【POJ3237】【树链剖分】Tree

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

【分析】

好久没写了。

写一道练练手。

 /*
 宋代苏轼
 《南乡子·重九涵辉楼呈徐君猷》
 霜降水痕收。浅碧鳞鳞露远洲。酒力渐消风力软，飕飕。破帽多情却恋头。
 佳节若为酬。但把清尊断送秋。万事到头都是梦，休休。明日黄花蝶也愁。
 */
 #include <iostream>
 #include <cstdio>
 #include <algorithm>
 #include <cstring>
 #include <vector>
 #include <utility>
 #include <iomanip>
 #include <string>
 #include <cmath>
 #include <queue>
 #include <assert.h>
 #include <map>
 #include <ctime>
 #include <cstdlib>
 #include <stack>
 #define LOCAL
 const int INF = 0x3f3f3f3f;
 const int maxn= + ;
 const int maxnode = ;
 const int maxm= *  + ;
 using namespace std;
 struct Node{//权值线段树
        int l, r;
        int Max, Min;
        bool neg;//取反标记
 }tree[maxn * ];
 struct Edge{
        int u, v, w;
 }edges[maxn];//输入的边 

 int n, fa[maxn], size[maxn];
 int son[maxn], dep[maxn], top[maxn];
 int pos[maxn], Time;
 int M, head[maxn], next[maxm], to[maxm], w[maxm];

 //第一次dfs
 void dfs_1(int u){
      size[u] = ;
      son[u] = ;
      for (int i = head[u]; i != -; i = next[i]){
          int v = to[i];
          if (v == fa[u]) continue;
          dep[v] = dep[u] + ;
          fa[v] = u;
          dfs_1(v);
          size[u] += size[v];
          if (size[v] > size[son[u]]) son[u] = v;
      }
      return;
 }
 void dfs_2(int u, int top_node){
      top[u] = top_node;
      pos[u] = ++Time;//给他和他的父亲的边在线段树中的位置
      //重边
      if (son[u]) dfs_2(son[u], top_node);
      //轻边
      for (int i = head[u]; i != -; i = next[i]){
          int v = to[i];
          if (v == fa[u] || v == son[u]) continue;
          dfs_2(v, v);
      }
 }
 //建树
 void build(int x, int l, int r){
      tree[x].l = l;tree[x].r = r;
      tree[x].Max = -INF;
      tree[x].Min = INF;
      tree[x].neg = ;
      if (l == r) return;

      int mid = (l + r) >> ;
      build(x << , l, mid);
      build((x << ) | , mid + , r);
 }
 void update(int x){
      tree[x].Max = max(tree[x << ].Max, tree[(x << ) | ].Max);
      tree[x].Min = min(tree[x << ].Min, tree[(x << ) | ].Min);
      return;
 }
 //标记下传
 void pushdown(int x){
      if (tree[x].l == tree[x].r) return;

      if (tree[x].neg){
         int l = (x << ), r = l | ;
         tree[l].neg ^= ;
         tree[l].Min *= -;
         tree[l].Max *= -;
         swap(tree[l].Min, tree[l].Max);

         tree[r].neg ^= ;
         tree[r].Min *= -;
         tree[r].Max *= -;
         swap(tree[r].Min, tree[r].Max);

         tree[x].neg = ;
      }
 }
 //在线段树中修改l,r为val
 void change2(int x, int l, int r, int val){
      pushdown(x);
      if (tree[x].l == l && tree[x].r == r){
         if (val == INF){//取反操作,注意已经pushdown过了
            tree[x].neg = ;
            tree[x].Min *= -;
            tree[x].Max *= -;
            swap(tree[x].Min, tree[x].Max);
         } else tree[x].Min = tree[x].Max = val;//更新val
         return;
      }

      int mid = (tree[x].l + tree[x].r) >> ;
      if (r <= mid) change2(x << , l, r, val);
      else if (l > mid) change2((x << ) | , l, r, val);
      else{
           change2(x << , l, mid, val);
           change2((x << ) | , mid + , r, val);
      }
      update(x);
 }
 int query2(int x, int l, int r){
      pushdown(x);
      if (tree[x].l == l && tree[x].r == r) return tree[x].Max;

      int mid = (tree[x].l + tree[x].r) >> ;
      if (r <= mid) return query2(x << , l, r);
      else if (l > mid) return query2((x << ) | , l, r);
      else return max(query2((x << ), l, mid), query2((x << ) | , mid + , r));
 }
 //树链剖分部分
 void change(int x, int y, int v){
      while (top[x] != top[y]){
            //总是矮的往上爬..
            //保证dep[top[x]] >= dep[top[y]]
            if (dep[top[x]] < dep[top[y]]) swap(x, y);

            change2(, pos[top[x]], pos[x], v);
            x = fa[top[x]];
      }

      if (x == y) return;
      if (dep[x] > dep[y]) swap(x, y);
      change2(, pos[son[x]], pos[y], v);
 }
 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, query2(, pos[top[x]], pos[x]));
           x = fa[top[x]];
     }
     if (x == y) return Ans;
     if (dep[x] > dep[y]) swap(x, y);
     Ans = max(Ans, query2(, pos[son[x]], pos[y]));
     return Ans == -INF ?  : Ans;
 }
 void work(){
     while(){
         char str[];
         scanf("%s", str);
         if(str[] == 'C'){
             int x, v;
             scanf("%d%d", &x, &v);
             change2(, pos[edges[x].v], pos[edges[x].v], v);
         }else if(str[] == 'N'){
             int l, r;
             scanf("%d%d", &l, &r);
             change(l, r, INF);
         }else if(str[] == 'Q'){//询问两点之间最大值
             int l, r;
             scanf("%d%d", &l, &r);
             printf("%d\n", query(l, r));
         }else break;
     }
 }
 //加边
 void addEdge(int u, int v, int c){
      to[M] = v;
      w[M] = c;
      next[M] = head[u];
      head[u] = M++;
 }
 void init(){
      memset(head, -, sizeof(head));//邻接表初始化
      memset(dep, , sizeof(dep));
      M = Time = ;//总边数和时间
      fa[] = size[] = ;
      //加边
      scanf("%d", &n);
      for (int i = ; i < n; i++){
          scanf("%d%d%d", &edges[i].u, &edges[i].v, &edges[i].w);
          addEdge(edges[i].u, edges[i].v, edges[i].w);
          addEdge(edges[i].v, edges[i].u, edges[i].w);
      }
      dfs_1();
      dfs_2(, );
      build(, , Time);
      for (int i = ; i < n; i++){
          int x = edges[i].u, y = edges[i].v;
          //判断父亲
          if (dep[x] > dep[y]) swap(edges[i].u, edges[i].v);
          //u一定是父亲
          change2(, pos[edges[i].v], pos[edges[i].v], edges[i].w);
     }
 }

 int main(){
     int T;

     scanf("%d", &T);
     while (T--){
           init();
           work();
     }
     //printf("%d\n", INF);
     return ;
 }