POJ 3237 树链剖分

 

题目链接：http://poj.org/problem?id=3237

题意：给定一棵n个结点n-1条边的树。 每条边都是一个边权。 现在有4种操作

1：CHANGE I V：把(输入的)第i条边的边权改为V

2：NEGATE a b:把点a到点b的路径上的边权取反

3：QUERY a b:输出点a到点b的路径上边权最大值。

4：DONE：结束操作。

思路：树链剖分。 涉及的是边权所以把边权转化为点权，做法是将边权赋值到这条边deep大的点上。 剖分后用线段树维护。 1操作对应单点更新 2操作对应区间更新 3操作对应区间查询。

对于2操作。用线段树维护一个结点的最大值和最小值。那么反正相当于把最大值和最小值互换然后分别乘上个(-1)。

#define _CRT_SECURE_NO_DEPRECATE
#include<iostream>
#include<cstring>
#include<string>
#include<algorithm>
#include<stdio.h>
#include<queue>
#include<vector>
#include<stack>
#include<map>
#include<set>
#include<time.h>
#include<cmath>
#include<sstream>
#include<assert.h>
using namespace std;
#define L(x) x<<1
#define R(x) x<<1|1
typedef long long int LL;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3fLL;
const int MAXN = 20000 + 10;
int val[MAXN],head[MAXN], tot, cnt, edgesId[MAXN];
struct Edge{
    int to, next;
    int value;
}Edges[MAXN * 2];
void add(int u, int v, int w){
    Edges[tot].to = v;
    Edges[tot].value = w;
    Edges[tot].next = head[u];
    head[u] = tot++;
}
int id[MAXN], son[MAXN], deep[MAXN], size[MAXN], fa[MAXN], reid[MAXN], top[MAXN];
void Init(){
    tot = 1; cnt = 0;
    memset(head, -1, sizeof(head));
    memset(son, -1, sizeof(son));
    memset(val, 0, sizeof(val));
}
void DFS1(int u, int p,int dep){
    fa[u] = p; size[u] = 1; deep[u] = dep;
    for (int i = head[u]; i != -1; i = Edges[i].next){
        if (Edges[i].to != p){
            val[Edges[i].to] = Edges[i].value; //deep大的点获得边权
            edgesId[(int)ceil(i / 2.0)] = Edges[i].to;
            DFS1(Edges[i].to, u,dep+1);
            size[u] += size[Edges[i].to];
            if (son[u] == -1 || size[Edges[i].to] > size[son[u]]){
                son[u] = Edges[i].to;
            }
        }
    }
}
void DFS2(int u, int tp){
    id[u] = ++cnt; reid[id[u]] = u; top[u] = tp;
    if (son[u] == -1){ return; }
    DFS2(son[u], tp);
    for (int i = head[u]; i != -1; i = Edges[i].next){
        if (son[u] != Edges[i].to&&Edges[i].to != fa[u]){
            DFS2(Edges[i].to, Edges[i].to);
        }
    }
}
struct Node{
    int st, ed;
    int lazy, Max, Min;
}Seg[MAXN * 4];
void Build(int l, int r, int k){
    Seg[k].st = l; Seg[k].ed = r;  Seg[k].lazy = 0;
    if (l == r){
        Seg[k].Max = Seg[k].Min = val[reid[l]];
        return;
    }
    int mid = (l + r) / 2;
    Build(l, mid, L(k)); Build(mid + 1, r, R(k));
    Seg[k].Max = max(Seg[L(k)].Max, Seg[R(k)].Max);
    Seg[k].Min = min(Seg[L(k)].Min, Seg[R(k)].Min);
}
void Modify(int k){
    swap(Seg[k].Min, Seg[k].Max);
    Seg[k].Min *= -1;
    Seg[k].Max *= -1;
}
void pushUp(int k){
    Seg[k].Max = max(Seg[L(k)].Max, Seg[R(k)].Max);
    Seg[k].Min = min(Seg[L(k)].Min, Seg[R(k)].Min);
}
void pushDown(int k){
    if (Seg[k].lazy){
        Seg[k].lazy ^= 1;
        Seg[L(k)].lazy ^= 1;
        Modify(L(k));
        Seg[R(k)].lazy ^= 1;
        Modify(R(k));
    }
}
void CHANGE(int pos, int val, int k){
    if (Seg[k].st ==Seg[k].ed){
        Seg[k].Max = Seg[k].Min = val;
        return;
    }
    pushDown(k);
    if (pos <= Seg[L(k)].ed){
        CHANGE(pos, val, L(k));
    }
    else{
        CHANGE(pos, val, R(k));
    }
    pushUp(k);
}
void NEGATE(int l, int r, int k){
    if (Seg[k].st == l&&Seg[k].ed == r){
        Seg[k].lazy ^= 1;
        Modify(k);
        return;
    }
    pushDown(k);
    if (r <= Seg[L(k)].ed){
        NEGATE(l, r, L(k));
    }
    else if (l >= Seg[R(k)].st){
        NEGATE(l, r, R(k));
    }
    else{
        NEGATE(l, Seg[L(k)].ed, L(k));
        NEGATE(Seg[R(k)].st, r, R(k));
    }
    pushUp(k);
}
void NEGATE(int u, int v){
    int f1 = top[u], f2 = top[v];
    while (f1 != f2){
        if (deep[f1] < deep[f2]){
            swap(f1, f2);
            swap(u, v);
        }
        NEGATE(id[f1], id[u], 1);
        u = fa[f1]; f1 = top[u];
    }
    if (u == v){ return; }
    if (deep[u] > deep[v]){
        swap(u, v);
    }
    NEGATE(id[son[u]], id[v], 1);
}
int Query(int l, int r, int k){
    if (Seg[k].st == l&&Seg[k].ed == r){
        return Seg[k].Max;
    }
    int _Max = -inf;
    pushDown(k);
    if (r <= Seg[L(k)].ed){
        _Max = Query(l, r, L(k));
    }
    else if (l >= Seg[R(k)].st){
        _Max = Query(l, r, R(k));
    }
    else{
        _Max = max(Query(l, Seg[L(k)].ed, L(k)), Query(Seg[R(k)].st, r, R(k)));
    }
    pushUp(k);
    return _Max;
}
int Query(int u, int v){
    int ans = -inf;
    int f1 = top[u], f2 = top[v];
    while (f1 != f2){
        if (deep[f1] < deep[f2]){
            swap(f1, f2);
            swap(u, v);
        }
        ans = max(ans, Query(id[f1], id[u], 1));
        u = fa[f1]; f1 = top[u];
    }
    if (u == v){ return ans; }
    if (deep[u] > deep[v]){
        swap(u, v);
    }
    ans = max(ans, Query(id[son[u]], id[v], 1));
    return ans;
}
int main(){
//#ifdef kirito
//    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
//#endif
//    int start = clock();
    int n,t;
    scanf("%d", &t);
    while (t--){
        scanf("%d", &n); Init();
        for (int i = 1; i < n; i++){
            int u, v, w;
            scanf("%d%d%d", &u, &v, &w);
            add(u, v, w); add(v, u, w);
        }
        DFS1(1, 1, 0); DFS2(1, 1); Build(1, n, 1);
        char ope[20];
        while (scanf("%s",ope)&&ope[0]!='D'){
            int u,v; 
            scanf("%d%d", &u,&v);
            switch (ope[0])
            {
            case 'Q': printf("%d\n", (u==v?0:Query(u, v))); break;
            case 'C': CHANGE(id[edgesId[u]], v, 1); break;
            default:  NEGATE(u, v); break;
            }
        }
    }
//#ifdef LOCAL_TIME
//    cout << "[Finished in " << clock() - start << " ms]" << endl;
//#endif
    return 0;
}