题目：Query on a tree
题意：给定一棵树，告诉了每条边的权值，然后给出两种操作：
(1)把第i条边的权值改为val
(2)询问a，b路径上权值最大的边
分析：本题与HDU3966差不多，区别就是：HDU3966是告诉树中点权的值，这里是边权。
所以我们可以转化，用边的孩子节点来表示该边。
#include <iostream>
#include <string.h>
#include <algorithm>
#include <stdio.h>using namespace std;
const int N=50010;
const int INF=1<<30;int n,tim;int num[N],siz[N],top[N],son[N];
int dep[N],tid[N],rank[N],fa[N];
int head[N],to[2*N],next[2*N],w[2*N],edge;struct Edge
{int u,v,c;
};
Edge tmp[2*N];void Init()
{memset(head,-1,sizeof(head));memset(son,-1,sizeof(son));tim=0;edge=0;
}void addedge(int u,int v,int c)
{to[edge]=v,w[edge]=c,next[edge]=head[u],head[u]=edge++;to[edge]=u,w[edge]=c,next[edge]=head[v],head[v]=edge++;
}//树链剖分部分
void dfs1(int u,int father,int d)
{dep[u]=d;fa[u]=father;siz[u]=1;for(int i=head[u]; ~i; i=next[i]){int v=to[i];if(v!=father){dfs1(v,u,d+1);siz[u]+=siz[v];if(son[u]==-1||siz[v]>siz[son[u]])son[u]=v;}}
}void dfs2(int u,int tp)
{top[u]=tp;tid[u]=++tim;rank[tid[u]]=u;if(son[u]==-1) return;dfs2(son[u],tp);for(int i=head[u]; ~i; i=next[i]){int v=to[i];if(v!=son[u]&&v!=fa[u])dfs2(v,v);}
}//线段树部分
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1int MAX[4*N];void PushUP(int rt)
{MAX[rt]=max(MAX[rt<<1],MAX[rt<<1|1]);
}void Build(int l,int r,int rt)
{if(l==r){MAX[rt]=num[l];return;}int mid=(l+r)>>1;Build(lson);Build(rson);PushUP(rt);
}void Update(int l,int r,int rt,int p,int val)
{if(l==r){MAX[rt]=val;return;}int mid=(l+r)>>1;if(p<=mid)Update(lson,p,val);elseUpdate(rson,p,val);PushUP(rt);
}int Query(int l,int r,int rt,int L,int R)
{if(L<=l&&R>=r)return MAX[rt];int mid=(l+r)>>1;int ret=-INF;if(L<=mid) ret=max(ret,Query(lson,L,R));if(R>mid) ret=max(ret,Query(rson,L,R));return ret;
}void Change(int x,int val)
{if(dep[tmp[x].u]>dep[tmp[x].v])Update(2,n,1,tid[tmp[x].u],val);elseUpdate(2,n,1,tid[tmp[x].v],val);
}int query(int x,int y)
{int ans=-INF;while(top[x]!=top[y]){if(dep[top[x]]<dep[top[y]]) swap(x,y);ans=max(ans,Query(2,n,1,tid[top[x]],tid[x]));x=fa[top[x]];}if(dep[x]>dep[y]) swap(x,y);if(x!=y) ans=max(ans,Query(2,n,1,tid[x]+1,tid[y]));return ans;
}int main()
{char oper[15];int a,b,c,t;scanf("%d",&t);while(t--){Init();scanf("%d",&n);for(int i=1; i<n; i++){scanf("%d%d%d",&a,&b,&c);tmp[i].u=a;tmp[i].v=b;tmp[i].c=c;addedge(a,b,c);}dfs1(1,1,1);dfs2(1,1);//用边的孩子节点来表示该边for(int i=1;i<n;i++){if(dep[tmp[i].u]>dep[tmp[i].v])num[tid[tmp[i].u]]=tmp[i].c;elsenum[tid[tmp[i].v]]=tmp[i].c;}Build(2,n,1);while(1){scanf("%s",oper);if(oper[0]=='D') break;scanf("%d%d",&a,&b);if(oper[0]=='Q')printf("%d\n",query(a,b));elseChange(a,b);}}return 0;
}
