【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=100000 + 10;
const int maxnode = 100000;
const int maxm=100000 * 2 + 10;
using namespace std;
struct Node{//权值线段树 
       int l, r;
       int Max, Min;
       bool neg;//取反标记 
}tree[maxn * 4];
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] = 1;
     son[u] = 0;
     for (int i = head[u]; i != -1; i = next[i]){
         int v = to[i];
         if (v == fa[u]) continue;
         dep[v] = dep[u] + 1;
         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 != -1; 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 = 0;
     if (l == r) return;
     
     int mid = (l + r) >> 1;
     build(x << 1, l, mid);
     build((x << 1) | 1, mid + 1, r);
}
void update(int x){
     tree[x].Max = max(tree[x << 1].Max, tree[(x << 1) | 1].Max);
     tree[x].Min = min(tree[x << 1].Min, tree[(x << 1) | 1].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 << 1), r = l | 1;
        tree[l].neg ^= 1;
        tree[l].Min *= -1;
        tree[l].Max *= -1;
        swap(tree[l].Min, tree[l].Max);
        
        tree[r].neg ^= 1;
        tree[r].Min *= -1;
        tree[r].Max *= -1;
        swap(tree[r].Min, tree[r].Max);
        
        tree[x].neg = 0;
     }
}
//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 = 1;
           tree[x].Min *= -1;
           tree[x].Max *= -1;
           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) >> 1;
     if (r <= mid) change2(x << 1, l, r, val);
     else if (l > mid) change2((x << 1) | 1, l, r, val);
     else{
          change2(x << 1, l, mid, val);
          change2((x << 1) | 1, mid + 1, 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) >> 1; 
     if (r <= mid) return query2(x << 1, l, r);
     else if (l > mid) return query2((x << 1) | 1, l, r);
     else return max(query2((x << 1), l, mid), query2((x << 1) | 1, mid + 1, 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(1, pos[top[x]], pos[x], v);
           x = fa[top[x]];
     }
     
     if (x == y) return;
     if (dep[x] > dep[y]) swap(x, y);
     change2(1, 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(1, 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(1, pos[son[x]], pos[y]));
    return Ans == -INF ? 0 : Ans;
}
void work(){
    while(1){
        char str[20];
        scanf("%s", str);
        if(str[0] == 'C'){
            int x, v;
            scanf("%d%d", &x, &v);
            change2(1, pos[edges[x].v], pos[edges[x].v], v);
        }else if(str[0] == 'N'){
            int l, r;
            scanf("%d%d", &l, &r);
            change(l, r, INF);
        }else if(str[0] == 'Q'){//询问两点之间最大值 
            int l, r;
            scanf("%d%d", &l, &r);
            printf("%d
", 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, -1, sizeof(head));//邻接表初始化
     memset(dep, 0, sizeof(dep));
     M = Time = 0;//总边数和时间 
     fa[1] = size[0] = 0;
     //加边 
     scanf("%d", &n);
     for (int i = 1; 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(1);
     dfs_2(1, 1);
     build(1, 1, Time);
     for (int i = 1; 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(1, pos[edges[i].v], pos[edges[i].v], edges[i].w);
    }
}

int main(){
    int T;
    
    scanf("%d", &T);
    while (T--){
          init();
          work();
    }
    //printf("%d
", INF); 
    return 0;
}