spoj375 樹鏈剖分（單點更新，區間查詢）

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

/**
spoj375 樹鏈剖分（單點更新，區間查詢）
參考：
http://blog.sina.com.cn/s/blog_7a1746820100wp67.html
總結的很經典，樹鏈剖分的第一題建議從它開始
*/
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <iostream>
///#define debug
using namespace std;
const int maxn=10005;
int fa[maxn],siz[maxn],son[maxn],num[maxn],top[maxn],dep[maxn];
int tree[maxn*4],d[maxn][3];
int n,z;
int head[maxn],ip;
void init()
{
    memset(head,-1,sizeof(head));
    ip=0;
}

struct note
{
    int v,w,next;
}edge[maxn*2];

void addedge(int u,int v,int w)
{
    edge[ip].v=v,edge[ip].w=w,edge[ip].next=head[u],head[u]=ip++;
}

void dfs(int u,int pre)
{
    son[u]=0,siz[u]=1;
    dep[u]=dep[pre]+1;
    fa[u]=pre;
    for(int i=head[u];i!=-1;i=edge[i].next)
    {
        int v=edge[i].v;
        if(v==pre)continue;
        dfs(v,u);
        if(siz[v]>siz[son[u]])
            son[u]=v;
        siz[u]+=siz[v];
    }
    #ifdef debug
    printf("%d:siz,son,dep,fa %d %d %d %d\n",u,siz[u],son[u],dep[u],fa[u]);
    #endif
}

void build(int u,int tp)
{
     num[u]=++z,top[u]=tp;
     if(son[u]!=0)
     {
        build(son[u],top[u]);
     }
     for(int i=head[u];i!=-1;i=edge[i].next)
     {
        int v=edge[i].v;
        if(v==fa[u]||v==son[u])continue;
        build(v,v);
     }
     #ifdef debug
     printf("%d num,top %d %d\n",u,num[u],top[u]);
     #endif // debug
}

void update(int root,int l,int r,int loc,int x)
{
    if(l>loc||r<loc)return;
    if(l==r)
    {
        tree[root]=x;
        return;
    }
    int mid=(l+r)>>1;
    update(root<<1,l,mid,loc,x);
    update(root<<1|1,mid+1,r,loc,x);
    tree[root]=max(tree[root<<1],tree[root<<1|1]);
    #ifdef debug
    printf("root,l,r,tree[root]%d %d %d %d\n",root,l,r,tree[root]);
    #endif // debug
}

int maxi(int root,int l,int r,int a,int b)
{
    if(r<a||l>b)return 0;
    if(b>=r&&a<=l)
    {
        return tree[root];
    }
    int mid=(l+r)>>1;
    return max(maxi(root<<1,l,mid,a,b),maxi(root<<1|1,mid+1,r,a,b));
}
int find(int va,int vb)
{
    int f1=top[va],f2=top[vb],tmp=0;
    while(f1!=f2)
    {
        if(dep[f1]<dep[f2])
        {
            swap(f1,f2);
            swap(va,vb);
        }
        tmp=max(tmp,maxi(1,1,z,num[f1],num[va]));
        va=fa[f1],f1=top[va];
    }
    if(va==vb)return tmp;
    ///兩點已經在同一條鏈上，但是不是同一個點
    if(dep[va]>dep[vb])swap(va,vb);
    return max(tmp,maxi(1,1,z,num[son[va]],num[vb]));
}
int main()
{
   /// freopen("data.txt","r",stdin);
    int T;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d",&n);
        init();
        memset(d,0,sizeof(d));
        for(int i=1;i<n;i++)
        {
            int x,y,z;
            scanf("%d%d%d",&x,&y,&z);
            d[i][0]=x,d[i][1]=y,d[i][2]=z;
            addedge(x,y,z);
            addedge(y,x,z);
        }
        int root=(n+1)>>1;
        z=0,dep[0]=0;
        dfs(root,0);
        build(root,root);
        for(int i=1;i<n;i++)
        {
            if(dep[d[i][0]]>dep[d[i][1]])
            {
                swap(d[i][0],d[i][1]);
            }
            update(1,1,z,num[d[i][1]],d[i][2]);
        }
        while(1)
        {
            char c[25];
            scanf("%s",c);
            if(c[0]=='D')break;
            int a,b;
            scanf("%d%d",&a,&b);
            if(c[0]=='Q')
            {
                printf("%d\n",find(a,b));
            }
            else
            {
                update(1,1,z,num[d[a][1]],b);
            }
        }
    }
    return 0;
}