\u4e00\u4e2a\u6700\u5c0f\u7684\u5143\u7d20\uff0c\u4f9d\u6b21\u4e0e\u4e0d\u65ad\u589e\u957f\u7684 i \u4f4d\u7f6e\u7684\u5143\u7d20\u4ea4\u6362\n            int MinIndex = i;\n            for(int j = i;j &lt; arr.length;j++){\n                if(arr[j] &lt; arr[MinIndex])\n                    MinIndex = j;\n            }\n            arr = swap(arr,MinIndex,i);\n            \/\/ \u6253\u5370\u8fd9\u4e00\u8f6e\u7684\u6392\u5e8f\u7ed3\u679c\n            System.out.println(Arrays.toString(arr));\n        }\n        return arr;\n    }\n\n    \/\/ ****** 4.\u5806\u6392\u5e8f ******\n    \/\/ \u4e3b\u51fd\u6570\n    public static int[] HeapSort(int[] arr){\n        if(arr.length == 0 || arr.length == 1)\n            return arr;\n        int len = arr.length;\n        \/\/ \u5806\u6392\u5e8f\u7b2c\u4e00\u6b65\u662f\u5148\u628a\u5f53\u524d\u6570\u7ec4\u53d8\u6210\u4e00\u4e2a\u6700\u5927\u5806\n        arr = AdjustMaxHeap(arr, len-1);\n        while(len > 0){\n            \/\/ \u53d6\u51fa\u5806\u9876\u7684\u5143\u7d20\uff08\u6700\u5927\u5143\u7d20\uff09\u4e0e\u672b\u5c3e\u8fd8\u6ca1\u6709\u786e\u5b9a\u4f4d\u7f6e\u7684\u5143\u7d20\u4ea4\u6362\n            arr = swap(arr,0,len - 1);\n            \/\/ \u6253\u5370\u8fd9\u4e00\u8f6e\u7684\u6392\u5e8f\u7ed3\u679c\n            System.out.println(Arrays.toString(arr));\n            len--;\n            arr = AdjustMaxHeap(arr,len - 1);\n            }\n        return arr;\n    }\n    \/\/ \u8c03\u6574\u4e3a\u6700\u5927\u5806\n    public static int[] AdjustMaxHeap(int[] arr, int lastIndex){\n        for(int i = (lastIndex - 1) \/ 2;i>=0;i--){\n            arr = AdjustLocalHeap(arr,lastIndex,i);\n        }\n        return arr;\n    }\n    \/\/\u8c03\u6574\u5c40\u90e8\u5806\u4f7f\u5176\u6210\u4e3a\u5c40\u90e8\u6700\u5927\u5806\n    \/*\n     \u6ce8\u610f\u4e8b\u9879\uff1a\u5806\u4e2d\u7ed3\u70b9\u662f\u4ece 1 \u5f00\u59cb\u7684\uff0c\u4f46\u628a\u6570\u7ec4\u770b\u4f5c\u5806\u7684\u8bdd\uff0c\u6570\u7ec4\u7684\u4e0b\u6807\u662f\u4ece 0 \u5f00\u59cb\u7684\n     \u90a3\u4e48\u7236\u7ed3\u70b9\u4e0e\u5b50\u7ed3\u70b9\u7684\u5173\u7cfb\u5c31\u4f1a\u53d1\u751f\u53d8\u5316\uff1a\n        \u7236\u7ed3\u70b9 = \uff08\u5b50\u7ed3\u70b9-1\uff09\/2\n        \u5de6\u5b50\u7ed3\u70b9 = \u7236\u7ed3\u70b9*2+1\n        \u53f3\u5b50\u7ed3\u70b9 = \u7236\u7ed3\u70b9*2+2\n     *\/\n    public static int[] AdjustLocalHeap(int[] arr,int lastIndex,int i){\n        \/\/ \u627e\u51fa\u5f53\u524d\u7ed3\u70b9\u548c\u5de6\u53f3\u5b50\u7ed3\u70b9\uff08\u5982\u679c\u6709\u5de6\u53f3\u5b50\u7ed3\u70b9\u7684\u8bdd\uff09\u4e2d\u6700\u5927\u7684\u5143\u7d20\uff0c\u8ba9\u8fd9\u4e2a\u6700\u5927\u7684\u5143\u7d20\u6210\u4e3a\u7236\u7ed3\u70b9\n        int maxIndex = i;\n        if(i*2+1 &lt;= lastIndex &amp;&amp; arr[i] &lt; arr[i*2+1])\n            maxIndex = i*2+1;\n        \/\/ \u8fd9\u91cc\u8981\u591a\u4e00\u4e2a\u53f3\u5b50\u7ed3\u70b9\u662f\u5426\u5927\u4e8e\u5de6\u5b50\u7ed3\u70b9\u7684\u5224\u5b9a\n        if(i*2+2 &lt;= lastIndex &amp;&amp; arr[i] &lt; arr[i*2+2] &amp;&amp; arr[i*2+1] &lt; arr[i*2+2])\n            maxIndex = i*2+2;\n        \/\/ \u5982\u679c\u7236\u7ed3\u70b9\u4e0d\u662f\u4e09\u4e2a\u7ed3\u70b9\u4e2d\u7684\u6700\u5927\u7ed3\u70b9\uff0c\u90a3\u4e48\u5c06\u6700\u5927\u7ed3\u70b9\u53d8\u6210\u7236\u7ed3\u70b9\n        \/\/ \u518d\u901a\u8fc7\u9012\u5f52\u770b\u770b\u8fd9\u4e2a\u6bd4\u8f83\u5c0f\u7684\u7236\u7ed3\u70b9\u80fd\u4e0d\u80fd\u518d\u201c\u5f80\u4e0b\u6c89\u201d\n        if(maxIndex != i){\n            arr = swap(arr,maxIndex,i);\n            arr = AdjustLocalHeap(arr,lastIndex,maxIndex);\n        }\n        return arr;\n    }\n\n    \/\/ ****** 5.\u5192\u6ce1\u6392\u5e8f ******\n    public static int[] BubbleSort(int[] arr){\n        if(arr.length == 0 || arr.length ==1)\n            return arr;\n        for(int i = arr.length-1;i > 0;i--){\n            for(int j = 1;j &lt;= i;j++){\n                if(arr[j] &lt; arr[j-1])\n                    arr = swap(arr,j,j-1);\n            }\n            \/\/ \u6253\u5370\u8fd9\u4e00\u8f6e\u7684\u6392\u5e8f\u7ed3\u679c\n            System.out.println(Arrays.toString(arr));\n        }\n        return arr;\n    }\n\n    \/\/ ****** 6.\u5feb\u901f\u6392\u5e8f ******\n    \/\/\u4e3b\u51fd\u6570\n    public static int[] QuickSort(int[] arr){\n        if(arr.length == 0 || arr.length ==1)\n            return arr;\n        arr = LocalQuickSort(arr,0,arr.length -1 );\n        return arr;\n    }\n    \/\/ \u5feb\u901f\u6392\u5e8f\n    public static int[] LocalQuickSort(int[] arr, int start, int last){\n        if(start >= last)\n            return arr;\n        \/\/ benchmark \u6307\u57fa\u51c6\u6570\uff0c\u4e5f\u5c31\u662f\u8fd9\u4e00\u8f6e\u5c06\u8981\u786e\u5b9a\u4f4d\u7f6e\u7684\u6570\n        int benchmark = arr[start];\n        int left = start;\n        int right = last;\n        while(left &lt; right){\n            \/\/ \u5fc5\u987b\u53f3\u6307\u9488\u5148\u8d70\n            while(arr[right] > benchmark &amp;&amp; left &lt; right) right--;\n            if(arr[right] &lt;= benchmark &amp;&amp; left &lt; right) arr[left++] = arr[right];\n            while(arr[left] &lt; benchmark &amp;&amp; left &lt; right) left++;\n            if(arr[left] >= benchmark &amp;&amp; left &lt; right) arr[right--] = arr[left];\n        }\n        arr[left] = benchmark;\n        \/\/ \u6253\u5370\u8fd9\u4e00\u8f6e\u7684\u6392\u5e8f\u7ed3\u679c\n        System.out.println(Arrays.toString(arr));\n        \/\/ \u901a\u8fc7\u9012\u5f52\uff0c\u5206\u522b\u5bf9\u5df2\u786e\u5b9a\u4f4d\u7f6e\u7684\u6570\u7684\u4e24\u8fb9\u533a\u57df\u8fdb\u884c\u5feb\u901f\u6392\u5e8f\n        arr = LocalQuickSort(arr,start,left-1);\n        arr = LocalQuickSort(arr,left+1,last);\n\n        return arr;\n    }\n\n    \/\/ ****** 7.\u5f52\u5e76\u6392\u5e8f ******\n    \/\/ \u4e3b\u51fd\u6570\n    public static int[] MergeSort(int[] arr){\n        if(arr.length == 0 || arr.length ==1)\n            return arr;\n        arr = Merge(arr,0,arr.length-1);\n        return arr;\n    }\n    \/\/ \u5f52\u5e76\u6392\u5e8f\n    public static int[] Merge(int[] arr,int start,int last){\n        \/\/ start &lt; last \u7684\u5224\u65ad\u610f\u5473\u7740 arr \u6307\u5b9a\u7684\u8303\u56f4\u5185\u5fc5\u987b\u81f3\u5c11\u6709\u4e24\u4e2a\u5143\u7d20\n        if(start &lt; last){\n            int mid = (start + last) \/ 2;\n            \/\/ \u5de6\u53f3\u90e8\u5206\u5206\u522b\u9012\u5f52\n            arr = Merge(arr,start,mid);\n            arr = Merge(arr,mid+1,last);\n            \/\/ \u9012\u5f52\u5c42\u9762\uff1a\u4ece\u91cc\u5f80\u5916\u4f9d\u6b21\u5c06\u5de6\u534a\u90e8\u5206\u548c\u53f3\u534a\u90e8\u5206\u6574\u5408\u6210\u4e00\u4e2a\u90e8\u5206\n            arr = merge(arr,start,mid,last);\n        }\n        return arr;\n    }\n    public static int[] merge(int[] arr,int start,int mid,int last){\n        \/\/ tempArr \u6307\u4e00\u4e2a\u989d\u5916\u6570\u7ec4\uff0c\u7528\u6765\u4e34\u65f6\u7ed9 arr \u4e2d\u540c\u4e00\u533a\u57df\u7684\u5143\u7d20\u6392\u5e8f\n        int[] tempArr = new int[arr.length];\n        \/\/ p1 \u6307 arr \u6307\u5b9a\u533a\u57df\u7684\u5de6\u534a\u90e8\u5206\u7684\u6307\u9488\uff0cp2 \u6307 arr \u6307\u5b9a\u533a\u57df\u7684\u53f3\u534a\u90e8\u5206\u7684\u6307\u9488\uff0cp \u6307\u989d\u5916\u6570\u7ec4 tempArr \u7684\u6307\u9488\n        int p1 = start, p2 = mid+1, p = start;\n        \/\/ \u4ece\u6307\u5b9a\u533a\u57df\u7684\u5de6\u53f3\u534a\u90e8\u5206\u4e2d\u53d6\u51fa\u6700\u5c0f\u5143\u7d20\u653e\u5165\u989d\u5916\u6570\u7ec4\uff0c\u5b8c\u6210\u6307\u5b9a\u533a\u57df\u5185\u7684\u6392\u5e8f\n        while(p1 &lt;= mid &amp;&amp; p2 &lt;= last){\n            if(arr[p1] &lt;= arr[p2])\n                tempArr[p++] = arr[p1++];\n            else\n                tempArr[p++] = arr[p2++];\n        }\n        while(p1 &lt;= mid) tempArr[p++] = arr[p1++];\n        while(p2 &lt;= last) tempArr[p++] = arr[p2++];\n        \/\/ \u5c06\u989d\u5916\u6570\u7ec4\u4e2d\u7684\u6570\u636e\u8986\u76d6\u5230\u539f arr \u6570\u7ec4\u4e2d\n        for(int i = start;i &lt;= last;i++)\n            arr[i] = tempArr[i];\n        System.out.println(Arrays.toString(arr));\n        return arr;\n    }\n\n    \/\/ ****** 8.\u57fa\u6570\u6392\u5e8f ******\n    public static int[] RadixSort(int[] arr){\n        if(arr.length == 0 || arr.length ==1)\n            return arr;\n        \/\/ max \u6307\u6570\u7ec4\u4e2d\u6700\u5927\u7684\u6570\uff0cmaxDigit \u6307\u8fd9\u4e2a\u6700\u5927\u7684\u6570\u662f\u51e0\u4f4d\u6570\n        int max = arr[0];\n        for(int x:arr)\n            max = Math.max(x,max);\n        int maxDigit = 0;\n        while(max != 0){\n            max \/= 10;\n            maxDigit++;\n        }\n        \/\/ mod \u7528\u4e8e\u4e3a\u6570\u7ec4\u4e2d\u7684\u6570\u53d6\u4f59\u6570\uff0cdiv \u7528\u4e8e\u628a\u901a\u8fc7 mod \u53d6\u7684\u4f59\u6570\u53d8\u6210\u4e2a\u4f4d\u6570\n        int mod = 10;\n        int div = 1;\n        ArrayList&lt;ArrayList&lt;Integer>> bucket = new ArrayList&lt;ArrayList&lt;Integer>>();\n        for(int j = 0;j &lt; 10;j++){\n            bucket.add(new ArrayList&lt;Integer>());\n        }\n        for(int i = 0;i&lt;maxDigit;i++,mod *= 10,div *= 10){\n            \/\/ \u6253\u5370\u8fd9\u4e00\u8f6e\u7684\u6392\u5e8f\u7ed3\u679c\n            System.out.println(Arrays.toString(arr));\n            for(int j = 0;j &lt; arr.length;j++){\n                \/\/ num \u6307\u5f53\u524d\u5143\u7d20 arr[j] \u7684\u4e2a\/\u5341\/\u767e\/\u5343\u4f4d\u662f\u51e0\n                int num = (arr[j] % mod) \/ div;\n                bucket.get(num).add(arr[j]);\n            }\n            int index = 0;\n            for(int j = 0;j &lt; 10;j++){\n                if(bucket.get(j).size() != 0){\n                    for(int x:bucket.get(j))\n                        arr[index++] = x;\n                    \/\/ \u5c06\u6876\u4e2d\u6240\u6709\u7684\u52a8\u6001\u6570\u7ec4\u6e05\u7a7a\uff0c\u5426\u5219\u7b2c\u4e8c\u6b21\u5faa\u73af\u5f00\u59cb\u518d\u7528\u5230\u8fd9\u4e9b\u52a8\u6001\u6570\u7ec4\u65f6\u91cc\u9762\u8fd8\u4f1a\u6709\u6570\u636e\n                    bucket.get(j).clear();\n                }\n            }\n        }\n        return arr;\n    }\n\n    \/\/ ****** 9.\u8ba1\u6570\u6392\u5e8f ******\n    public static int[] CountingSort(int[] arr){\n        if(arr.length ==0 || arr.length == 1)\n            return arr;\n        int min, max;\n        min = max = arr[0];\n        for(int x: arr){\n            if(x > max)\n                max = x;\n            if(x &lt; min)\n                min = x;\n        }\n        \/\/ bucket \u6307\u7528\u6765\u5b58\u50a8\u6bcf\u4e2a\u5143\u7d20\u51fa\u73b0\u6b21\u6570\u7684\u6876\uff0c\u957f\u5ea6\u4e3a\u5143\u7d20\u7684\u8303\u56f4\n        int[] bucket = new int[max - min +1];\n        \/\/ \u628a bucket \u7528 0 \u586b\u6ee1\uff0c\u56e0\u4e3a\u4e4b\u540e\u8981\u7d2f\u52a0\n        Arrays.fill(bucket,0);\n        \/\/ \u5728 bucket \u4e2d\u76f8\u5e94\u7684\u4f4d\u7f6e\u8bb0\u5f55\u6bcf\u4e2a\u5143\u7d20\u51fa\u73b0\u7684\u6b21\u6570\n        for(int x:arr){\n            bucket[x - min]++;\n        }\n        int index = 0;\n        \/\/ \u4f9d\u6b21\u4ece bucket \u4e2d\u63d0\u53d6\u5143\u7d20\u8986\u76d6\u5230\u539f\u6765\u7684 arr \u4e0a\n        for(int i =0;i&lt;bucket.length;i++){\n            while(bucket[i] != 0){\n                arr[index++] = i + min;\n                bucket[i]--;\n            }\n        }\n        return arr;\n    }\n\n    \/\/ ****** 10.\u6876\u6392\u5e8f ******\n    \/\/ \u4e3b\u51fd\u6570\n    public static int[] BucketSort(int[] arr){\n        if(arr.length == 0 || arr.length == 1)\n            return arr;\n        arr = Bucket(arr,5);\n        return  arr;\n    }\n    \/\/ \u6876\u6392\u5e8f\n    \/\/ bucketSize \u6307\u6bcf\u4e2a\u6876\u7684\u5bb9\u91cf\uff0cbucketCount \u6307\u6876\u7684\u4e2a\u6570\n    public static int[] Bucket(int[] arr,int bucketSize){\n        int min,max;\n        min = max = arr[0];\n        for(int x:arr){\n            if(x > max)\n                max = x;\n            if(x > min)\n                min = x;\n        }\n        int bucketCount = (max - min) \/ bucketSize +1;\n        ArrayList&lt;ArrayList&lt;Integer>> bucket = new ArrayList&lt;ArrayList&lt;Integer>>();\n        for(int i = 0;i &lt; bucketCount;i++)\n            bucket.add(new ArrayList&lt;Integer>());\n        for(int x: arr){\n            \/\/ \u904d\u5386\u6bcf\u4e2a\u6876\n            for(int bucketIndex = 0;bucketIndex &lt; bucketCount;bucketIndex++){\n                \/\/ \u5982\u679c arr \u5f53\u524d\u5143\u7d20\u5728\u8be5\u6876\u7684\u8303\u56f4\u5185\uff0c\u5219\u5c06\u8be5\u5143\u7d20\u653e\u5165\u8be5\u6876\u5185\uff0c\u5e76\u7ed3\u675f\u904d\u5386\u6bcf\u4e2a\u6876\u7684\u5faa\u73af\n                if(x >= min + bucketIndex*bucketSize &amp;&amp; x &lt; min + (bucketIndex+1)*bucketSize){\n                    bucket.get(bucketIndex).add(x);\n                    break;\n                }\n            }\n        }\n        int index = 0;\n        for(int i = 0;i &lt; bucketCount;i++){\n            \/\/ \u5bf9\u6bcf\u4e2a\u6876\u4f7f\u7528\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\uff0c\u8c03\u6574\u6876\u5185\u5143\u7d20\u7684\u987a\u5e8f\n            bucket.set(i,InsertionSortOfArrayList(bucket.get(i)));\n            for(int x:bucket.get(i))\n                arr[index++] = x;\n        }\n        return arr;\n    }\n    \/\/ \u9488\u5bf9\u52a8\u6001\u6570\u7ec4\u7684\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\n    public static ArrayList&lt;Integer> InsertionSortOfArrayList(ArrayList&lt;Integer> arr){\n        if(arr.size() == 0 || arr.size() ==1)\n            return arr;\n        int current;\n        int pre;\n        for(int i = 0;i &lt; arr.size() - 1;i++){\n            pre = i;\n            current = arr.get(i+1);\n            while(arr.get(pre) > current &amp;&amp; pre >= 0){\n                arr.set(pre+1,arr.get(pre));\n                pre--;\n            }\n            arr.set(pre+1,current);\n        }\n        return arr;\n    }\n}<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u7248\u6743\u58f0\u660e\uff1a\u672c\u6587\u4e3a\u535a\u4e3b\u539f\u521b\u6587\u7ae0\uff0c\u8f6c\u8f7d\u8bf7\u6ce8\u660e\u51fa\u5904\uff1ahttps:\/\/twocups.cn\/index.php\/202 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":65,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[76],"tags":[32,84,77],"_links":{"self":[{"href":"https:\/\/twocups.cn\/index.php\/wp-json\/wp\/v2\/posts\/249"}],"collection":[{"href":"https:\/\/twocups.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/twocups.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/twocups.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/twocups.cn\/index.php\/wp-json\/wp\/v2\/comments?post=249"}],"version-history":[{"count":1,"href":"https:\/\/twocups.cn\/index.php\/wp-json\/wp\/v2\/posts\/249\/revisions"}],"predecessor-version":[{"id":465,"href":"https:\/\/twocups.cn\/index.php\/wp-json\/wp\/v2\/posts\/249\/revisions\/465"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/twocups.cn\/index.php\/wp-json\/wp\/v2\/media\/65"}],"wp:attachment":[{"href":"https:\/\/twocups.cn\/index.php\/wp-json\/wp\/v2\/media?parent=249"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/twocups.cn\/index.php\/wp-json\/wp\/v2\/categories?post=249"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/twocups.cn\/index.php\/wp-json\/wp\/v2\/tags?post=249"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}