bzoj 3091 城市旅行 lct

版权声明：本文为博主原创文章，未经博主允许不得转载。 https://blog.csdn.net/liufengwei1/article/details/86663378

orz SongHL https://www.cnblogs.com/songorz/p/9912208.html

上课讲的例题，讲得比qt清楚多了，lct也讲的很透，很好理解

#include<bits/stdc++.h>
#define maxl 50010
#define LL long long

using namespace std;

const int inf=0x3f3f3f3f;

int n,m;
int fa[maxl];
struct node
{
	int son[2];
	long long sum,tag,rev,ans,val,lsum,rsum,size;
	int& operator [] (int x) {return son[x];} 
}tree[maxl];

long long gcd(long long a,long long b)
{
	if(b==0)
		return a;
	else
		return gcd(b,a%b);
}

namespace LCT
{
	void reverse(int k) 
    {
        swap(tree[k][0],tree[k][1]);
        swap(tree[k].lsum,tree[k].rsum);
        tree[k].rev^=1;
    }
    void add(int k,LL val) 
    {
        tree[k].val+=val;
        tree[k].sum+=tree[k].size*val;
        tree[k].tag+=val;
        tree[k].ans+=tree[k].size*(tree[k].size+1)*(tree[k].size+2)/6*val;
        tree[k].lsum+=tree[k].size*(tree[k].size+1)/2*val;
        tree[k].rsum+=tree[k].size*(tree[k].size+1)/2*val;
    }
    int find(int x) {return fa[x] ? find(fa[x]):x;}
    void pushdown(int k) 
    {
        if(tree[fa[k]][0]==k || tree[fa[k]][1]==k) pushdown(fa[k]);
        int l=tree[k][0],r=tree[k][1];
        if(tree[k].rev) 
        {
            if(l) reverse(l);
            if(r) reverse(r);
            tree[k].rev^=1;
        }
        if(tree[k].tag) 
        {
            if(l) add(l,tree[k].tag);
            if(r) add(r,tree[k].tag);
            tree[k].tag=0;
        }
    }
    void pushup(int k) 
    {
        int l=tree[k][0],r=tree[k][1];
        tree[k].size=tree[l].size+tree[r].size+1;
        tree[k].lsum=tree[l].lsum+(tree[l].size+1)*tree[k].val+tree[r].lsum+tree[r].sum*(tree[l].size+1);
        tree[k].rsum=tree[r].rsum+(tree[r].size+1)*tree[k].val+tree[l].rsum+tree[l].sum*(tree[r].size+1);
        tree[k].sum=tree[l].sum+tree[r].sum+tree[k].val;
        tree[k].ans=tree[l].ans+tree[r].ans+tree[l].lsum*(tree[r].size+1)+tree[r].rsum*(tree[l].size+1)+tree[k].val*(tree[l].size+1)*(tree[r].size+1);
    }
	void rotate(int x)
	{
		int y=fa[x],z=fa[y],l,r;
		l=(tree[y][1]==x);r=l^1;
		if(tree[z][0]==y || tree[z][1]==y)
			tree[z][tree[z][1]==y]=x;
		fa[tree[x][r]]=y;fa[x]=z;fa[y]=x;
		tree[y][l]=tree[x][r];tree[x][r]=y;
		pushup(y);pushup(x);
	}
	void splay(int x)
	{
		pushdown(x);
		while(tree[fa[x]][0]==x || tree[fa[x]][1]==x)
		{
			int y=fa[x],z=fa[y];
			if(tree[z][0]==y || tree[z][1]==y)
			{
				if(tree[z][0]==y ^ tree[y][0]==x)
					rotate(x);
				else
					rotate(y);
			}
			rotate(x);
		}
	}
	void access(int x)
	{
		for(int y=0;x;y=x,x=fa[x]) 
			splay(x),tree[x][1]=y,pushup(x);
	}
	int findroot(int x)
	{
		access(x),splay(x);
		while(tree[x][0]) pushdown(x),x=tree[x][0];
		return x;
	}
	void makeroot(int x)
	{
		access(x);splay(x);reverse(x);
	}
	void split(int x,int y)
	{
		makeroot(x);
		access(y);splay(y);
	}
	void link(int x,int y)
	{
		makeroot(x);fa[x]=y;
	}
	void cut(int x,int y)
	{
		makeroot(x);access(y);splay(y);
		if(tree[y][0]==x && tree[x][1]==0)
			tree[y][0]=0,fa[x]=0,pushup(y);
	}
	void modify(int x,int y,long long val)
	{
		makeroot(x);access(y);
		splay(y);add(y,val);
	}
	void query(int x,int y)
	{
		split(x,y);
		long long A=tree[y].ans;
		long long B=tree[y].size*(tree[y].size+1)/2;
		long long D=gcd(A,B);
		printf("%lld/%lld\n",A/D,B/D);
	}
}
using namespace LCT;

int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++)
		scanf("%lld",&tree[i].val);
	int u,v;
	for(int i=1;i<n;i++)
	{
		scanf("%d%d",&u,&v);
		link(u,v);
	}
	int opt,x,y,d;
	for(int i=1;i<=m;i++)
	{
		scanf("%d%d%d",&opt,&x,&y);
		if(opt==1)
			if(find(x)==find(y))
				cut(x,y);
		if(opt==2)
			if(find(x)!=find(y))
				link(x,y);
		if(opt==3)
		{
			scanf("%d",&d);
			if(find(x)==find(y))
				modify(x,y,d);
		}
		if(opt==4)
			if(find(x)==find(y))
				query(x,y);
			else
				puts("-1");
	}
	return 0;
}