[国家集训队]Tree

Tree

题解

一道LCT板题。

看样子就像是一道LCT的板题，只需要将乘与加的懒标记分别传下去即可。

‘-’就是简单的树上加边与删边

‘/'就是查询和，update时更新即可。

不过需要注意一下在乘与加时懒标记与总数的变化。

mul是乘的懒标记，add是加的懒标记，sum是当前和，siz是子树大小。

公式其实很好推的，关键是别直接乘与加，笔者就因为这个WA了

源码

#include<cstdio>
#include<cmath>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<queue>
#include<vector>
#include<map>
using namespace std;
#define MAXN 100010
typedef long long LL;
#define int LL
typedef pair<LL,LL> pii;
#define gc() getchar()
const int INF=0x7f7f7f7f;
const int mo=51061;
template<typename _T>
inline void read(_T &x){
	_T f=1;x=0;char s=gc();
	while(s>'9'||s<'0'){if(s=='-')f=-1;s=gc();}
	while(s>='0'&&s<='9'){x=(x<<3)+(x<<1)+(s^48);s=gc();}
	x*=f;
}
class LCT{
	private:
		int val[MAXN],father[MAXN];
		int ch[MAXN][2];
		int lzyadd[MAXN],lzymul[MAXN];
		int siz[MAXN],sum[MAXN],rev[MAXN];
		int stak,sta[MAXN];
		void pushup(int x){
			siz[x]=(1+siz[ch[x][0]]+siz[ch[x][1]])%mo;
			sum[x]=(val[x]+sum[ch[x][0]]+sum[ch[x][1]])%mo;
		}
		void pushdown(int x){
			if(rev[x]){
				swap(ch[x][0],ch[x][1]);rev[x]=0;
				rev[ch[x][0]]^=1;rev[ch[x][1]]^=1;
			}
			if(lzymul[x]!=1||lzyadd[x]){
				(val[ch[x][0]]*=lzymul[x])%=mo;(val[ch[x][1]]*=lzymul[x])%=mo;
				(val[ch[x][0]]+=lzyadd[x])%=mo;(val[ch[x][1]]+=lzyadd[x])%=mo;
				(lzymul[ch[x][0]]*=lzymul[x])%=mo;(lzymul[ch[x][1]]*=lzymul[x])%=mo;
				(lzyadd[ch[x][0]]*=lzymul[x])%=mo;(lzyadd[ch[x][1]]*=lzymul[x])%=mo;
				(lzyadd[ch[x][0]]+=lzyadd[x])%=mo;(lzyadd[ch[x][1]]+=lzyadd[x])%=mo;
				(sum[ch[x][0]]*=lzymul[x])%=mo;(sum[ch[x][0]]+=siz[ch[x][0]]*lzyadd[x])%=mo;
				(sum[ch[x][1]]*=lzymul[x])%=mo;(sum[ch[x][1]]+=siz[ch[x][1]]*lzyadd[x])%=mo;
				lzyadd[x]=0;lzymul[x]=1;
			}
		}
		bool identify(int x){
			return ch[father[x]][1]==x;
		}
		bool isRoot(int x){
			return ch[father[x]][0]!=x&&ch[father[x]][1]!=x;
		}
		void connect(int x,int fa,int tag){
			father[x]=fa;ch[fa][tag]=x;
		}
		void rotate(int x){
			int y=father[x],z=father[y];
			pushdown(x);pushdown(y);
			int d1=identify(y),d2=identify(x);
			int B=ch[x][d2^1];father[x]=z;
			if(!isRoot(y))connect(x,z,d1);
			connect(B,y,d2);connect(y,x,d2^1);
			pushup(y);pushup(x);
		}
		void splay(int x){
			int y=x,top=0;
			sta[++top]=y;while(!isRoot(y))sta[++top]=(y=father[y]);
			while(top)pushdown(sta[top--]);
			for(int y=father[x];!isRoot(x);rotate(x),y=father[x])
				if(!isRoot(y))rotate(identify(x)==identify(y)?y:x);
		}
	public:
		void access(int x){
			for(int y=0;x;x=father[y=x])splay(x),ch[x][1]=y,pushup(x);
		}
		void makeroot(int x){
			access(x);splay(x);rev[x]^=1;//pushdown(x);
		}
		int findroot(int x){
			access(x);splay(x);pushdown(x);
			while(ch[x][0])pushdown(x=ch[x][0]);
			return x;
		}
		int split(int x,int y){
			makeroot(x);access(y);splay(y);
			return sum[y];
		}
		void linkTree(int x,int y){
			//printf("Link%d %d\n",x,y);
			makeroot(x);pushdown(x);
			if(findroot(y)!=x)father[x]=y;
		}
		void cutTree(int x,int y){
			//printf("Cut%d %d\n",x,y);
			makeroot(x);pushdown(x);
			if(findroot(y)!=x||father[x]!=y||ch[y][0]!=x||ch[x][1])return ;
			father[x]=ch[y][0]=0,pushup(x);
		}
		void modifyTree(int x,int y){
			if(val[x]==y)return ;
			splay(x);val[x]=y;
		}
		void addTree(int x,int y,int d){
			makeroot(x);access(y);splay(y);
			(val[y]+=d)%=mo;(sum[y]+=siz[y]*d)%=mo;
			(lzyadd[y]+=d)%=mo;
			pushdown(y);
		}
		void mulTree(int x,int y,int d){
			makeroot(x);access(y);splay(y);
			(val[y]*=d)%=mo;(sum[y]*=d)%=mo;
			(lzymul[y]*=d)%=mo;(lzyadd[y]*=d)%=mo;
			pushdown(y);
		}
		bool queryLink(int x,int y){
			makeroot(x);
			if(findroot(y)==x)return 1;
			return 0;
		}
		void build(int n){
			for(int i=1;i<=n;i++)val[i]=lzymul[i]=1;
		}
}Tree;
int n,q;
signed main(){ 
	read(n);read(q);Tree.build(n);
	for(int i=1;i<n;i++){
		int u,v;read(u);read(v);
		Tree.linkTree(u,v);
	}
	for(int i=1;i<=q;i++){
		char opt[5];scanf("\n%s",opt);
		if(opt[0]=='+'){
			int u,v,c;read(u);read(v);read(c);
			Tree.addTree(u,v,c);
		}
		if(opt[0]=='-'){
			int u1,v1,u2,v2;
			read(u1);read(v1);read(u2);read(v2);
			Tree.cutTree(u1,v1);Tree.linkTree(u2,v2);
		}
		if(opt[0]=='*'){
			int u,v,c;read(u);read(v);read(c);
			Tree.mulTree(u,v,c);
		}
		if(opt[0]=='/'){
			int u,v;read(u);read(v);
			printf("%lld\n",Tree.split(u,v));
		}
	}
    return 0;
}

谢谢！！！