{"id":21,"date":"2011-10-31T23:07:00","date_gmt":"2011-10-31T15:07:00","guid":{"rendered":"https:\/\/andy9999678.me\/blog\/?p=21"},"modified":"2021-09-27T02:02:31","modified_gmt":"2021-09-26T18:02:31","slug":"kmp%e7%9a%84%e7%a7%91%e6%99%ae%e6%96%87%e7%ab%a0-%e4%b8%ba%e4%bb%80%e4%b9%88kmp%e6%8f%90%e9%ab%98%e4%ba%86%e6%95%88%e7%8e%87","status":"publish","type":"post","link":"https:\/\/andy9999678.me\/blog\/archives\/21","title":{"rendered":"KMP\u7684\u79d1\u666e\u6587\u7ae0: \u4e3a\u4ec0\u4e48KMP\u63d0\u9ad8\u4e86\u6548\u7387"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">2021.09.26 \u8865\u5145\uff1a\u539f\u6587\u5728 <strong>2011\u5e7410\u670831\u65e5<\/strong>\u53d1\u8868\u5728\u4e4b\u524d\u7684 Blog \u4e0a\uff0c\u672c\u6587\u662f\u57fa\u4e8e Internet Archive \u4e0a\u9762\u7684<strong><a href=\"https:\/\/web.archive.org\/web\/20120505035557\/http:\/\/www.atarss.com\/blog\/\" data-type=\"URL\" data-id=\"https:\/\/web.archive.org\/web\/20120505035557\/http:\/\/www.atarss.com\/blog\/\">\u8bb0\u5f55<\/a><\/strong>\u624b\u52a8\u8fc1\u79fb\u8fc7\u6765\u7684\u5185\u5bb9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u4e3a\u6b63\u6587\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u6587\u539f\u521b\uff0c\u8f6c\u8f7d\u8bf7\u6ce8\u660e\u51fa\u5904\uff1a&nbsp;<a href=\"http:\/\/atarss.com\/blog\/?p=193\">http:\/\/atarss.com\/blog\/?p=193<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8ba1\u79d1\u65e0\u80fd\u8005\u65e0\u89c6\u7b2c\u4e00\u6bb5\uff0c\u7740\u6025\u5199\u4f5c\u4e1a\u7684\u5efa\u8bae\u4e0d\u7528\u770b\u7b2c\u4e09\u90e8\u5206\uff0c\u76f4\u63a5\u7528\u7b2c\u4e8c\u6bb5\u7684\u65b9\u6cd5\u3002<\/p>\n\n\n\n<p 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class=\"wp-image-22\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6d45\u7eff\u8272\u7684\u8868\u793a\u5df2\u7ecf\u88ab\u5339\u914d\u7684\u5b57\u7b26\uff0c\u6211\u4eec\u5b9a\u4e49\u6b63\u5728\u88ab\u5339\u914d\u7684\u957f\u5b57\u7b26\u4e32\u91cc\u9762\u7684\u4f4d\u7f6e\u662fi=5\uff0c\u8981\u641c\u7d22\u7684\u6a21\u5f0f\u4e32\u5df2\u7ecf\u5339\u914d\u5230j=6\u7b2c6\u4e2a\u5b57\u7b26\u800c\u4e14\u4e0e\u539f\u59cb\u7684\u5b57\u7b26\u4e32\u4e0d\u5339\u914d\u3002\u6309\u7167\u6734\u7d20\u7684\u5339\u914d\u7b97\u6cd5\uff0c\u6211\u4eec\u5e94\u8be5\u8ba9i++\uff0c\u5373\u4ecei=6\u5f00\u59cb\u5339\u914d\u3002\u4f46\u662f\u6211\u4eec\u5df2\u7ecf\u77e5\u9053i\u4ece5~9\u4e0eB\u4e32\u7684j=1~5\u662f\u5b8c\u5168\u76f8\u540c\u7684\u3002\u56e0\u6b64\u5373\u4f7f\u6211\u4eec\u4e0d\u77e5\u9053A\u4e32\u7684\u5185\u5bb9\uff0c\u53ea\u901a\u8fc7B\u4e32\u7684\u5185\u5bb9\u4ee5\u53ca\u6211\u4eec\u5df2\u7ecf\u5339\u914d\u5230\u7b2c6\u4e2a\u5b57\u7b26\u8fd9\u4e24\u9879\u6570\u636e\uff0c\u5c31\u53ef\u4ee5\u77e5\u9053\u4ecei\u7684\u4e0b\u4e00\u9879\u6570\u636e\u4e00\u5b9a\u662f\u4e0d\u5339\u914d\u7684\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"157\" src=\"https:\/\/andy9999678.me\/blog\/wp-content\/uploads\/2021\/09\/kmp-2.png\" alt=\"\" class=\"wp-image-23\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"422\" height=\"160\" src=\"https:\/\/andy9999678.me\/blog\/wp-content\/uploads\/2021\/09\/kmp-3.png\" alt=\"\" class=\"wp-image-24\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u540c\u7406\u6211\u4eec\u77e5\u9053\u4e3b\u4e32\u5728i=7\u65f6\u7684\u5339\u914d\u53ef\u80fd\u662f\u6210\u529f\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u8bbe\u8ba1\u7b97\u6cd5\u4e0d\u53bb\u5339\u914di=6\u65f6\u7684\u60c5\u51b5\u800c\u76f4\u63a5\u8df3\u5230i=7\u53bb\u5339\u914d\uff0c\u800c\u4e14\u53f3\u79fb2\u4f4d\u8fd9\u4e2a\u6570\u5b572\u53ea\u662f\u901a\u8fc7B\u4e32(\u8981\u641c\u7d22\u7684\u4e32)\u7684\u81ea\u6211\u5339\u914d\u6765\u5b8c\u6210\u7684\uff0c\u4e5f\u5c31\u662f\u53ef\u4ee5\u5728\u5339\u914d\u524d\u5b8c\u6210\u8ba1\u7b97\u3002\u800c\u8fd9\u5c31\u662fKMP\u8f83\u6734\u7d20\u5339\u914d\u7b97\u6cd5\u7684\u4f18\u5316\u4e4b\u5904\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.\u5982\u4f55\u8ba1\u7b97\u5f53\u4e0d\u5339\u914d\u65f6\u4e3b\u4e32\u8981\u79fb\u52a8\u591a\u5c11\u4f4d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f9d\u65e7\u8981\u641c\u7d22\u8fd9\u4e2a\u4e32\u201dababaca\u201d\uff0c\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u8981\u8df3\u8fc7\u591a\u5c11\u4e2a\u5b57\u7b26\u7684\u5b57\u7b26\u6570\u91cf\u662f\u4e0e\u8981\u641c\u7d22\u7684\u5b57\u7b26\u4e32(A\u4e32)\u65e0\u5173\u7684\uff0c\u5b9e\u8d28\u662f\u8981\u641c\u7d22\u7684\u4e32(B\u4e32)\u7684\u81ea\u6211\u5339\u914d\u3002\u800c\u8fd9\u4e2a\u4fe1\u606f\u53ef\u4ee5\u88ab\u9884\u5148\u8ba1\u7b97\u51fa\u6765\u5e76\u88ab\u5b58\u50a8\u8d77\u6765\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bcf\u6b21\u504f\u79fb\u591a\u5c11\u4f4d\u663e\u7136\u4e0e\u5339\u914d\u5230B\u4e32\u7b2c\u51e0\u4e2a\u5b57\u7b26\u65f6\u5f00\u59cb\u4e0d\u5339\u914d\u7684j\u4f4d\u7f6e\u6709\u5173\uff0c\u56e0\u6b64\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a\u6570\u7ec4\u6765\u5b58\u50a8\u8fd9\u4e2a\u504f\u79fb\u91cf\u7684\u4fe1\u606f\uff0c\u5b9a\u4e49\u4e3aD[1..t]\uff0ct\u4e3aB\u4e32\u7684\u957f\u5ea6\uff0c\u4e0b\u6807\u4ece1\u5f00\u59cb\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u203b\u6211\u4eec\u524d\u63d0\u5047\u8bbe\uff0c\u6bcf\u4e2a\u5b57\u7b26\u53ea\u80fd\u8bfb\u53d6\u4e00\u6b21\uff0c\u771f\u6b63\u7684\u5b57\u7b26\u6307\u9488\u4e0d\u80fd\u540e\u9000\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b9e\u8d28\u5373\u4e3a\uff0c\u5047\u8bbe\u5f53\u5339\u914d\u5230j=n\u65f6\u4e0d\u5339\u914d\uff0c\u5373j\u4ece1~(n-1)\u90fd\u662f\u5339\u914d\u7684\uff0c\u90a3\u4e48\u504f\u79fb\u91cf\u5c31\u662f\u5b57\u7b26\u4e32\u4ece\u540e\u5411\u524d\u81ea\u6211\u5339\u914d\u65f6\u5230\u8fbe\u524d\u9762\u4e4b\u524d\u6240\u80fd\u8fbe\u5230\u7684\u6700\u5927\u7684\u4f4d\u7f6e\u3002\u4e3e\u4f8b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1050\" height=\"193\" src=\"https:\/\/andy9999678.me\/blog\/wp-content\/uploads\/2021\/09\/kmp-4.png\" alt=\"\" class=\"wp-image-25\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6309\u627e\u4ece\u4e0b\u5f80\u4e0a\u770b\u7684\u987a\u5e8f\u5c31\u80fd\u627e\u5230\u504f\u79fb\u91cf\uff0c\u663e\u7136\u6700\u957f\u7684\u5339\u914d\u7684\u504f\u79fb\u91cf\u4e3a2\u3002\u6309\u7167\u8fd9\u79cd\u65b9\u6cd5\u5c31\u80fd\u627e\u5230\u6240\u6709\u7684\u504f\u79fb\u6570\u7ec4\u7684\u503c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u82e5j=1\u65f6\u4e0d\u5339\u914d\uff0c\u6beb\u65e0\u60ac\u5ff5\uff0c\u504f\u79fb\u91cf\u4e3a1,\uff1b<br>\u82e5j=2\u65f6\u4e0d\u5339\u914d\uff0c\u5219\u53f3\u79fb\u4e00\u4f4d\u4e5f\u6ca1\u6709\u610f\u4e49\uff0c\u76f4\u63a5\u53f3\u79fb\u4e24\u4f4d\uff0c\u504f\u79fb\u91cf\u4e3a2\uff1b<br>\u82e5j=3\u65f6\u4e0d\u5339\u914d\uff0ci=3\u4e0ej=1\u65f6\u76f8\u540c\uff0c\u56e0\u6b64\u504f\u79fb\u91cf\u4e3a3-1=2\uff1b<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"295\" height=\"148\" src=\"https:\/\/andy9999678.me\/blog\/wp-content\/uploads\/2021\/09\/kmp-5.png\" alt=\"\" class=\"wp-image-26\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"338\" height=\"153\" src=\"https:\/\/andy9999678.me\/blog\/wp-content\/uploads\/2021\/09\/kmp-6.png\" alt=\"\" class=\"wp-image-27\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u82e5j=4\u65f6\u4e0d\u5339\u914d\uff0c\u540c\u7406\u5f97\u504f\u79fb\u91cf\u4e3a2\uff1b<br>j=5\u65f6\u4e0a\u9762\u5df2\u7ecf\u5206\u6790\u8fc7\uff0c\u504f\u79fb\u91cf\u4e3a5-3=2\uff1b<br>j=6\u65f6\uff0c\u540c\u7406\uff0c\u504f\u79fb\u91cf\u4e3a6\uff1b<br>j=7\u65f6\uff0c\u504f\u79fb\u91cf\u4e3a7-1=6\uff1b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u8ba1\u7b97\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u77e5\u9053\uff0c\u771f\u6b63\u627e\u5230\u7684\u5e76\u4e0d\u662f\u504f\u79fb\u91cf\uff0c\u800c\u662f\u6700\u957f\u771f\u5b57\u4e32\u7684\u957f\u5ea6\u3002\u6211\u4eec\u6210\u8fd9\u4e2a\u5173\u4e8ej\u7684\u6570\u7ec4(\u51fd\u6570)\u4e3a<strong>\u524d\u7f00\u51fd\u6570<\/strong>Pi[j]\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.\u524d\u7f00\u51fd\u6570\u7684\u9012\u63a8\u8ba1\u7b97<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6839\u636e\u4e0a\u9762\u7684\u7b97\u6cd5\uff0c\u6211\u4eec\u540c\u65f6\u5f97\u5230\u524d\u7f00\u51fd\u6570\u7684\u503c<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"897\" height=\"118\" src=\"https:\/\/andy9999678.me\/blog\/wp-content\/uploads\/2021\/09\/kmp-7.png\" alt=\"\" class=\"wp-image-28\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0b\u9762\u8bf4\u660e\u9012\u63a8\u7684\u8fc7\u7a0b\uff1a<br>\u5047\u8bbe\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u4e86j=1~4\u65f6Pi[j]\u7684\u503c\u4e86\uff0c\u5982\u4f55\u63a8\u5f97Pi[5]\u548cPi[6]\u5462\uff1f<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"82\" src=\"https:\/\/andy9999678.me\/blog\/wp-content\/uploads\/2021\/09\/kmp-8.png\" alt=\"\" class=\"wp-image-29\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pi[4]=2\uff0c\u8bf4\u660e\u5b57\u7b26\u4e32B[1..2]\u4e0eB[3..4]\u76f8\u540c\uff0c\u53c8B[5]==B[3]\uff0c\u6240\u4ee5\uff0cP[5]=P[4]+1=3\uff1b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u800cPi[6]\u5374\u4e0d\u7b49\u4e8ePi[5]+1\uff0c\u8fd9\u662f\u56e0\u4e3aB[4]\u2260B[6]\uff0c\u56e0\u6b64\u6ca1\u6cd5\u901a\u8fc7Pi[5]+1\u5f97\u5230Pi[3]\uff0c\u4f46\u540c\u65f6\uff0cB[1],B[3],B[5]\u5747\u4e3a\u5b57\u7b26\u2019a\u2019\uff0c\u6216\u8bb8\u8fd8\u53ef\u80fd\u901a\u8fc7Pi[3]\u6216Pi[1]\u5f97\u5230Pi[6]\uff0c\u4f46\u4e00\u6b21\u6b21\u5339\u914d\u90fd\u53d1\u73b0B[6]\u4e0d\u7b49\u4e8eB[4]\u4e14B[6]\u4e0d\u7b49\u4e8eB[2]\uff0c\u8fd9\u65f6\uff0cPi[6]\u53ea\u80fd\u662f0\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u62bd\u8c61\u4e00\u4e0b\uff0c\u5c31\u5f97\u5230Pi[j]\u7684\u7b97\u6cd5\uff1a<br>\u5148\u7528\u4e00\u4e2a\u4e34\u65f6\u53d8\u91cfT=Pi[j-1]<br>\u82e5B[T] == B[j]\uff0c\u90a3\u4e48Pi[j] = Pi[j-1]<br>\u5426\u5219\uff0cT=Pi[T]\uff0c\u7ee7\u7eed\u4e0a\u9762\u7684\u64cd\u4f5c\uff0c\u76f4\u5230Pi[T] == 0\uff0c\u8fd9\u65f6Pi[j]=0\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u540e\u9644\u4e0a\u8ba1\u7b97Pi[6]\u7684\u793a\u610f\u56fe:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"906\" height=\"359\" src=\"https:\/\/andy9999678.me\/blog\/wp-content\/uploads\/2021\/09\/kmp-9.png\" alt=\"\" class=\"wp-image-30\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u540e\u4e00\u90e8\u5206\u53c2\u8003\u4e86M67\u7684\u6587\u7ae0\uff0c\u5728\u6b64\u5bf9\u5176\u8868\u793a\u611f\u8c22\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/web.archive.org\/web\/20120505035557\/http:\/\/www.matrix67.com\/blog\/archives\/115\">http:\/\/www.matrix67.com\/blog\/archives\/115<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>2021.09.26 \u8865\u5145\uff1a\u539f\u6587\u5728 2011\u5e7410\u670831\u65e5\u53d1\u8868\u5728\u4e4b\u524d\u7684 Blog \u4e0a\uff0c\u672c\u6587\u662f\u57fa\u4e8e Intern &hellip; <a href=\"https:\/\/andy9999678.me\/blog\/archives\/21\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">KMP\u7684\u79d1\u666e\u6587\u7ae0: \u4e3a\u4ec0\u4e48KMP\u63d0\u9ad8\u4e86\u6548\u7387<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-21","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/andy9999678.me\/blog\/wp-json\/wp\/v2\/posts\/21","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/andy9999678.me\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/andy9999678.me\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/andy9999678.me\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/andy9999678.me\/blog\/wp-json\/wp\/v2\/comments?post=21"}],"version-history":[{"count":1,"href":"https:\/\/andy9999678.me\/blog\/wp-json\/wp\/v2\/posts\/21\/revisions"}],"predecessor-version":[{"id":31,"href":"https:\/\/andy9999678.me\/blog\/wp-json\/wp\/v2\/posts\/21\/revisions\/31"}],"wp:attachment":[{"href":"https:\/\/andy9999678.me\/blog\/wp-json\/wp\/v2\/media?parent=21"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/andy9999678.me\/blog\/wp-json\/wp\/v2\/categories?post=21"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/andy9999678.me\/blog\/wp-json\/wp\/v2\/tags?post=21"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}