{"id":26301,"date":"2023-04-25T11:39:44","date_gmt":"2023-04-25T03:39:44","guid":{"rendered":"https:\/\/docs.pingcode.com\/?p=26301"},"modified":"2023-07-30T23:30:56","modified_gmt":"2023-07-30T15:30:56","slug":"%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84%e4%b8%adkmp%e7%ae%97%e6%b3%95%e6%98%af%e4%bb%80%e4%b9%88","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/26301.html","title":{"rendered":"\u6570\u636e\u7ed3\u6784\u4e2dKMP\u7b97\u6cd5\u662f\u4ec0\u4e48"},"content":{"rendered":"<blockquote class=\"wp-block-quote\">\n<p>KMP\u7b97\u6cd5\u662f\u4e00\u79cd\u6539\u8fdb\u7684\u5b57\u7b26\u4e32\u5339\u914d\u7b97\u6cd5\uff0c\u7531D.E.Knuth\uff0cJ.H.Morris\u548cV.R.Pratt\u63d0\u51fa\u7684\uff0c\u56e0\u6b64\u4eba\u4eec\u79f0\u5b83\u4e3a\u514b\u52aa\u7279\u2014\u83ab\u91cc\u65af\u2014\u666e\u62c9\u7279\u64cd\u4f5c\uff08\u7b80\u79f0KMP\u7b97\u6cd5\uff09\u3002KMP\u7b97\u6cd5\u662f\u5728 BF \u7b97\u6cd5\u57fa\u7840\u4e0a\u6539\u8fdb\u5f97\u5230\u7684\u7b97\u6cd5\u3002<\/p>\n<\/blockquote>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" alt=\"\" class=\"wp-image-26305\" decoding=\"async\" height=\"421\" sizes=\"(max-width: 680px) 100vw, 680px\" src=\"https:\/\/cdn-docs.pingcode.com\/wp-content\/uploads\/2023\/04\/\u6dfb\u52a0\u6807\u9898-11-15.png?x-oss-process=image\/auto-orient,1\/format,webp\" srcset=\"https:\/\/cdn-docs.pingcode.com\/wp-content\/uploads\/2023\/04\/\u6dfb\u52a0\u6807\u9898-11-15.png?x-oss-process=image\/auto-orient,1\/format,webp 680w, https:\/\/cdn-docs.pingcode.com\/wp-content\/uploads\/2023\/04\/\u6dfb\u52a0\u6807\u9898-11-15-300x186.png 300w\" width=\"680\"\/><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><strong>\u4e00\u3001\u6570\u636e\u7ed3\u6784\u4e2dKMP\u7b97\u6cd5<\/strong><\/h2>\n<h3 class=\"wp-block-heading\"><strong>KMP<\/strong><strong>\u7b97\u6cd5\u4ecb\u7ecd<\/strong><\/h3>\n<p>KMP\u7b97\u6cd5\u662f\u4e00\u79cd\u6539\u8fdb\u7684\u5b57\u7b26\u4e32\u5339\u914d\u7b97\u6cd5\uff0c\u7531D.E.Knuth\uff0cJ.H.Morris\u548cV.R.Pratt\u63d0\u51fa\u7684\uff0c\u56e0\u6b64\u4eba\u4eec\u79f0\u5b83\u4e3a\u514b\u52aa\u7279\u2014\u83ab\u91cc\u65af\u2014\u666e\u62c9\u7279\u64cd\u4f5c\uff08\u7b80\u79f0KMP\u7b97\u6cd5\uff09\u3002KMP\u7b97\u6cd5\u662f\u5728 BF \u7b97\u6cd5\u57fa\u7840\u4e0a\u6539\u8fdb\u5f97\u5230\u7684\u7b97\u6cd5\u3002\u5b66\u4e60 BF \u7b97\u6cd5\u6211\u4eec\u77e5\u9053\uff0c\u8be5\u7b97\u6cd5\u7684\u5b9e\u73b0\u8fc7\u7a0b\u5c31\u662f \u201c\u50bb\u74dc\u5f0f\u201d \u5730\u7528\u6a21\u5f0f\u4e32\uff08\u5047\u5b9a\u4e3a\u5b50\u4e32\u7684\u4e32\uff09\u4e0e\u4e3b\u4e32\u4e2d\u7684\u5b57\u7b26\u4e00\u4e00\u5339\u914d\uff0c\u5339\u914d\u4e0d\u6210\u529f\u5219\u8fd4\u56de\u5230\u4e0a\u4e00\u6b21\u4e0e\u4e3b\u4e32\u5339\u914d\u7684\u4e0b\u4e00\u4f4d\u5b57\u7b26\u8fdb\u884c\u5339\u914d\uff0c\u7b97\u6cd5\u6267\u884c\u6548\u7387\u4e0d\u9ad8\u3002<\/p>\n<h3 class=\"wp-block-heading\"><strong>KMP<\/strong><strong>\u7b97\u6cd5\u7684\u89e3\u51b3\u9898\u578b<\/strong><\/h3>\n<p>KMP\u7b97\u6cd5\u662f\u5728\u6570\u636e\u7ed3\u6784\u4e2d\u4e24\u4e2a\u5b57\u7b26\u4e32\u76f8\u4e92\u5339\u914d\u884d\u751f\u51fa\u6765\u7684\u7b97\u6cd5\u3002KMP\u7b97\u6cd5\u7684\u4f5c\u7528\u662f\u5728\u4e00\u4e2a\u5df2\u77e5\u5b57\u7b26\u4e32\u4e2d\u67e5\u627e\u5b50\u4e32\u7684\u4f4d\u7f6e,\u4e5f\u53eb\u505a\u4e32\u7684\u6a21\u5f0f\u5339\u914d\u3002\u4f8b\u5982\uff0c\u5bf9\u4e3b\u4e32 A\uff08\u201cABCABCE\u201d\uff09\u548c\u6a21\u5f0f\u4e32 B\uff08\u201cABCE\u201d\uff09\u8fdb\u884c\u6a21\u5f0f\u5339\u914d\uff0c\u5982\u679c\u4eba\u4e3a\u53bb\u5224\u65ad\uff0c\u4ec5\u9700\u5339\u914d\u4e24\u6b21\u3002\u867d\u7136\u5728\u4ee5\u4e0a\u5b57\u7b26\u8f83\u5c11\u7684\u4e32\u4e2d\u4eba\u4e3a\u5339\u914d\u5f88\u5bb9\u6613\uff0c\u4f46\u662f\u8ba9\u8ba1\u7b97\u673a\u6765\u5339\u914d\u5c31\u76f8\u5bf9\u6162\u4e00\u4e9b\uff0c\u4f46\u662f\u5f53\u5b57\u7b26\u4e32\u4e2d\u7684\u5b57\u7b26\u975e\u5e38\u591a\u7684\u65f6\u5019\uff0c\u5c31\u4e0d\u53ef\u80fd\u4eba\u4e3a\u53bb\u5339\u914d\u3002\u6240\u4ee5\u6253\u94c1\u8fd8\u9700\u81ea\u8eab\u786c\uff0c\u6211\u4eec\u628a\u8fd9\u79cd\u67af\u71e5\u7684\u4e8b\u4ee5\u4e00\u5b9a\u7684\u7b97\u6cd5\u4ea4\u7ed9\u8ba1\u7b97\u673a\u5904\u7406\u3002<\/p>\n<h3 class=\"wp-block-heading\"><strong>KMP<\/strong><strong>\u7b97\u6cd5\u76f8\u6bd4BF\u7b97\u6cd5\u7684\u6539\u8fdb<\/strong><\/h3>\n<p>\u6bcf\u5f53\u4e00\u8d9f\u5339\u914d\u8fc7\u7a0b\u4e2d\u51fa\u73b0\u5b57\u7b26\u6bd4\u8f83\u4e0d\u7b49\u65f6\uff0c\u65e0\u9700\u56de\u6eafi\u6307\u9488\uff08\u5373\u65e0\u9700\u5c06i\u6307\u9488\u5b8c\u5168\u9000\u56de\u81f3i-j+1\uff09\uff0c\u800c\u662f\u5229\u7528\u5df2\u7ecf\u5f97\u5230\u7684\u201c\u90e8\u5206\u5339\u914d\u201d\u7684\u7ed3\u679c\u5c06\u6a21\u5f0f\u5411\u53f3\u201c\u6ed1\u52a8\u201d\u5c3d\u53ef\u80fd\u8fdc\u7684\u4e00\u6bb5\u8ddd\u79bb\u540e\uff0c\u7ee7\u7eed\u8fdb\u884c\u6bd4\u8f83\u3002<strong><\/strong><\/p>\n<p>\u9700\u8981\u89e3\u51b3\u7684\u95ee\u9898\uff1a\u5f53\u4e3b\u4e32\u4e2d\u7684\u7b2ci\u4e2a\u5b57\u7b26\u4e0e\u6a21\u5f0f\u4e2d\u7b2cj\u4e2a\u5b57\u7b26\u6bd4\u8f83\u4e0d\u76f8\u7b49\u65f6\uff0c\u4e3b\u4e32\u4e2d\u7b2ci\u4e2a\u5b57\u7b26\uff08i\u6307\u9488\u4e0d\u56de\u6eaf\uff09\u5e94\u4e0e\u6a21\u5f0f\u4e2d\u54ea\u4e2a\u5b57\u7b26\u518d\u6bd4\u8f83\uff1f\u2014-\u5047\u8bbe\u4ece\u4e3b\u4e32\u4e2d\u7b2ci\u4e2a\u5b57\u7b26\u4e0e\u6a21\u5f0f\u4e2d\u7684\u7b2ck\u4e2a\u5b57\u7b26\u518d\u8fdb\u884c\u6bd4\u8f83<\/p>\n<p>\u5b83\u662f\u5219\u5462\u6837\u6765\u6d88\u9664\u56de\u6eaf\u7684\u5462\uff1f\u5c31\u662f\u56e0\u4e3a\u5b83\u63d0\u53d6\u5e76\u8fd0\u7528\u4e86\u52a0\u901f\u5339\u914d\u7684\u4fe1\u606f\uff01<\/p>\n<p>\u3000\u3000\u8fd9\u79cd\u4fe1\u606f\u5c31\u662f\u5bf9\u4e8e\u6bcf\u6a21\u5f0f\u4e32 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class=\"wp-block-heading\"><strong>\u4e8c\u3001KMP\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6<\/strong><\/h2>\n<p>\u4e3b\u8981\u7531\u4e24\u90e8\u5206\u7ec4\u6210\uff1a\u9884\u5904\u7406\u90e8\u5206\u548c\u5339\u914d\u90e8\u5206\u3002<\/p>\n<ol start=\"1\" type=\"1\">\n<li>\u9884\u5904\u7406\u90e8\u5206\uff1a\u5728\u8fd9\u4e00\u6b65\uff0c\u7b97\u6cd5\u8ba1\u7b97\u6a21\u5f0f\u4e32\u7684\u6700\u957f\u516c\u5171\u524d\u7f00\u548c\u540e\u7f00\uff08\u4e5f\u79f0\u4e3a\u90e8\u5206\u5339\u914d\u8868\u6216\u5931\u6548\u51fd\u6570\uff09\u3002\u8fd9\u4e00\u6b65\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(m)\uff0c\u56e0\u4e3a\u5b83\u904d\u5386\u4e86\u6574\u4e2a\u6a21\u5f0f\u4e32\u3002<\/li>\n<li>\u5339\u914d\u90e8\u5206\uff1a\u5728\u8fd9\u4e00\u6b65\uff0c\u7b97\u6cd5\u5728\u76ee\u6807\u6587\u672c\u4e2d\u67e5\u627e\u6a21\u5f0f\u4e32\u3002\u5728\u6700\u574f\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e00\u6b65\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n)\u3002\u8fd9\u662f\u56e0\u4e3a\u7b97\u6cd5\u5728\u8fdb\u884c\u6bd4\u8f83\u65f6\uff0c\u53ef\u4ee5\u6839\u636e\u5931\u6548\u51fd\u6570\u8df3\u8fc7\u4e0d\u5339\u914d\u7684\u5b57\u7b26\uff0c\u56e0\u6b64\uff0c\u5b83\u4e0d\u9700\u8981\u5bf9\u6bcf\u4e2a\u5b57\u7b26\u8fdb\u884c\u9010\u4e00\u6bd4\u8f83\u3002<\/li>\n<\/ol>\n<p>\u7efc\u5408\u8003\u8651\u8fd9\u4e24\u90e8\u5206\uff0cKMP\u7b97\u6cd5\u7684\u603b\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(m+n)\u3002\u4e0e\u6734\u7d20\u7684\u5b57\u7b26\u4e32\u5339\u914d\u7b97\u6cd5\u76f8\u6bd4\uff08\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(mn)\uff09\uff0cKMP\u7b97\u6cd5\u5177\u6709\u66f4\u9ad8\u7684\u6548\u7387\uff0c\u5c24\u5176\u5728\u5904\u7406\u5927\u91cf\u6570\u636e\u65f6\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"KMP\u7b97\u6cd5\u662f\u4e00\u79cd\u6539\u8fdb\u7684\u5b57\u7b26\u4e32\u5339\u914d\u7b97\u6cd5\uff0c\u7531D.E.Knuth\uff0cJ.H.Morris\u548cV.R.Pratt\u63d0\u51fa\u7684\uff0c\u56e0 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