后缀数组模板总结

将字符串s的所有后缀排序

洛谷P3809 后缀排序

#include<algorithm>
#include<iostream>
#include<cstring>
#include<iomanip>
#include<sstream>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<cmath>
#include<stack>
#include<set>
#include<map>
#define rep(i,x,n) for(int i=x;i<=n;++i)
#define per(i,n,x) for(int i=n;i>=x;--i)
#define sz(a) int(a.size())
#define rson mid+1,r,p<<1|1
#define pii pair<int,int>
#define lson l,mid,p<<1
#define ll long long
#define pb push_back
#define mp make_pair
#define se second
#define fi first
using namespace std;
const double eps=1e-8;
const int mod=1e9+7;
const int N=1e6+10;
const int inf=1e9;
char s[N];
int n;
int sa[N],rk[N],wb[N],c[N];
void bd(int m){
	int *x=rk,*y=wb;
	rep(i,1,m) c[i]=0;
	rep(i,1,n) ++c[ x[i]=s[i] ];
	rep(i,2,m) c[i]+=c[i-1];
	per(i,n,1) sa[ c[x[i]]-- ]=i;
	for(int k=1;k<=n;k<<=1){
		int p=0;
		rep(i,n-k+1,n)  y[++p]=i;
		rep(i,1,n) if(sa[i]>k) y[++p]=sa[i]-k;
		rep(i,1,m) c[i]=0;
		rep(i,1,n) ++c[ x[y[i]] ];
		rep(i,2,m) c[i]+=c[i-1];
		per(i,n,1) sa[ c[x[y[i]]]-- ]=y[i],y[i]=0;
		swap(x,y);
		x[sa[1]]=1;
		p=1;
		rep(i,2,n) 
			x[sa[i]] = (y[sa[i]]==y[sa[i-1]]&&y[sa[i]+k]==y[sa[i-1]+k]) ? p : ++p;
		if(p>=n) break;
		m=p;
	}
}
int main(){
	//ios::sync_with_stdio(false);
	//freopen("in","r",stdin);
	scanf("%s",s+1);
	n=strlen(s+1);
	bd(256);
	rep(i,1,n){
		printf("%d%c",sa[i],i==n?'
':' ');
	}
	return 0;
}

查询字符串t在字符串s中出现的所有位置

洛谷P3375 KMP字符串匹配

#include<algorithm>
#include<iostream>
#include<cstring>
#include<iomanip>
#include<sstream>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<cmath>
#include<stack>
#include<set>
#include<map>
#define rep(i,x,n) for(int i=x;i<=n;++i)
#define per(i,n,x) for(int i=n;i>=x;--i)
#define sz(a) int(a.size())
#define rson mid+1,r,p<<1|1
#define pii pair<int,int>
#define lson l,mid,p<<1
#define ll long long
#define pb push_back
#define mp make_pair
#define se second
#define fi first
using namespace std;
const double eps=1e-8;
const int mod=1e9+7;
const int N=1e6+10;
const int inf=1e9;
char s[N],t[N];
int n,m;
int sa[N],rk[N],wb[N],c[N],nex[N];
void bd(int m){
	int *x=rk,*y=wb;
	rep(i,1,m) c[i]=0;
	rep(i,1,n) ++c[ x[i]=s[i] ];
	rep(i,2,m) c[i]+=c[i-1];
	per(i,n,1) sa[ c[x[i]]-- ]=i;
	for(int k=1;k<=n;k<<=1){
		int p=0;
		rep(i,n-k+1,n)  y[++p]=i;
		rep(i,1,n) if(sa[i]>k) y[++p]=sa[i]-k;
		rep(i,1,m) c[i]=0;
		rep(i,1,n) ++c[ x[y[i]] ];
		rep(i,2,m) c[i]+=c[i-1];
		per(i,n,1) sa[ c[x[y[i]]]-- ]=y[i],y[i]=0;
		swap(x,y);
		x[sa[1]]=1;
		p=1;
		rep(i,2,n)
			x[sa[i]] = (y[sa[i]]==y[sa[i-1]]&&y[sa[i]+k]==y[sa[i-1]+k]) ? p : ++p;
		if(p>=n) break;
		m=p;
	}
}
void get(char *s){
	int n=strlen(s+1);
	for(int i=2,j=0;i<=n;i++){
		while(j&&s[i]!=s[j+1]) j=nex[j];
		if(s[i]==s[j+1]) ++j;
		nex[i]=j;
	}
}
int main(){
	//ios::sync_with_stdio(false);
	//freopen("in","r",stdin);
	scanf("%s",s+1);
	n=strlen(s+1);
	bd(256);
	scanf("%s",t+1);
	m=strlen(t+1);
	int l=1,r=n,L=n+1,R=0;
	while(l<=r){
		int mid=l+r>>1;
		int res=strncmp(t+1,s+sa[mid],m);
		if(res<=0) r=mid-1;
		else l=mid+1;
	}
	L=l;
	l=1,r=n;
	while(l<=r){
		int mid=l+r>>1;
		int res=strncmp(t+1,s+sa[mid],m);
		if(res>=0) l=mid+1;
		else r=mid-1;
	}
	R=r;
	rep(i,1,n) c[i]=0;
   	rep(i,L,R) ++c[sa[i]];
   	rep(i,1,n) if(c[i]) printf("%d
",i);
    get(t);
    rep(i,1,m) printf("%d%c",nex[i],i==n?'
':' ');
	return 0;
}

字符串s的任意两个后缀的最长公共前缀LCP

利用引理(height[rk[i]]ge height[rk[i-1]]-1)来(O(n))求出(height)数组。

#include<algorithm>
#include<iostream>
#include<cstring>
#include<iomanip>
#include<sstream>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<cmath>
#include<stack>
#include<set>
#include<map>
#define rep(i,x,n) for(int i=x;i<=n;++i)
#define per(i,n,x) for(int i=n;i>=x;--i)
#define sz(a) int(a.size())
#define rson mid+1,r,p<<1|1
#define pii pair<int,int>
#define lson l,mid,p<<1
#define ll long long
#define pb push_back
#define mp make_pair
#define se second
#define fi first
using namespace std;
const double eps=1e-8;
const int mod=1e9+7;
const int N=1e6+10;
const int inf=1e9;
char s[N],t[N];
int n,m;
int sa[N],rk[N],wb[N],c[N],ht[N],st[N][20];
void bd(int m){
	int *x=rk,*y=wb;
	rep(i,1,m) c[i]=0;
	rep(i,1,n) ++c[ x[i]=s[i] ];
	rep(i,2,m) c[i]+=c[i-1];
	per(i,n,1) sa[ c[x[i]]-- ]=i;
	for(int k=1;k<=n;k<<=1){
		int p=0;
		rep(i,n-k+1,n)  y[++p]=i;
		rep(i,1,n) if(sa[i]>k) y[++p]=sa[i]-k;
		rep(i,1,m) c[i]=0;
		rep(i,1,n) ++c[ x[y[i]] ];
		rep(i,2,m) c[i]+=c[i-1];
		per(i,n,1) sa[ c[x[y[i]]]-- ]=y[i],y[i]=0;
		swap(x,y);
		x[sa[1]]=1;
		p=1;
		rep(i,2,n)
			x[sa[i]] = (y[sa[i]]==y[sa[i-1]]&&y[sa[i]+k]==y[sa[i-1]+k]) ? p : ++p;
		if(p>=n) break;
		m=p;
	}
}
void get(){
	for(int i=1,k=0;i<=n;i++){
		if(k) --k;
		while(s[i+k]==s[ sa[rk[i]-1] ]+k) ++k;
		ht[rk[i]]=k;
	}
	rep(i,1,n) st[i][0]=ht[i];
	for(int j=1;(1<<j)<=n;j++){
		for(int i=1;i+(1<<j)-1<=n;i++){
			st[i][j]=min(st[i][j-1],st[i+1<<(j-1)][j-1]);
		}
	}
}
int lcp(int l,int r){
	int k=(int)log2(r-l+1);
	return min(st[l][k],st[r-(1<<k)+1][k]);
}
int main(){
	//ios::sync_with_stdio(false);
	//freopen("in","r",stdin);
	scanf("%s",s+1);
	n=strlen(s+1);
	bd(256);
	get();
	return 0;
}

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