SPOJ 题目375 Query on a tree（link cut tree边权更新，求两点最大值）

You are given a tree (an acyclic undirected connected graph) with N nodes, and edges numbered 1, 2, 3...N-1.

We will ask you to perfrom some instructions of the following form:

• CHANGE i ti : change the cost of the i-th edge to ti
  or
• QUERY a b : ask for the maximum edge cost on the path from node a to node b

Input

The first line of input contains an integer t, the number of test cases (t <= 20). t test cases follow.

For each test case:

• In the first line there is an integer N (N <= 10000),
• In the next N-1 lines, the i-th line describes the i-th edge: a line with three integers a b c denotes an edge between a,b of cost c (c <= 1000000),
• The next lines contain instructions "CHANGE i ti" or "QUERY a b",
• The end of each test case is signified by the string "DONE".

There is one blank line between successive tests.

Output

For each "QUERY" operation, write one integer representing its result.

Example

Input:
1

3
1 2 1
2 3 2
QUERY 1 2
CHANGE 1 3
QUERY 1 2
DONE

Output:
1
3

#include<stdio.h>   
#include<string.h>   
#include<stdlib.h>   
#include<queue>   
#include<iostream>   
#define max(a,b) (a>b?a:b)
using namespace std;  
int head[50050],cnt,vis[50050];  
struct s  
{  
    int u,v,w,next;  
}edge[50050<<1];  
struct LCT    
{    
    int bef[50050],pre[50050],next[50050][2],key[50050],val[50050],belong[50050];  
    void init()    
    {    
        memset(pre,0,sizeof(pre));  
        memset(next,0,sizeof(next));    
    }  
    void pushup(int x)  
    {  
        val[x]=max(key[x],max(val[next[x][1]],val[next[x][0]]));  
    }  
    void rotate(int x,int kind)    
    {    
        int y,z;    
        y=pre[x];    
        z=pre[y];    
        next[y][!kind]=next[x][kind];    
        pre[next[x][kind]]=y;    
        next[z][next[z][1]==y]=x;    
        pre[x]=z;    
        next[x][kind]=y;    
        pre[y]=x;  
        pushup(y);  
    }    
    void splay(int x)    
    {    
        int rt;    
        for(rt=x;pre[rt];rt=pre[rt]);    
        if(x!=rt)    
        {    
            bef[x]=bef[rt];    
            bef[rt]=0;    
            while(pre[x])    
            {    
                if(next[pre[x]][0]==x)    
                {    
                    rotate(x,1);    
                }    
                else    
                    rotate(x,0);    
            }    
            pushup(x);  
        }    
    }   
    void access(int x)    
    {    
        int fa;    
        for(fa=0;x;x=bef[x])    
        {    
            splay(x);    
            pre[next[x][1]]=0;    
            bef[next[x][1]]=x;    
            next[x][1]=fa;    
            pre[fa]=x;    
            bef[fa]=0;    
            fa=x;    
            pushup(x);  
        }    
    }  
    void change(int x,int val)  
    {  
        int t;  
        t=belong[x-1];  
        key[t]=val;  
        splay(t);  
    }  
    int query(int x,int y)  
    {  
        access(y);  
        for(y=0;x;x=bef[x])  
        {  
            splay(x);  
            if(!bef[x])  
                return max(val[y],val[next[x][1]]);  
            pre[next[x][1]]=0;  
            bef[next[x][1]]=x;  
            next[x][1]=y;  
            pre[y]=x;  
            bef[y]=0;  
            y=x;  
            pushup(x);  
        }  
    }  
}lct;  
void add(int u,int v,int w)  
{  
    edge[cnt].u=u;  
    edge[cnt].v=v;  
    edge[cnt].w=w;  
    edge[cnt].next=head[u];  
    head[u]=cnt++;  
}  
void bfs(int u)  
{  
    int i,y;  
    queue<int>q;  
    memset(vis,0,sizeof(vis));  
    vis[u]=1;  
    q.push(u);  
    while(!q.empty())  
    {  
        u=q.front();  
        q.pop();  
        for(int i=head[u];i!=-1;i=edge[i].next)  
        {  
            int v=edge[i].v;  
            if(!vis[v])  
            {  
                lct.bef[v]=u;  
                lct.key[v]=lct.val[v]=edge[i].w;  
                lct.belong[i>>1]=v;  
                vis[v]=1;  
                q.push(v);  
            }  
        }  
    }  
}  
int main()
{
	int t;
	scanf("%d",&t);
	while(t--)
	{
		int n;
		memset(head,-1,sizeof(head));
		cnt=0;
		int i;
		char s[10];
		scanf("%d",&n);
		for(i=1;i<n;i++)
		{
			int a,b,c;
			scanf("%d%d%d",&a,&b,&c);
			add(a,b,c);
			add(b,a,c);
		}
		lct.init();
		bfs(1);
		while(scanf("%s",s)!=EOF)
		{
			int a,b;
			if(strcmp(s,"DONE")==0)
				break;
			scanf("%d%d",&a,&b);
			if(s[0]=='Q')
			{
				printf("%d\n",lct.query(a,b));
			}
			else
				lct.change(a,b);
		}
	}
}

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