HDU 2874 connections between cities

The question ： Because most roads have been completely destroyed during the war , There may be no path between the two cities , No ring exists . Now? , After telling you the road conditions , We want to know whether there is a path between any two cities . If the answer is yes , Then output the shortest path between them .

Answer key ： Union checking set +lca Multiplication method
First use and check the set shrink point , There must be no path if it is not in the same set , then dfs Preprocess each set .

Here we use the multiplication method to find lca.

#define _CRT_SECURE_NO_WARNINGS
#include<iostream>
#include<cstdio>
#include<string>
#include<cstring>
#include<algorithm>
#include<queue>
#include<stack>
#include<cmath>
#include<vector>
#include<fstream>
#include<set>
#include<map>
#include<sstream>
#include<iomanip>
#define ll long long
#define pii pair<int, int>
using namespace std;
int n, m, q, x, y, k;
const int MAXN = 1e4 + 5;
vector<int> v[MAXN], w[MAXN];
int fa[MAXN][31], cost[MAXN][31], dep[MAXN];
void init() {
    
    for (int i = 1; i <= n; i++) v[i].clear(), w[i].clear();
    // memset(fa, 0, sizeof(fa));
    // memset(cost, 0, sizeof(cost));
    // memset(dep, 0, sizeof(dep));
}
void dfs(int root, int fno) {
       //1 0
    fa[root][0] = fno;
    dep[root] = dep[fa[root][0]] + 1;
    for (int i = 1; i < 31; ++i) {
    
        fa[root][i] = fa[fa[root][i - 1]][i - 1];
        cost[root][i] = cost[fa[root][i - 1]][i - 1] + cost[root][i - 1];
    }
    int sz = v[root].size();
    for (int i = 0; i < sz; ++i) {
    
        if (v[root][i] == fno) continue;
        cost[v[root][i]][0] = w[root][i];
        dfs(v[root][i], root);
    }
}
int lca(int x, int y) {
    
    if (dep[x] > dep[y]) swap(x, y);
    int tmp = dep[y] - dep[x], ans = 0;
    for (int j = 0; tmp; ++j, tmp >>= 1)
        if (tmp & 1) ans += cost[y][j], y = fa[y][j];
    if (y == x) return ans;
    for (int j = 30; j >= 0 && y != x; --j) {
    
        if (fa[x][j] != fa[y][j]) {
    
            ans += cost[x][j] + cost[y][j];
            x = fa[x][j];
            y = fa[y][j];
        }
    }
    ans += cost[x][0] + cost[y][0];
    return ans;
}
int pa[MAXN];
int Find(int u) {
    
    return u == pa[u] ? u : pa[u] = Find(pa[u]);
}
bool vis[MAXN];
int main() {
    
	while (~scanf("%d%d%d", &n, &m, &q)) {
    
        init();
        for (int i = 1; i <= n; i++) pa[i] = i, vis[i] = 0;
		for (int i = 1; i <= m; i++) {
    
			scanf("%d%d%d", &x, &y, &k);
            int fx = Find(x);
            int fy = Find(y);
            if (fx != fy) pa[fx] = fy;
            v[x].push_back(y);
            v[y].push_back(x);
            w[x].push_back(k);
            w[y].push_back(k);
		}
        for (int i = 1; i <= n; i++) {
    
            int f = Find(i);
            if (vis[f]) continue;
            dfs(f, 0);
            vis[f] = 1;
        }
        while (q--) {
    
            scanf("%d%d", &x, &y);
            int fx = Find(x);
            int fy = Find(y);
            if (fx != fy) puts("Not connected");
            else printf("%d\n", lca(x, y));
        }
	}
	return 0;
}