什么是KMP算法（详解）

{"type":"doc","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"什么是KMP算法：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"KMP是三位大牛：D.E.Knuth、J.H.Morris和V.R.Pratt同时发现的。其中第一位就是《计算机程序设计艺术》的作者！！","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"KMP算法要解决的问题就是在字符串（也叫主串）中的模式（pattern）定位问题。说简单点就是我们平时常说的关键字搜索。模式串就是关键字（接下来称它为P），如果它在一个主串（接下来称为T）中出现，就返回它的具体位置，否则返回-1（常用手段）。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/29/29c6fb366c7c169c842cc17ac59cf39b.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"首先，对于这个问题有一个很单纯的想法：从左到右一个个匹配，如果这个过程中有某个字符不匹配，就跳回去，将模式串向右移动一位。这有什么难的？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们可以这样初始化：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81766a0b3bf8d87131284e128337c592.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"之后我们只需要比较i指针指向的字符和j指针指向的字符是否一致。如果一致就都向后移动，如果不一致，如下图：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d2/d271cc93c2f1423840def6e245eeb88a.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"A和E不相等，那就把i指针移回第1位（假设下标从0开始），j移动到模式串的第0位，然后又重新开始这个步骤：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/08/08cb453f3db7366fec3c58d9f27714d1.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于这个想法我们可以得到以下的程序：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":"cpp"},"content":[{"type":"text","text":"/**\n\n * 暴力破解法\n\n * @param ts 主串\n\n * @param ps 模式串\n\n * @return 如果找到，返回在主串中第一个字符出现的下标，否则为-1\n\n */\n\npublic static int bf(String ts, String ps) {\n\n char[] t = ts.toCharArray();\n\n char[] p = ps.toCharArray();\n\n int i = 0; // 主串的位置\n\n int j = 0; // 模式串的位置\n\n while (i < t.length && j < p.length) {\n\n if (t[i] == p[j]) { // 当两个字符相同，就比较下一个\n\n i++;\n\n j++;\n\n } else {\n\n i = i - j + 1; // 一旦不匹配，i后退\n\n j = 0; // j归0\n\n }\n\n }\n\n if (j == p.length) {\n\n return i - j;\n\n } else {\n\n return -1;\n\n }\n\n}","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面的程序是没有问题的，但不够好！","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果是人为来寻找的话，肯定不会再把i移动回第1位，因为主串匹配失败的位置前面除了第一个A之外再也没有A了，我们为什么能知道主串前面只有一个A？因为我们已经知道前面三个字符都是匹配的！（这很重要）。移动过去肯定也是不匹配的！有一个想法，i可以不动，我们只需要移动j即可，如下图：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4d/4d442f8784ff70c1050764af3fc9848e.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面的这种情况还是比较理想的情况，我们最多也就多比较了再次。但假如是在主串“SSSSSSSSSSSSSA”中查找“SSSSB”，比较到最后一个才知道不匹配，然后i回溯，这个的效率是显然是最低的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"大牛们是无法忍受“暴力破解”这种低效的手段的，于是他们三个研究出了KMP算法。其思想就如同我们上边所看到的一样：“利用已经部分匹配这个有效信息，保持i指针不回溯，通过修改j指针，让模式串尽量地移动到有效的位置。”","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所以，整个KMP的重点就在于当某一个字符与主串不匹配时，我们应该知道j指针要移动到哪？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"接下来我们自己来发现j的移动规律：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/da/da0a9590f6ee16862d2073df5d648bc0.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如图：C和D不匹配了，我们要把j移动到哪？显然是第1位。为什么？因为前面有一个A相同啊：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a7/a7b174f5639c94cecde714a5a99e4990.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如下图也是一样的情况：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e3/e36689070bfc97e4e699cd10e9e8d99b.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"可以把j指针移动到第2位，因为前面有两个字母是一样的：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c2/c28183de475d62b7f3f5b191c57ac480.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"至此我们可以大概看出一点端倪，当匹配失败时，j要移动的下一个位置k。存在着这样的性质：最前面的k个字符和j之前的最后k个字符是一样的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果用数学公式来表示是这样的","attrs":{}}]},{"type":"codeblock","attrs":{"lang":null},"content":[{"type":"text","text":"P[0 ~ k-1] == P[j-k ~ j-1]\n","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这个相当重要，如果觉得不好记的话，可以通过下图来理解：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/9b/9b17c56fde4e22d244bc1549d0b268ab.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"弄明白了这个就应该可能明白为什么可以直接将j移动到k位置了。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"因为:","attrs":{}}]},{"type":"codeblock","attrs":{"lang":null},"content":[{"type":"text","text":"当T[i] != P[j]时\n有T[i-j ~ i-1] == P[0 ~ j-1]\n由P[0 ~ k-1] == P[j-k ~ j-1]\n必然：T[i-k ~ i-1] == P[0 ~ k-1]","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"公式很无聊，能看明白就行了，不需要记住。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这一段只是为了证明我们为什么可以直接将j移动到k而无须再比较前面的k个字符。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"好，接下来就是重点了，怎么求这个（这些）k呢？因为在P的每一个位置都可能发生不匹配，也就是说我们要计算每一个位置j对应的k，所以用一个数组next来保存，next[j] = k，表示当T[i] != P[j]时，j指针的下一个位置。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ba/baddcaf043c24ab6e46062a6b484298c.jpeg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"很多教材或博文在这个地方都是讲得比较含糊或是根本就一笔带过，甚至就是贴一段代码上来，为什么是这样求？怎么可以这样求？根本就没有说清楚。而这里恰恰是整个算法最关键的地方。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":"cpp"},"content":[{"type":"text","text":"public static int[] getNext(String ps) {\n\n char[] p = ps.toCharArray();\n\n int[] next = new int[p.length];\n\n next[0] = -1;\n\n int j = 0;\n\n int k = -1;\n\n while (j < p.length - 1) {\n\n if (k == -1 || p[j] == p[k]) {\n\n next[++j] = ++k;\n\n } else {\n\n k = next[k];\n\n }\n\n }\n\n return next;\n\n}\n","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这个版本的求next数组的算法应该是流传最广泛的，代码是很简洁。可是真的很让人摸不到头脑，它这样计算的依据到底是什么？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"好，先把这个放一边，我们自己来推导思路，现在要始终记住一点，next[j]的值（也就是k）表示，当P[j] != T[i]时，j指针的下一步移动位置。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"先来看第一个：当j为0时，如果这时候不匹配，怎么办？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6db3efd5e9db83b7a17a305698bcf7be.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"像上图这种情况，j已经在最左边了，不可能再移动了，这时候要应该是i指针后移。所以在代码中才会有next[0] = -1;这个初始化。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果是当j为1的时候呢？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4b/4babe4a002d4bf3df1759a63fb84a4bd.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"显然，j指针一定是后移到0位置的。因为它前面也就只有这一个位置了~~~","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"下面这个是最重要的，请看如下图：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/38567666c7aa859bac474a24572e8887.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/26/2687d027ae132f1ca0f7aab19e381a8b.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"请仔细对比这两个图。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们发现一个规律：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":"cpp"},"content":[{"type":"text","text":"当P[k] == P[j]时，\n有next[j+1] == next[j] + 1","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"其实这个是可以证明的：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":"cpp"},"content":[{"type":"text","text":"因为在P[j]之前已经有P[0 ~ k-1] == p[j-k ~ j-1]。（next[j] == k）\n这时候现有P[k] == P[j]，我们是不是可以得到P[0 ~ k-1] + P[k] == p[j-k ~ j-1] + P[j]。\n即：P[0 ~ k] == P[j-k ~ j]，即next[j+1] == k + 1 == next[j] + 1。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这里的公式不是很好懂，还是看图会容易理解些。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"那如果P[k] != P[j]呢？比如下图所示：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/115fa2e15aa954d1b0a373fd855730ad.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"像这种情况，如果你从代码上看应该是这一句：k = next[k];为什么是这样子？你看下面应该就明白了。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e3/e32edc7ff6b3eda49b60daa957b67c86.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"现在你应该知道为什么要k = next[k]了吧！像上边的例子，我们已经不可能找到[ A，B，A，B ]这个最长的后缀串了，但我们还是可能找到[ A，B ]、[ B ]这样的前缀串的。所以这个过程像不像在定位[ A，B，A，C ]这个串，当C和主串不一样了（也就是k位置不一样了），那当然是把指针移动到next[k]啦。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了next数组之后就一切好办了，我们可以动手写KMP算法了：","attrs":{}}]},{"type":"codeblock","attrs":{"lang":"cpp"},"content":[{"type":"text","text":"public static int KMP(String ts, String ps) {\n\n char[] t = ts.toCharArray();\n\n char[] p = ps.toCharArray();\n\n int i = 0; // 主串的位置\n\n int j = 0; // 模式串的位置\n\n int[] next = getNext(ps);\n\n while (i < t.length && j < p.length) {\n\n if (j == -1 || t[i] == p[j]) { // 当j为-1时，要移动的是i，当然j也要归0\n\n i++;\n\n j++;\n\n } else {\n\n // i不需要回溯了\n\n // i = i - j + 1;\n\n j = next[j]; // j回到指定位置\n\n }\n\n }\n\n if (j == p.length) {\n\n return i - j;\n\n } else {\n\n return -1;\n\n }\n\n}\n","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"和暴力破解相比，就改动了4个地方。其中最主要的一点就是，i不需要回溯了。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"最后，来看一下上边的算法存在的缺陷。来看第一个例子：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f2/f291e033c738ed918176768f011a390f.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"显然，当我们上边的算法得到的next数组应该是[ -1，0，0，1 ]","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所以下一步我们应该是把j移动到第1个元素咯：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7a/7a96920ae0e8c038858a53380db5b0fd.png","alt":"在这里插入图片描述","title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"不难发现，这一步是完全没有意义的。因为后面的B已经不匹配了，那前面的B也一定是不匹配的，同样的情况其实还发生在第2个元素A上。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"显然，发生问题的原因在于P[j] == P[next[j]]。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所以我们也只需要添加一个判断条件即可：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":"cpp"},"content":[{"type":"text","text":"public static int[] getNext(String ps) {\n char[] p = ps.toCharArray();\n\n int[] next = new int[p.length];\n\n next[0] = -1;\n\n int j = 0;\n\n int k = -1;\n\n while (j < p.length - 1) {\n\n if (k == -1 || p[j] == p[k]) {\n\n if (p[++j] == p[++k]) { // 当两个字符相等时要跳过\n\n next[j] = next[k];\n\n } else {\n\n next[j] = k;\n\n }\n\n } else {\n\n k = next[k];\n\n }\n\n }\n\n return next;\n\n}","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}}]}