POJ 3237 Tree （树链剖分）

Tree

Time Limit: 5000MS		Memory Limit: 131072K
Total Submissions: 2825		Accepted: 769

Description

You are given a tree with N nodes. The tree’s nodes are numbered 1 through N and its edges are numbered 1 through N − 1. Each edge is associated with a weight. Then you are to execute a series of instructions on the tree. The instructions can be one of the following forms:

CHANGE i v	Change the weight of the ith edge to v
NEGATE a b	Negate the weight of every edge on the path from a to b
QUERY a b	Find the maximum weight of edges on the path from a to b

Input

The input contains multiple test cases. The first line of input contains an integer t (t ≤ 20), the number of test cases. Then follow the test cases.

Each test case is preceded by an empty line. The first nonempty line of its contains N (N ≤ 10,000). The next N − 1 lines each contains three integers a, b and c, describing an edge connecting nodes a and b with weight c. The edges are numbered in the order they appear in the input. Below them are the instructions, each sticking to the specification above. A lines with the word “DONE” ends the test case.

Output

For each “QUERY” instruction, output the result on a separate line.

Sample Input

1

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

Sample Output

1
3

Source

POJ Monthly--2007.06.03, Lei, Tao

树链剖分+线段树实现

 /* ***********************************************
 Author        :kuangbin
 Created Time  :2013/8/17 4:04:42
 File Name     :F:\2013ACM练习\专题学习\数链剖分\POJ3237Tree.cpp
 ************************************************ */

 #include <stdio.h>
 #include <string.h>
 #include <iostream>
 #include <algorithm>
 #include <vector>
 #include <queue>
 #include <set>
 #include <map>
 #include <string>
 #include <math.h>
 #include <stdlib.h>
 #include <time.h>
 using namespace std;

 const int MAXN = ;
 struct Edge
 {
     int to,next;
 }edge[MAXN*];
 int head[MAXN],tot;
 int top[MAXN];//top[v]表示v所在的重链的顶端节点
 int fa[MAXN]; //父亲节点
 int deep[MAXN];//深度
 int num[MAXN];//num[v]表示以v为根的子树的节点数
 int p[MAXN];//p[v]表示v与其父亲节点的连边在线段树中的位置
 int fp[MAXN];//和p数组相反
 int son[MAXN];//重儿子
 int pos;
 void init()
 {
     tot = ;
     memset(head,-,sizeof(head));
     pos = ;
     memset(son,-,sizeof(son));
 }
 void addedge(int u,int v)
 {
     edge[tot].to = v;edge[tot].next = head[u];head[u] = tot++;
 }
 void dfs1(int u,int pre,int d) //第一遍dfs求出fa,deep,num,son
 {
     deep[u] = d;
     fa[u] = pre;
     num[u] = ;
     for(int i = head[u];i != -; i = edge[i].next)
     {
         int v = edge[i].to;
         if(v != pre)
         {
             dfs1(v,u,d+);
             num[u] += num[v];
             if(son[u] == - || num[v] > num[son[u]])
                 son[u] = v;
         }
     }
 }
 void getpos(int u,int sp) //第二遍dfs求出top和p
 {
     top[u] = sp;
     p[u] = pos++;
     fp[p[u]] = u;
     if(son[u] == -) return;
     getpos(son[u],sp);
     for(int i = head[u] ; i != -; i = edge[i].next)
     {
         int v = edge[i].to;
         if(v != son[u] && v != fa[u])
             getpos(v,v);
     }
 }

 //线段树
 struct Node
 {
     int l,r;
     int Max;
     int Min;
     int ne;
 }segTree[MAXN*];
 void build(int i,int l,int r)
 {
     segTree[i].l = l;
     segTree[i].r = r;
     segTree[i].Max = ;
     segTree[i].Min = ;
     segTree[i].ne = ;
     if(l == r)return;
     int mid = (l+r)/;
     build(i<<,l,mid);
     build((i<<)|,mid+,r);
 }
 void push_up(int i)
 {
     segTree[i].Max = max(segTree[i<<].Max,segTree[(i<<)|].Max);
     segTree[i].Min = min(segTree[i<<].Min,segTree[(i<<)|].Min);
 }
 void push_down(int i)
 {
     if(segTree[i].l == segTree[i].r)return;
     if(segTree[i].ne)
     {
         segTree[i<<].Max = -segTree[i<<].Max;
         segTree[i<<].Min = -segTree[i<<].Min;
         swap(segTree[i<<].Min,segTree[i<<].Max);
         segTree[(i<<)|].Max = -segTree[(i<<)|].Max;
         segTree[(i<<)|].Min = -segTree[(i<<)|].Min;
         swap(segTree[(i<<)|].Max,segTree[(i<<)|].Min);
         segTree[i<<].ne ^= ;
         segTree[(i<<)|].ne ^= ;
         segTree[i].ne = ;
     }
 }
 void update(int i,int k,int val) // 更新线段树的第k个值为val
 {
     if(segTree[i].l == k && segTree[i].r == k)
     {
         segTree[i].Max = val;
         segTree[i].Min = val;
         segTree[i].ne = ;
         return;
     }
     push_down(i);
     int mid = (segTree[i].l + segTree[i].r)/;
     if(k <= mid)update(i<<,k,val);
     else update((i<<)|,k,val);
     push_up(i);
 }
 void ne_update(int i,int l,int r) // 更新线段树的区间[l,r]取反
 {
     if(segTree[i].l == l && segTree[i].r == r)
     {
         segTree[i].Max = -segTree[i].Max;
         segTree[i].Min = -segTree[i].Min;
         swap(segTree[i].Max,segTree[i].Min);
         segTree[i].ne ^= ;
         return;
     }
     push_down(i);
     int mid = (segTree[i].l + segTree[i].r)/;
     if(r <= mid)ne_update(i<<,l,r);
     else if(l > mid) ne_update((i<<)|,l,r);
     else
     {
         ne_update(i<<,l,mid);
         ne_update((i<<)|,mid+,r);
     }
     push_up(i);
 }
 int query(int i,int l,int r)  //查询线段树中[l,r] 的最大值
 {
     if(segTree[i].l == l && segTree[i].r == r)
         return segTree[i].Max;
     push_down(i);
     int mid = (segTree[i].l + segTree[i].r)/;
     if(r <= mid)return query(i<<,l,r);
     else if(l > mid)return query((i<<)|,l,r);
     else return max(query(i<<,l,mid),query((i<<)|,mid+,r));
     push_up(i);
 }
 int findmax(int u,int v)//查询u->v边的最大值
 {
     int f1 = top[u], f2 = top[v];
     int tmp = -;
     while(f1 != f2)
     {
         if(deep[f1] < deep[f2])
         {
             swap(f1,f2);
             swap(u,v);
         }
         tmp = max(tmp,query(,p[f1],p[u]));
         u = fa[f1]; f1 = top[u];
     }
     if(u == v)return tmp;
     if(deep[u] > deep[v]) swap(u,v);
     return max(tmp,query(,p[son[u]],p[v]));
 }
 void Negate(int u,int v)//把u-v路径上的边的值都设置为val
 {
     int f1 = top[u], f2 = top[v];
     while(f1 != f2)
     {
         if(deep[f1] < deep[f2])
         {
             swap(f1,f2);
             swap(u,v);
         }
         ne_update(,p[f1],p[u]);
         u = fa[f1]; f1 = top[u];
     }
     if(u == v)return;
     if(deep[u] > deep[v]) swap(u,v);
     return ne_update(,p[son[u]],p[v]);
 }
 int e[MAXN][];
 int main()
 {
     //freopen("in.txt","r",stdin);
     //freopen("out.txt","w",stdout);
     int T;
     int n;
     scanf("%d",&T);
     while(T--)
     {
         init();
         scanf("%d",&n);
         for(int i = ;i < n-;i++)
         {
             scanf("%d%d%d",&e[i][],&e[i][],&e[i][]);
             addedge(e[i][],e[i][]);
             addedge(e[i][],e[i][]);
         }
         dfs1(,,);
         getpos(,);
         build(,,pos-);
         for(int i = ;i < n-; i++)
         {
             if(deep[e[i][]] > deep[e[i][]])
                 swap(e[i][],e[i][]);
             update(,p[e[i][]],e[i][]);
         }
         char op[];
         int u,v;
         while(scanf("%s",op) == )
         {
             if(op[] == 'D')break;
             scanf("%d%d",&u,&v);
             if(op[] == 'Q')
                 printf("%d\n",findmax(u,v));//查询u->v路径上边权的最大值
             else if(op[] == 'C')
                 update(,p[e[u-][]],v);//改变第u条边的值为v
             else Negate(u,v);
         }
     }
     return ;
 }