2021.11.11 EXKMP

2021.11.11 EXKMP

https://www.luogu.com.cn/problem/P5410

下标以1开头：

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;

const int N=2e7+10;
typedef long long ll;
int lenp,lens,z[N],ext[N];
char t[N],s[N];

inline void getz(char *s){
	int n=strlen(s+1);
	memset(z,0,sizeof(z));
	z[1]=n;
	for(int 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&&1+z[i]<=n&&s[z[i]+1]==s[(i+z[i]-1)+1])++z[i];
		if(i+z[i]-1>r)l=i,r=i+z[i]-1;
	}
	//z[0]=n;
	//cout<<"z "<<endl;//
	//for(int i=0;i<=n;i++)cout<<z[i]<<" ";cout<<endl;//
}
inline void exkmp(char *s,char *t){
	int n=strlen(s+1),m=strlen(t+1);
	getz(t);
	ll ans=0;
	for(int i=1;i<=m;i++)ans^=1ll*(i)*(z[i]+1);
	cout<<ans<<endl;
	memset(ext,0,sizeof(ext));
	for(int i=1,l=0,r=0;i<=n;i++){
		if(i<=r)ext[i]=min(z[i-l+1],r-i+1);
		while(i+ext[i]<=n&&1+ext[i]<=m&&t[ext[i]+1]==s[(i+ext[i]-1)+1])++ext[i];
		if(r<i+ext[i]-1)l=i,r=i+ext[i]-1;
	}
	ans=0;
	for(int i=1;i<=n;i++)ans^=1ll*(i)*(ext[i]+1);
	cout<<ans;
	//cout<<"ext"<<endl;//
	//for(int i=0;i<=n;i++)cout<<ext[i]<<" ";cout<<endl;//
}

int main(){
	scanf("%s",s+1);scanf("%s",t+1);
	exkmp(s,t);
	return 0;
}

下标以0开始：

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;

const int N=2e7+10;
typedef long long ll;
int lenp,lens,z[N],ext[N];
char t[N],s[N];

inline void getz(char *s){
	int len=strlen(s);
	memset(z,0,sizeof(z));
	z[0]=len;
	for(int i=1,l=0,r=0;i<len;i++){
		if(i<=r)z[i]=min(z[(i-l+1)-1],r-i+1);
		while(i+z[i]<len&&s[z[i]]==s[(i+z[i]-1)+1])++z[i];
		if(i+z[i]-1>r)l=i,r=i+z[i]-1;
	}
	ll ans=0;
	for(int i=0;i<len;i++)ans^=1ll*(i+1)*(z[i]+1);
	cout<<ans<<endl;
}
inline void exkmp(char *s,char *t){
	getz(t);
	int lens=strlen(s),lent=strlen(t);
	for(int i=0,l=-1,r=-1;i<lens;i++){
		if(i<=r)ext[i]=min(z[(i-l+1)-1],r-i+1);
		while(i+ext[i]<lens&&ext[i]<lent&&t[ext[i]]==s[(i+ext[i]-1)+1])++ext[i];
		if(i+ext[i]-1>r)l=i,r=i+ext[i]-1;
	}
	ll ans=0;
	for(int i=0;i<lens;i++)ans^=1ll*(i+1)*(ext[i]+1);
	cout<<ans<<endl;
}

int main(){
	scanf("%s",s);scanf("%s",t);
	exkmp(s,t);
	return 0;
}

练习题

https://www.luogu.com.cn/problem/CF432D

论树状数组的好用 ~

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;

const int N=1e5+10;
int z[N],ext[N],t[N],top;
char s[N*2];
struct node{
	int len,tot;
	bool operator <(const node &b)const{
		return len<b.len;
	}
}ans[N];

inline void getz(char *s){
	int n=strlen(s+1);
	z[1]=n;
	for(int 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&&s[z[i]+1]==s[(i+z[i]-1)+1])++z[i];
		if(i+z[i]-1>r)l=i,r=i+z[i]-1;
	}
}
inline void exkmp(char *s,char *t){
	int lens=strlen(s+1),lent=strlen(t+1);
	getz(t);
	for(int i=1,l=-1,r=-1;i<=lens;i++){
		if(i<=r)ext[i]=min(z[i-l+1],r-i+1);
		while(i+ext[i]<=lens&&1+ext[i]<=lent&&t[ext[i]+1]==s[(i+ext[i]-1)+1])++ext[i];
		if(i+ext[i]-1>r)l=i,r=i+ext[i]-1;
	}
}
inline int lowbit(int x){
	return x&-x;
}
inline void add(int x,int k,int len){
	for(int i=x;i<=len;i+=lowbit(i))t[i]+=k;
}
inline int query(int x){
	int fin=0;
	for(int i=x;i>0;i-=lowbit(i))fin+=t[i];
	return fin;
}

int main(){
	scanf("%s",s+1);
	int len=strlen(s+1);
	//cout<<len<<endl;
	s[len+1]='|';
	for(int i=1;i<=len;i++)s[i+len+1]=s[i];
	//for(int i=1;i<=len*2+2;i++)printf("%c",s[i]);cout<<endl;
	int leni=strlen(s+1);
	//cout<<leni<<endl;
	getz(s);
	//for(int i=1;i<=leni;i++)cout<<z[i]<<" ";cout<<endl;
	for(int i=len+2;i<=leni;i++)if(z[i])add(z[i],1,len);
	for(int i=len+2;i<=leni;i++)if(i+z[i]-1==leni){
		++top;
		ans[top].len=z[i];ans[top].tot=query(len)-query(z[i]-1);
	}
	sort(ans+1,ans+top+1);
	cout<<top<<endl;
	for(int i=1;i<=top;i++)cout<<ans[i].len<<" "<<ans[i].tot<<endl;
	return 0;
}

https://www.luogu.com.cn/problem/P7114

https://www.luogu.com.cn/blog/nitubenben/solution-p7114

PS：树状数组是EXKMP的好帮手~

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;

const int N=(1<<20)+10;
typedef long long ll;
int t,z[N],before[N],after[N],tree[N];
char s[N];

inline void getz(char *s){
	int n=strlen(s);
	z[0]=n;
	for(int i=1,l=0,r=0;i<n;i++){
		if(i<=r)z[i]=min(z[(i-l+1)-1],r-i+1);
		while(i+z[i]<n&&s[z[i]]==s[(i+z[i]-1)+1])++z[i];
		if(i+z[i]-1>r)l=i,r=i+z[i]-1;
	}
}
inline int lowbit(int x){
	return x&-x;
}
inline void add(int x,int k,int n){
	for(int i=x;i<=n;i+=lowbit(i))tree[i]+=k; 
}
inline int query(int x){
	int fin=0;
	for(int i=x;i>0;i-=lowbit(i))fin+=tree[i];
	return fin;
}

int main(){
	cin>>t;
	while(t--){
		memset(z,0,sizeof(z));
		memset(after,0,sizeof(after));
		memset(before,0,sizeof(before));
		memset(tree,0,sizeof(tree));
		scanf("%s",s);
		getz(s);
		int n=strlen(s);
		for(int i=0;i<n;i++)if((i+z[i]-1)+1==n)--z[i];
		for(int i=0;i<n;i++)++after[s[i]-'a'];
		int all=0,pre=0,suf=0;
		ll ans=0;
		for(int i=0;i<26;i++)if(after[i]&1)++all;
		suf=all;
		for(int i=0;i<n;i++){
			int x=s[i]-'a';
			if(after[x]&1)--suf;
			else ++suf;
			--after[x];
			if(before[x]&1)--pre;
			else ++pre;
			++before[x];
			if(i&&i!=n-1){
				int num=z[i+1]/(i+1)+1;
				ans+=1ll*(num/2)*query(all+1)+1ll*(num-num/2)*query(suf+1);
			}
			add(pre+1,1,n);
		}
		cout<<ans<<endl;
	}
	return 0;
}