货车运输

https://www.luogu.org/problemnew/show/P1967

题解：最大瓶颈路径问题

并查集+最大生成树+LCA

/*
*@Author:   STZG
*@Language: C++
*/
#include <bits/stdc++.h>
#include<iostream>
#include<algorithm>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<deque>
#include<stack>
#include<cmath>
#include<list>
#include<map>
#include<set>
//#define DEBUG
#define RI register int
#define endl "\n"
using namespace std;
typedef long long ll;
//typedef __int128 lll;
const int N=100000+10;
const int M=100000+10;
const int MOD=1e9+7;
const double PI = acos(-1.0);
const double EXP = 1E-8;
const int INF = 0x3f3f3f3f;
int t,n,m,k,p,l,r,u,v,q;
int ans,cnt,flag,temp,sum;
int pre[N],dp[23][N],dep[N],maxl[23][N];
bool vis[N];
char str;
int find(int x){return pre[x]==x?x:pre[x]=find(pre[x]);}
struct node{
    int u,v,w;
    bool operator < (const node &S)const{
        return w>S.w;
    }
}e[N],x;
vector<node>G[N];

void dfs(int u){
    vis[u]=1;
    for(int i=0,j=G[u].size();i<j;i++){
        int v=G[u][i].v;
        if(!vis[v]){
            maxl[0][v]=G[u][i].w;
            dp[0][v]=u;
            dep[v]=dep[u]+1;
            dfs(v);
        }
    }
}
void ST(){
    for(int i=0;i<21;i++){
        for(int j=1;j<=n;j++){
            dp[i+1][j]=dp[i][dp[i][j]];
            maxl[i+1][j]=min(maxl[i][j],maxl[i][dp[i][j]]);
            //cout<<maxl[i+1][j]<<endl;
        }
    }
}
int LCA(int x,int y){
    int maxans=INF;
    if(dep[x]<dep[y])
        swap(x,y);
    while(dep[x]!=dep[y]){
        maxans=min(maxans,maxl[(int)log2(dep[x]-dep[y])][x]);
        x=dp[(int)log2(dep[x]-dep[y])][x];

    }
    if(x==y)
        return maxans;
    for(int i=log2(dep[x]);i>=0;i--){
        if(dp[i][x]!=dp[i][y]){
            maxans=min(maxans,min(maxl[i][x],maxl[i][y]));
            x=dp[i][x];
            y=dp[i][y];
        }
    }
    maxans=min(maxans,min(maxl[0][x],maxl[0][y]));
    return maxans;
}
int main()
{
#ifdef DEBUG
	freopen("input.in", "r", stdin);
	//freopen("output.out", "w", stdout);
#endif
    //ios::sync_with_stdio(false);
    //cin.tie(0);
    //cout.tie(0);
    //scanf("%d",&t);
    //while(t--){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;i++){
        scanf("%d%d%d",&e[i].u,&e[i].v,&e[i].w);
    }
    sort(e+1,e+m+1);
    for(int i=1;i<=n;i++)pre[i]=i;
    for(int i=1;i<=m;i++){
        int tx=find(e[i].u);
        int ty=find(e[i].v);
        if(tx!=ty){
            x=e[i];
            G[e[i].u].push_back(x);
            swap(x.u,x.v);
            G[e[i].v].push_back(x);
            pre[tx]=ty;
        }
    }
    for(int i=0;i<21;i++){
        for(int j=0;j<N;j++){
            maxl[i][j]=INF;
        }
    }
    for(int i=1;i<=n;i++){
        if(!vis[i]){
            dfs(i);
        }
    }
    ST();
    scanf("%d",&q);
    while(q--){
        scanf("%d%d",&u,&v);
        int tx=find(u);
        int ty=find(v);
        if(tx!=ty){
            cout<<-1<<endl;
        }else{
            cout<<LCA(u,v)<<endl;
        }
    }

    //}

#ifdef DEBUG
	printf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC);
#endif
    //cout << "Hello world!" << endl;
    return 0;
}