From c28ef2546e54a3b8cf1dcce8f9ddf30c59559d14 Mon Sep 17 00:00:00 2001 From: ShusenTang Date: Tue, 25 Feb 2020 21:23:52 +0800 Subject: [PATCH] add 28. Implement strStr() :beer: --- README.md | 1 + solutions/28. Implement strStr().md | 175 ++++++++++++++++++++++++++++ solutions/img/28/kmp.png | Bin 0 -> 25943 bytes solutions/img/28/sunday1.png | Bin 0 -> 32964 bytes solutions/img/28/sunday2.png | Bin 0 -> 34940 bytes solutions/img/28/sunday3.png | Bin 0 -> 29042 bytes 6 files changed, 176 insertions(+) create mode 100644 solutions/28. Implement strStr().md create mode 100644 solutions/img/28/kmp.png create mode 100644 solutions/img/28/sunday1.png create mode 100644 solutions/img/28/sunday2.png create mode 100644 solutions/img/28/sunday3.png diff --git a/README.md b/README.md index ea67920..d6f1628 100644 --- a/README.md +++ b/README.md @@ -34,6 +34,7 @@ My LeetCode solutions with Chinese explanation. 我的LeetCode中文题解。 | 24 |[Swap Nodes in Pairs](https://leetcode.com/problems/swap-nodes-in-pairs)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/24.%20Swap%20Nodes%20in%20Pairs.md)|Medium| | | 26 |[Remove Duplicates from Sorted Array](https://leetcode.com/problems/remove-duplicates-from-sorted-array)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/26.%20Remove%20Duplicates%20from%20Sorted%20Array.md)|Easy| | | 27 |[Remove Element](https://leetcode.com/problems/remove-element)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/27.%20Remove%20Element.md)|Easy| | +| 28 |[Implement strStr()](https://leetcode.com/problems/implement-strstr/)|[C++](solutions/28.%20Implement%20strStr().md)|Easy| | | 29 |[Divide Two Integers](https://leetcode.com/problems/divide-two-integers)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/29.%20Divide%20Two%20Integers.md)|Medium| | | 31 |[Next Permutation](https://leetcode.com/problems/next-permutation)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/31.%20Next%20Permutation.md)|Medium| | | 34 |[Find First and Last Position of Element in Sorted ](https://leetcode.com/problems/find-first-and-last-position-of-element-in-sorted-array/)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/34.%20Find%20First%20and%20Last%20Position%20of%20Element%20in%20Sorted%20Array.md)|Medium| | diff --git a/solutions/28. Implement strStr().md b/solutions/28. Implement strStr().md new file mode 100644 index 0000000..4c65664 --- /dev/null +++ b/solutions/28. Implement strStr().md @@ -0,0 +1,175 @@ +# [28. Implement strStr()](https://leetcode.com/problems/implement-strstr/) + +# 思路 + +字符串匹配。 + +## 思路一、暴力 + +用一个两层循环暴力匹配,可能测试样例比较弱,所以亲测时间并不慢(8ms)。 + +时间复杂度O(mn),空间复杂度O(1) + +## 思路二、KMP + +字符串匹配经典的解法应该就是KMP(Knuth-Morris-Pratt)算法了,与暴力匹配(每次失配时,回到模式串开头重新匹配)不同,**KMP的核心思想就是每次失配时,根据模式串的特点,将模式串回退到适当的位置。** + + +先来定义next数组: + +* `next[i]`表示模式串中前i个字符串(即P[0,...,i-1])中相同前缀后缀的最大长度,`next[0]`和`next[1]`固定为-1和0。 + +举例: +* 若`next[5] = 2`,则说明`P[0,1] == P[3,4]` +* 又如`abcabd`的`next = {-1, 0, 0, 0, 1, 2}` + + +若某个模式串P如下图所示,若匹配到`P[k]`与待匹配的字符串`S[i]`失配,即`P[k]!=S[i]`;对于暴力匹配来说,我们需要从头开始匹配P和S,即从`P[0]`开始匹配;但是由于我们知道了蓝色部分的子串是相等的,所以我们可以从`P[next[k]]`开始匹配。 + +
+ +
+
一个模式串P的示意图,颜色相同的子串相等
+ + +所以问题就是如何求next数组,仔细分析一下下图也很简单,如果我们求得了`next[0,...,j]`, + +* 令`k = next[j]`, 如果`P[j] == P[k]`,那么`next[j+1] = k + 1`; +* 否则,令`k = next[k]`,重复上述过程; + +此外,next还可以优化,因为如果`P[k] == P[next[k]]`,那么如果`P[k]`与待匹配的字符串`S[i]`失配,那么`P[next[k]]`肯定还是与`S[i]`失配,所以如果`P[k] == P[next[k]]`,我们可更新 `next[k] = next[next[k]]`。 + +关于KMP比较详细的介绍可参考[从头到尾彻底理解KMP](https://blog.csdn.net/v_july_v/article/details/7041827)。 + +KMP算法时间复杂度为O(m+n),空间复杂度为O(n),其中n为模式串的长度 + +## 思路三、Sunday + +关于字符串匹配还有比KMP更好理解的算法,叫做Sunday算法。 + +参考[字符串匹配——Sunday算法](https://blog.csdn.net/q547550831/article/details/51860017),举个例子来说明: + +* 刚开始时,把模式串与主串左边对齐: +
+ +
+ +* 结果发现在第2个字符处发现不匹配,不匹配时**关注主串中参加匹配的最末位字符的下一位字符**,即标粗的字符 i,因为模式串search中并不存在i,所以模式串直接跳过一大片,向右移动位数 = 匹配串长度 + 1 = 6 + 1 = 7,从 i 之后的那个字符(即字符n)开始下一步的匹配,如下图 +
+ +
+ +* 结果第一个字符就不匹配,再看主串中参加匹配的最末位字符的下一位字符,是 r,它在模式串位于倒数第3位(如果模式串有多个 r 我们应该以最后一个为准,因为那样移动次数较少才不会错过),于是把模式串向右移动3位(m - 3 = 6 - 3 = r 到模式串末尾的距离 + 1 = 2 + 1 =3),使两个 r 对齐,如下 +
+ +
+ +* 匹配成功。 + +可见我们需要一个数组,记录了某个字符在模式串中最后一次出现的位置到末尾的距离,由于ASCII用0-127来编码字符,所以我们可以用一个长度为128的数组,即代码中的move数组。 + +平均复杂度O(m+n),move数组的大小时固定的,所以可认为空间复杂度O(1) + +最坏情况下,时间复杂度为O(mn),例如主串为baaaabaaaabaaaabaaaa而模式串为aaaaa。 + +## 思路四、Boyer-Moore + +实际应用最多字符串匹配算法貌似是Boyer-Moore算法,有兴趣的可以去看看: +* [字符串匹配的Boyer-Moore算法](https://www.ruanyifeng.com/blog/2013/05/boyer-moore_string_search_algorithm.html); +* [BM算法和Sunday快速字符串匹配算法](https://www.cnblogs.com/Philip-Tell-Truth/p/5185267.html)。 + +# C++ +## 思路一 +``` C++ +class Solution { +public: + int strStr(string haystack, string needle) { + if (needle.empty()) return 0; + int m = haystack.size(), n = needle.size(); + if (m < n) return -1; + for (int i = 0; i <= m - n; ++i) { + int j = 0; + for (j = 0; j < n; ++j) { + if (haystack[i + j] != needle[j]) break; + } + if (j == n) return i; + } + return -1; + } +}; +``` + + +## 思路二 + +``` C++ +class Solution { +private: + vectorcompute_next(const string& pattern){ + int pn = pattern.size(); + vectornext(pn, 0); next[0] = -1; + + for(int i = 2; i < pn; i++){ + int j = next[i-1]; + while(j >= 0 && pattern[j] != pattern[i-1]) j = next[j]; + next[i] = j + 1; + } + + // // next数组优化 + // for(int i = 2; i < pn; i++){ + // int t1 = i, t2 = next[i]; + // while(t2 >= 0 && pattern[t1] == pattern[t2]){ + // t1 = t2; + // t2 = next[t2]; + // } + // next[i] = t2; + // } + return next; + } +public: + int strStr(string haystack, string needle) { + int sn = haystack.size(), pn = needle.size(); + if(!pn) return 0; + if(sn < pn) return -1; + vectornext = compute_next(needle); + + int i = 0, j = 0; + while(i < sn){ + if(j == -1 || haystack[i] == needle[j]){ + i++; + j++; + if(j == pn) return i - pn; + } + else j = next[j]; + } + + return -1; + } +}; +``` + +## 思路三 +``` C++ +class Solution { +public: + int strStr(string haystack, string needle) { + int sn = haystack.size(), pn = needle.size(); + if(!pn) return 0; + if(sn < pn) return -1; + + vectormove(128, pn + 1); + for(int i = 0; i < pn; i++) + move[needle[i]] = pn - i; + + int i = 0; + while(i <= sn - pn){ + int j = 0; + while(haystack[i + j] == needle[j]) + if(++j == pn) return i; + + i += move[haystack[i + pn]]; + } + return -1; + } +}; +``` \ No newline at end of file diff --git a/solutions/img/28/kmp.png b/solutions/img/28/kmp.png new file mode 100644 index 0000000000000000000000000000000000000000..120e8db963906303fe6e545e6400bb37d9360fdd GIT binary patch literal 25943 zcmaI7b9iMzvo{)BlT4h6Cbn&B$F`jv+n#u0dt%$x#I|kQH}jrzzVH5V&)v^Pul00Q zS6BTC-Md$qysS7P91a`^2neF2goq*t2$;uLdjbaR>zfRLX`@iK2;tvAg}S2@ePeII)GYx|2FUhRev-hR)z$A38T1yDw@G5FUOv zI|Cyt6DLAL6Eh1SFY#qt7crrQF)y(iD}VuDCv0MFA>rX*qU0f~Y~*2O#A!^-&qv7P z#`VR(#>B~h(9Omg=*Z>9OZ*?cTwm>fx9N!q|I@|EikJAmgi;5{6AIfpm=LnkG1D3` zFftOdvC%QIu(Gi+(hxE+Ff!3Ie7)Id8Ckek*|?b43IF>={56_`u_>3Lh}eIR^>xKd zZ0_V_$3;)?>gr18%1meLU`Ef#$;tVT2NM(RR}Wf8cc7Dj8!gcB=l^gJF>y3+Hl!{3YpsO~JjjosJCA|?(N zE+)oe4z@Og|CutE#s4mg;Qz|+ziEyCcUgq~S6ccnVd(!E_Wxz*|GD*ro`22%1KY2Q 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