Kruskal重构树（货车运输）

。。。
和Kruskal生成树一样

本来是u，v连一条f的边

现在变成新建一个点，点权为f，u v都像它连无边权的边

（实际上应该是u的根和v的根）

这样树有一些性质：

1.二叉树

2.原树与新树两点间路径上边权(点权)的最大（最小）值相等

3.子节点的边权（大于等于）小于等于父亲节点

4.原树中两点之间路径上边权的最大（最小）值等于新树上两点的LCA的点权

# include <iostream>
# include <stdio.h>
# include <stdlib.h>
# include <algorithm>
# include <string.h>
# define IL inline
# define ll long long
# define Fill(a, b) memset(a, b, sizeof(a));
using namespace std;

IL ll Read(){
    char c = '%'; ll x = 0, z = 1;
    for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
    for(; c >= '0' && c <= '9'; c = getchar()) x = x * 10 + c - '0';
    return x * z;
}

const int MAXN = 20001, MAXM = 200001;
int ft[MAXN], n, m, cnt, fa[MAXN][20], w[MAXN], deep[MAXN], Fa[MAXN], num;
struct Edge{
    int to, nt;
} edge[MAXM];
struct Kruskal{
    int u, v, f;
    IL bool operator <(Kruskal b) const{
        return f > b.f;
    }
} road[MAXM];

IL int Find(int x){
    return Fa[x] == x ? x : Fa[x] = Find(Fa[x]);
}

IL void Add(int u, int v){
    edge[cnt] = (Edge){v, ft[u]}; ft[u] = cnt++;
    edge[cnt] = (Edge){u, ft[v]}; ft[v] = cnt++;
}

IL void Dfs(int u){
    for(int e = ft[u]; e != -1; e = edge[e].nt){
        int v = edge[e].to;
        if(!deep[v]){
            deep[v] = deep[u] + 1;
            fa[v][0] = u;
            Dfs(v);
        }
    }
}

IL int LCA(int u, int v){
    if(Find(u) != Find(v)) return -1;
    if(deep[u] < deep[v]) swap(u, v);
    for(int i = 18; i >= 0; i--)
        if(deep[fa[u][i]] >= deep[v]) u = fa[u][i];
    if(u == v) return w[u];
    for(int i = 18; i >= 0; i--)
        if(fa[u][i] != fa[v][i]) u = fa[u][i], v = fa[v][i];
    return w[fa[u][0]];
}

int main(){
    Fill(ft, -1);
    num = n = Read(); m = Read();
    for(int i = 1; i <= 2 * n; i++)
        Fa[i] = i;
    for(int i = 1; i <= m; i++)
        road[i] = (Kruskal){Read(), Read(), Read()};
    sort(road + 1, road + m + 1);
    for(int i = 1, tot = 0; i <= m && tot < n; i++){
        int u = Find(road[i].u), v = Find(road[i].v);
        if(u != v){
            tot++;
            w[++num] = road[i].f;
            Fa[u] = Fa[v] = num;
            Add(u, num); Add(v, num);
        }
    }
    for(int i = num; i; i--)
        if(!deep[i]) deep[i] = 1, Dfs(i);
    for(int i = 1; i <= 18; i++)
        for(int j = 1; j <= num; j++)
            fa[j][i] = fa[fa[j][i - 1]][i - 1];
    int Q = Read();
    while(Q--){
        int u = Read(), v = Read();
        printf("%d
", LCA(u, v));
    }
    return 0;
}