Z-function

P5410 【模板】扩展 KMP（Z 函数）

用更容易理解的方法处理出

s[l…………r]=s[1…………r-l+1]

常数比KMP略大，时间复杂度\(O(n)\)，方法和manacher很像

#include<bits/stdc++.h>
using namespace std;
#define rint register int
const int N=20000010;
char a[N],b[N];
int z[N],p[N];
long long ans;
inline void Z_function(char *a) {
	int n=strlen(a+1);
	z[1]=n;for(rint i=2;i<=n;++i)z[i]=0;
	for(rint i=2,l=0,r=0;i<=n;++i) {
		if(i<=r)z[i]=min(z[i-l+1],r-i+1);
		while(i+z[i]<=n&&a[i+z[i]]==a[z[i]+1])++z[i];
		if(i+z[i]-1>r)l=i,r=i+z[i]-1;
	}
}
inline void exkmp(char *a,char *b) {
	int n=strlen(a+1);
	for(rint i=1;i<=n;++i)p[i]=0;
	for(rint i=1,l=0,r=0;i<=n;++i) {
		if(i<=r)p[i]=min(z[i-l+1],r-i+1);
		while(i+p[i]<=n&&a[i+p[i]]==b[p[i]+1])++p[i];
		if(i+p[i]-1>r)l=i,r=i+p[i]-1;
	}
}
int main() {
	scanf("%s%s",a+1,b+1);
	Z_function(b);ans=0;for(rint i=1,m=strlen(b+1);i<=m;++i)ans^=1ll*(z[i]+1)*i;printf("%lld\n",ans);
	exkmp(a,b);   ans=0;for(rint i=1,n=strlen(a+1);i<=n;++i)ans^=1ll*(p[i]+1)*i;printf("%lld\n",ans);
	return 0;
}

这东西也可以做字符串匹配。把模式串接在文本串前面，跑一遍Z-function，找到 \(Z_i \geq lenb\) 的即可