spoj375 树链剖分（单点更新，区间查询）

http://www.spoj.com/problems/QTREE/

QTREE - Query on a tree

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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 树链剖分（单点更新，区间查询）
参考：
http://blog.sina.com.cn/s/blog_7a1746820100wp67.html
总结的很经典，树链剖分的第一题建议从它开始
*/
#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;
    ///两点已经在同一条链上，但是不是同一个点
    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;
}