洛谷P1967题解

首先找出图中每个连通分量的最大生成树，然后在树上跑LCA。寻找LCA的时候寻找路径上的最小权值。

#include <cstdio>
#include <cmath>
#include <iostream>
#include <algorithm>
using namespace std;

#define MaxN 10005
#define MaxM 50005
#define LogN 20
#define INF 0x7fffffff

int N, M, Q;

int point[MaxN], tot;
int nxt[MaxM], v[MaxM], w[MaxM];

void add(int x, int y, int z){
    ++tot; nxt[tot] = point[x];
    v[tot] = y; w[tot] = z; point[x] = tot;
}

int fa[MaxN];
bool isfa[MaxN];
int find(int x){
    return x == fa[x] ? fa[x] : fa[x] = find(fa[x]);
}

int deep[MaxN];
bool flag[MaxN];
int f[MaxN][LogN];
int g[MaxN][LogN];

void dfs(int node, int ff, int ww, int d){
    deep[node] = d;
    flag[node] = true;
    f[node][0] = ff;
    g[node][0] = ww;
    for(int i = point[node]; i; i = nxt[i]){
        if(flag[v[i]]) continue;
        dfs(v[i], node, w[i], d+1);
    }
}

void process(){
    for(int j = 1; j<LogN; ++j)
        for(int i = 1; i<=N; ++i){
            f[i][j] = f[f[i][j-1]][j-1];
            g[i][j] = min(g[i][j-1], g[f[i][j-1]][j-1]);
        }
}

struct EDGE{
    int x, y, z;
    bool operator < (const EDGE &e) const{
        return z > e.z;
    }
}edge[MaxM];

void Kruskal(){
    sort(edge+1, edge+1+M);
    for(int i = 1; i<=N; ++i) fa[i] = i;
    for(int i = 1; i<=M; ++i){
        int fx = find(edge[i].x);
        int fy = find(edge[i].y);
        if(fx == fy) continue;
        fa[fx] = fy;
        add(edge[i].x, edge[i].y, edge[i].z);
        add(edge[i].y, edge[i].x, edge[i].z);
    }
}

int find_LCA(int x, int y){
    int fx = find(x);
    int fy = find(y);
    if(fx != fy) return -1;
    int _min = INF;
    if(deep[x]<deep[y]) swap(x, y);
    for(int j = LogN-1; j>=0; --j){
        if(deep[f[x][j]]>=deep[y]){
             _min = min(_min, g[x][j]);
            x = f[x][j];
        }
    }
    if(x == y) return _min;
    for(int j = LogN-1; j>=0; --j){
        if(f[x][j] != f[y][j]){
            _min = min(_min, min(g[x][j], g[y][j]));
            x = f[x][j]; y = f[y][j];
        }
    }
    return min(_min, min(g[x][0], g[y][0]));
}

int main(){
    scanf("%d %d", &N, &M);
    for(int i = 1; i<=M; ++i){
        scanf("%d %d %d", &edge[i].x, &edge[i].y, &edge[i].z);
    }
    Kruskal();    
    for(int i = 1; i<=N; ++i) isfa[find(i)] = true;
    for(int i = 0; i<=N; ++i)
        for(int j = 0; j<LogN; ++j)
            g[i][j] = INF;
    for(int i = 1; i<=N; ++i) 
        if(isfa[i]) dfs(i, 0, INF, 1);
    process();
    scanf("%d", &Q);
    for(int i = 1; i<=Q; ++i){
        int x, y;
        scanf("%d %d", &x, &y);
        printf("%d\n", find_LCA(x, y));
    }
    return 0;
}