kmp学习笔记

kmp，扩展 kmp 学习笔记

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说再前边

字符串水平基本为0，学了第4遍KMP了，总是忘。。。网上资料很多，就不详细讲解了。抄的kuangbin神犇模板

kmp

一些知识

1. 循环节大小：n - nxt[n]

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模板[HDU2087]

下标从0开始
nxt[i] 为满足p[i-z...i-1]=p[0...z-1]最大的z值

#include <cstdio>
#include <cstring>
#define rep(i,a,b) for(int i=a;i<=b;++i)
typedef long long ll;
const int N = 100000 + 7;
using namespace std;
char s[N], p[N];
int nxt[N], n, m;
void getnxt() {int i, j;j = nxt[0] =-1;i = 0;while(i < m) {while(j != -1 && p[i] != p[j]) j = nxt[j];nxt[++i] = ++j;}
}
int kmp_ct() {int i, j;int ans = 0;i = j = 0;while(i <= n) {while(j != -1 && s[i] != p[j]) j = nxt[j];++i; ++j;if(j >= m) {++ans;j = 0;//不可重叠//j = nxt[j] 可以重叠}}return ans;
}
int main() {while(~scanf(" %s", s)) {if(s[0] == '#') break;scanf(" %s", p);n = strlen(s), m = strlen(p);getnxt();printf("%d\n",kmp_ct());}return 0;
}

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下标从1开始

#include <cstdio>
#include <cstring>
using namespace std;
const int N=1e6+5;
int T,nxt[N],n,m;
char s[N],p[N];
void getnxt(char p[],int n){nxt[1]=0;for(int i=2;i<=n;i++){int j=nxt[i-1];while(j&&s[j+1]!=s[i]) j=nxt[j];if(s[j+1]==s[i]) nxt[i]=j+1;else nxt[i] = 0;}
}
int kmp(){int ans=0;getnxt(p,m);int j=0;for(int i=1;i<=n;i++){while(j&&p[j+1]!=s[i]) j=nxt[j];if(p[j+1]==s[i])++j;if(j==m) {ans++;j=0;}}return ans;
}
int main(){while(scanf(" %s",s+1)!=EOF){if(s[1] == '#') break;scanf(" %s",p+1);n=strlen(s+1),m=strlen(p+1);printf("%d\n",kmp());}return 0;
}

扩展kmp

nxt[i] 表示 x[i...m-1] 与 x[0...m-1] 的最长公共前缀
ex[i] 表示 y[i...n-1] 与 x[0...m-1] 的最长公共前缀

#include <bits/stdc++.h>
const int N = 1e5 + 7;
using namespace std;
char x[N], y[N];
int n, m, nxt[N], ex[N];
void get_nxt(char x[], int m, int nxt[]) {nxt[0] = m;int j = 0, k = 1;while(j+1 < m && x[j] == x[j+1]) ++j;nxt[1] = j;for(int i = 2; i < m; ++i) {int p = nxt[k] + k - 1, L = nxt[i-k];if(i+L < p+1) nxt[i] = L;else {j = max(0, p-i+1);while(i+j < m && x[i+j] == x[j]) ++j;nxt[i] = j;k = i;}}
}
void exkmp(char x[], int m, char y[], int n, int nxt[], int ex[]) {get_nxt(x, m, nxt);int j = 0, k = 0;while(j < n && j < m && x[j] == y[j]) ++j;ex[0] = j;for(int i = 1; i < n; ++i) {int p = ex[k] + k - 1, L = nxt[i-k];if(i+L < p+1) ex[i] = L;else {j = max(0, p-i+1);while(i+j < n && j < m && y[i+j] == x[j]) ++j;ex[i] = j;k = i;}}
}
int main() {scanf(" %s %s", x, y);m = strlen(x), n = strlen(y);exkmp(x, m, y, n, nxt, ex);for(int i = 0; i < m; ++i) printf("%d ", nxt[i]);puts("");for(int i = 0; i < n; ++i) printf("%d ", ex[i]);puts("");return 0;
}