LUOGU P1501 [国家集训队]Tree II (lct)

传送门

##解题思路
　　\(lct\)，比较模板的一道题，路径加和乘的维护标记与线段树$2$差不多，然后剩下就没啥了。但调了我将近一下午。。

##代码

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#define int long long

using namespace std;
const int MAXN = 100005;
const int MOD = 51061;

inline int rd(){
	int x=0,f=1;char ch=getchar();
	while(!isdigit(ch)) {f=ch=='-'?0:1;ch=getchar();}
	while(isdigit(ch))  {x=(x<<1)+(x<<3)+ch-'0';ch=getchar();}
	return f?x:-x;
}

int n,q,fa[MAXN],sum[MAXN],ch[MAXN][2],w[MAXN];
int tag_mul[MAXN],tag_add[MAXN],siz[MAXN];
bool tag[MAXN];

inline void pushup(int x){
	sum[x]=sum[ch[x][0]]+sum[ch[x][1]]+w[x];sum[x]%=MOD;
	siz[x]=siz[ch[x][0]]+siz[ch[x][1]]+1;
}

inline bool isroot(int x){
	return (x!=ch[fa[x]][0] && x!=ch[fa[x]][1]);
}

inline bool check(int x){
	return (x==ch[fa[x]][1]);
}

inline void pushdown(int x){
	if(tag[x]){
		if(ch[x][0]) tag[ch[x][0]]^=1,swap(ch[ch[x][0]][0],ch[ch[x][0]][1]);
		if(ch[x][1]) tag[ch[x][1]]^=1,swap(ch[ch[x][1]][0],ch[ch[x][1]][1]);
		tag[x]=0;
	}
	if(tag_mul[x]!=-1){
		if(ch[x][0]){
			if(tag_add[ch[x][0]]!=-1) (tag_add[ch[x][0]]*=tag_mul[x])%=MOD;
			if(tag_mul[ch[x][0]]==-1) tag_mul[ch[x][0]]=tag_mul[x];
			else (tag_mul[ch[x][0]]*=tag_mul[x])%=MOD;
			w[ch[x][0]]*=tag_mul[x];w[ch[x][0]]%=MOD;
			sum[ch[x][0]]*=tag_mul[x];sum[ch[x][0]]%=MOD;
		}
		if(ch[x][1]){
			if(tag_add[ch[x][1]]!=-1) (tag_add[ch[x][1]]*=tag_mul[x])%=MOD;
			if(tag_mul[ch[x][1]]==-1) tag_mul[ch[x][1]]=tag_mul[x];
			else (tag_mul[ch[x][1]]*=tag_mul[x])%=MOD;
			w[ch[x][1]]*=tag_mul[x];w[ch[x][1]]%=MOD;
			sum[ch[x][1]]*=tag_mul[x];sum[ch[x][1]]%=MOD;
		}
		tag_mul[x]=-1;
	}
	if(tag_add[x]!=-1) {
		if(ch[x][0]) {
			if(tag_add[ch[x][0]]==-1) tag_add[ch[x][0]]=tag_add[x];
			else (tag_add[ch[x][0]]+=tag_add[x])%=MOD;
			(w[ch[x][0]]+=tag_add[x])%=MOD;
			sum[ch[x][0]]+=siz[ch[x][0]]*tag_add[x];sum[ch[x][0]]%=MOD;
		}
		if(ch[x][1]){
			if(tag_add[ch[x][1]]==-1) tag_add[ch[x][1]]=tag_add[x];
			else (tag_add[ch[x][1]]+=tag_add[x])%=MOD;
			(w[ch[x][1]]+=tag_add[x])%=MOD;
			sum[ch[x][1]]+=siz[ch[x][1]]*tag_add[x];sum[ch[x][1]]%=MOD;
		}
		tag_add[x]=-1;
	}
}

inline void update(int x){
	if(!isroot(x)) update(fa[x]);pushdown(x);
}

inline void rotate(int x){
	int y=fa[x],z=fa[y];bool chk=check(x);
	if(!isroot(y)) ch[z][y==ch[z][1]]=x;
	ch[y][chk]=ch[x][chk^1];fa[ch[x][chk^1]]=y;
	fa[y]=x;ch[x][chk^1]=y;fa[x]=z;
	pushup(y);pushup(x);
}

inline void splay(int x){
	update(x);
	for(;!isroot(x);rotate(x))
		if(!isroot(fa[x])) rotate(check(fa[x])==check(x)?fa[x]:x);
}

inline void access(int x){
	for(int y=0;x;y=x,x=fa[x])
		splay(x),ch[x][1]=y,pushup(x);
}

inline int findroot(int x){
	access(x);splay(x);
	while(ch[x][0]) pushdown(x),x=ch[x][0];
	return x;
}

inline void makeroot(int x){
	access(x);splay(x);
	tag[x]^=1;swap(ch[x][0],ch[x][1]);
}

inline void split(int x,int y){
	makeroot(x);access(y);splay(y);
}

inline void link(int x,int y){
	if(findroot(x)==findroot(y)) return;
	makeroot(x);fa[x]=y;
}

inline void cut(int x,int y){
	if(findroot(x)!=findroot(y)) return;
	split(x,y);
	if(ch[y][0]==x && !ch[x][1])
		fa[x]=0,ch[y][0]=0,pushup(y);
}

inline void update_add(int x,int y,int k){
	split(x,y);
	if(tag_add[y]!=-1) (tag_add[y]+=k)%=MOD ;else tag_add[y]=k;
	w[y]+=k;pushup(y);w[y]%=MOD;
}

inline void update_mul(int x,int y,int k){
	split(x,y);
	if(tag_add[y]!=-1) (tag_add[y]*=k)%=MOD;
	if(tag_mul[y]!=-1) (tag_mul[y]*=k)%=MOD;else tag_mul[y]=k;
	w[y]*=k;pushup(y);w[y]%=MOD;
}

signed main(){
	memset(tag_mul,-1,sizeof(tag_mul));
	memset(tag_add,-1,sizeof(tag_add));
	int x,y,a,b;char c;n=rd(),q=rd();
	for(int i=1;i<=n;i++) w[i]=1;
	for(int i=1;i<n;i++){
		x=rd(),y=rd();
		link(x,y);
	}
	while(q--){
		scanf("%c",&c);
		if(c=='+'){
			x=rd(),y=rd(),a=rd();
			update_add(x,y,a);
		}
		else if(c=='-'){
			x=rd(),y=rd(),a=rd(),b=rd();
			cut(x,y);link(a,b);
		}
		else if(c=='*') {
			x=rd(),y=rd(),a=rd();
			update_mul(x,y,a);
		}
		else {
			x=rd(),y=rd();
			split(x,y);printf("%lld\n",sum[y]);
		}
	}
	return 0;
}