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
",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
",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;
}