CF1073G Yet Another LCP Problem 后缀自动机 + 虚树 + 树形DP

Posted 2022-03-15 guangheli

Code: 

#include <bits/stdc++.h>
#define setIO(s) freopen(s".in","r",stdin) 
#define maxn 400004 
#define ll long long 
using namespace std;  
int edges,n,Q; 
int hd[maxn],to[maxn],nex[maxn],tr[maxn];   
char str[maxn]; 
void addedge(int u,int v,int c)
 
	nex[++edges]=hd[u],hd[u]=edges,to[edges]=v; 

namespace SAM
  
	int last, tot; 
	int len[maxn],f[maxn],trans[maxn][27];  
	void init()  last=tot=1;  
	int extend(int c) 
	
		int np=++tot,p=last; 
		len[np]=len[p]+1,last=np; 
		while(p&&!trans[p][c]) trans[p][c]=np, p=f[p]; 
		if(!p) f[np]=1; 
		else 
		
			int q=trans[p][c]; 
			if(len[q]==len[p]+1) f[np]=q; 
			else 
			
				int nq=++tot; 
				len[nq]=len[p]+1; 
				memcpy(trans[nq],trans[q],sizeof(trans[q])); 
				f[nq]=f[q],f[q]=f[np]=nq;    
				while(p&&trans[p][c]==q) trans[p][c]=nq,p=f[p]; 
			
		  
		return np; 
	 
	void build() 
	
		for(int i=2;i<=tot;++i) addedge(f[i],i,len[f[i]]-len[i]); 
	
  
int tim; 
int dfn[maxn],Top[maxn],hson[maxn],siz[maxn],fa[maxn],dis[maxn];   
void dfs1(int u,int ff)

	fa[u]=ff,siz[u]=1,dfn[u]=++tim,dis[u]=dis[ff]+1; 
	for(int i=hd[u];i;i=nex[i])
	
		int v=to[i]; 
		if(v==ff) continue;  
		dfs1(v,u); 
		siz[u]+=siz[v]; 
		if(siz[v]>siz[hson[u]]) hson[u]=v; 
	

void dfs2(int u,int tp)

	Top[u]=tp; 
	if(hson[u]) dfs2(hson[u],tp); 
	for(int i=hd[u];i;i=nex[i])
	
		int v=to[i]; 
		if(v==fa[u]||v==hson[u]) continue; 
		dfs2(v,v); 
	

int LCA(int x,int y)

	while(Top[x]!=Top[y]) 
	
		dis[Top[x]]>dis[Top[y]]?x=fa[Top[x]]:y=fa[Top[y]]; 
	
	return dis[x]<dis[y]?x:y; 
 
vector<int>G[maxn]; 
ll ans=0; 
int t=0,tot=0; 
int arr[maxn],brr[maxn],A[maxn<<1],mk[maxn],mka[maxn],mkb[maxn],sizea[maxn],sizeb[maxn],S[maxn];  
bool cmp(int i,int j) 

	return dfn[i]<dfn[j]; 

void addvir(int x,int y)
  
	G[x].push_back(y); 

void insert(int x)

	if(t<=1)  S[++t]=x; return; 
	int lca=LCA(S[t],x); 
	if(lca==S[t])  S[++t]=x; return;  
	while(t>1&&dis[S[t-1]]>=dis[lca]) addvir(S[t-1],S[t]),--t; 
	if(S[t]!=lca) addvir(lca,S[t]),S[t]=lca; 
	S[++t]=x;   
 
void DP(int x)
           
	for(int i=0;i<G[x].size();++i) 
		DP(G[x][i]), sizea[x]+=sizea[G[x][i]], sizeb[x]+=sizeb[G[x][i]];      
	for(int i=0;i<G[x].size();++i) 
	   
		ans+=1ll*(sizea[x]-sizea[G[x][i]])*sizeb[G[x][i]]*SAM::len[x]; 
	       
	ans+=(1ll*mka[x]*mkb[x]+1ll*mka[x]*sizeb[x]+1ll*mkb[x]*sizea[x])*SAM::len[x];    
	sizea[x]+=mka[x],sizeb[x]+=mkb[x];    

void erase(int x) 

	mka[x]=mkb[x]=sizea[x]=sizeb[x]=0; 
	for(int i=0;i<G[x].size();++i) erase(G[x][i]); 
	G[x].clear(); 

void work() 

	tot=0; 
	int k1,k2; 
	scanf("%d%d",&k1,&k2);  
	for(int i=1;i<=k1;++i) scanf("%d",&arr[i]),A[++tot]=tr[arr[i]],mka[tr[arr[i]]]=1; 
	for(int i=1;i<=k2;++i) scanf("%d",&brr[i]),A[++tot]=tr[brr[i]],mkb[tr[brr[i]]]=1;
	sort(A+1,A+1+tot,cmp);     
    tot=unique(&A[1],&A[tot+1])-A-1; 
    t=ans=0;    
    if(A[1]!=1) S[t=1]=1;         
    for(int i=1;i<=tot;++i) insert(A[i]);   
    while(t>1) addvir(S[t-1],S[t]),--t;     
    DP(1); 
	printf("%I64d\n",ans);   
	erase(1);  

int main() 

	// setIO("input");   
	scanf("%d%d%s",&n,&Q,str+1); 
	SAM::init();      
	for(int i=n;i>=1;--i) tr[i]=SAM::extend(str[i]-‘a‘);    
	SAM::build();      
	dfs1(1,0),dfs2(1,1);        
    for(int i=1;i<=Q;++i) work();   
	return 0;