Codeforces 1073G Yet Another LCP Problem $SA$+单调栈

题意

给出一个字符串\(s\)和\(q\)个询问。

每次询问给出两个长度分别为\(k,l\)的序列\(a\)和序列\(b\)。

求\(\sum_{i=1}^{k}\sum_{j=1}^{l}lcp(s[a_i…n],s[b_j…n])\)

Solution

\(SA\)练习题。

求出\(height\)数组后，每次询问相当于询问\(l*k\)个区间\(min\)之和。

岂不单调栈？

对没错，这个题解就是提供给你代码对拍的

#include<bits/stdc++.h>
#define For(i,x,y) for (register int i=(x);i<=(y);i++)
#define Dow(i,x,y) for (register int i=(x);i>=(y);i--)
#define cross(i,k) for (register int i=first[k];i;i=last[i])
using namespace std;
typedef long long ll;
inline ll read(){
    ll x=0;int ch=getchar(),f=1;
    while (!isdigit(ch)&&(ch!='-')&&(ch!=EOF)) ch=getchar();
    if (ch=='-'){f=-1;ch=getchar();}
    while (isdigit(ch)){x=(x<<1)+(x<<3)+ch-'0';ch=getchar();}
    return x*f;
}
const int N = 2e5+10;
int n,Q,l[N],k[N];
char s[N];
int SA[N],height[N],rk[N],cnt[N],x[N],y[N];
inline void RadixSort(){
	int Max=0;
	For(i,1,n) cnt[x[i]]++,Max=max(Max,x[i]);
	For(i,1,Max) cnt[i]+=cnt[i-1];
    Dow(i,n,1) SA[cnt[x[y[i]]]--]=y[i];
	For(i,1,Max) cnt[i]=0;
}
inline void GetSA(){
	For(i,1,n) x[i]=s[i],y[i]=i;
	RadixSort();
	for (int i=1,p;p<n;i<<=1){
		p=0;
		For(j,n-i+1,n) y[++p]=j;
		For(j,1,n) if (SA[j]>i) y[++p]=SA[j]-i;
		RadixSort(),swap(x,y),x[SA[1]]=p=1;
		For(j,2,n) x[SA[j]]=(y[SA[j]]==y[SA[j-1]]&&y[SA[j]+i]==y[SA[j-1]+i])?p:++p;
	}
	For(i,1,n) rk[SA[i]]=i;
	int now=0;
	For(i,1,n){
		if (rk[i]==1) continue;now=max(now-1,0);
        for (int j=SA[rk[i]-1];j+now<=n&&i+now<=n&&s[j+now]==s[i+now];now++);
		height[rk[i]]=now;
	}
}
int Min[N][20],Log[N];
inline void init(){
	For(i,1,n) Log[i]=log(i)/log(2);
	For(i,1,n) Min[i][0]=height[i];
	For(j,1,Log[n]) For(i,1,n-(1<<j)+1) Min[i][j]=min(Min[i][j-1],Min[i+(1<<j-1)][j-1]);
}
inline int Query(int l,int r){
	int L=Log[r-l+1];
	return min(Min[l][L],Min[r-(1<<L)+1][L]);
}
struct node{
	int x,y;
}a[N<<1];
inline bool cmp(node a,node b){return a.x==b.x?a.y<b.y:a.x<b.x;}
int top,q[N<<1],c[N<<1];
ll Sum,ans;
inline void solve(int m,int M){
	int cnt=0;
	For(i,1,M) a[++cnt]=(node){rk[read()],1};
	For(i,1,m) a[++cnt]=(node){rk[read()],0};
	sort(a+1,a+1+cnt,cmp),ans=top=Sum=0;
	a[cnt+1]=(node){-1,0};
	int r=cnt;while (a[r].y==1) r--;
	Dow(i,r,1){
		if (i!=r){
			int x=Query(a[i].x+1,a[i+1].x),s=a[i+1].y^1;
			while (x<=q[top]&&top) Sum-=c[top]*q[top],s+=c[top--];
			q[++top]=x,c[top]=s,Sum+=1ll*s*x;
		}
		if (a[i].y) ans+=Sum;
		else if (a[i+1].x==a[i].x) ans+=n-SA[a[i].x]+1;
	}
	For(i,2,cnt) if (a[i].x==a[i-1].x) swap(a[i],a[i-1]);
	top=Sum=0;
	r=1;while (a[r].y==1) r++;
	For(i,r,cnt){
		if (i!=r){
			int x=Query(a[i-1].x+1,a[i].x),s=a[i-1].y^1;
			while (x<=q[top]&&top) Sum-=c[top]*q[top],s+=c[top--];
			q[++top]=x,c[top]=s,Sum+=1ll*s*x;
		}
		if (a[i].y) ans+=Sum;
	}
}
ll Ans[N];
int main(){
	n=read(),Q=read(),scanf("%s",s+1);
	GetSA(),init();
	For(i,1,Q) solve(read(),read()),Ans[i]=ans;
	For(i,1,Q) printf("%lld\n",Ans[i]);
}