例题:P3366 【模板】最小生成树 - 洛谷 | 计算机科学教育新生态 (luogu.com.cn)

Kruskal

#include <bits/stdc++.h>
#define debug(a) cout<<#a<<"="<<a<<'\n';

using namespace std;
using i64 = long long;

typedef pair<i64, i64> PII;

struct UFS {
	int sz;
	vector<int> rank, p;
	void link(int x, int y) {
		if (x == y)
			return;
		if (rank[x] > rank[y])
			p[y] = x;
		else
			p[x] = y;
		if (rank[x] == rank[y])
			rank[y]++;
	}
	void init(int n) {
		sz = n;
		rank.resize(n + 1);
		p.resize(n + 1);
		for (int i = 0; i <= sz; i++) {
			p[i] = i;
			rank[i] = 0;
		}
	}
	int find(int x) {
		return x == p[x] ? x : (p[x] = find(p[x]));
	}
	void unin(int x, int y) {
		link(find(x), find(y));
	}
	void compress() {
		for (int i = 0; i < sz; i++)
			find(i);
	}
};
//种类并查集 merge(y + n, x),merge(x + n, y)

int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);

	int n, m;
	cin >> n >> m;
	vector<pair<int, PII>> e;
	for (int i = 0; i < m; i ++) {
		int u, v, w;
		cin >> u >> v >> w;
		e.emplace_back(w, PII(u, v));
	}

	sort(e.begin(), e.end());
	UFS ufs;
	ufs.init(n);
	i64 ans = 0;
	for (int i = 0; i < m; i ++) {
		auto [w, uv] = e[i];
		auto [u, v] = uv;
		if (ufs.find(u) != ufs.find(v)) {
			ufs.unin(u, v);
			ans += w;
		}
	}

	int op = ufs.find(1);
	for (int i = 1; i <= n; i ++) {
		if (ufs.find(i) != op) {
			cout << "orz" << '\n';
			return 0;
		}
	}

	cout << ans << '\n';

	return 0;
}

Prim

#include <bits/stdc++.h>
#define debug(a) cout<<#a<<"="<<a<<'\n';

using namespace std;
using i64 = long long;

typedef pair<i64, i64> PII;

int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);

	int n, m;
	cin >> n >> m;
	vector g(n + 1, vector<PII>());
	vector<int> dis(n + 1);
	vector<bool> vis(n + 1);
	i64 ans = 0, cnt = 0;
	for (int i = 0; i < m; i ++) {
		int u, v, w;
		cin >> u >> v >> w;
		g[u].emplace_back(v, w);
		g[v].emplace_back(u, w);
	}

	priority_queue<PII, vector<PII>, greater<PII>> Q;
	Q.push({0, 1});
	while (Q.size()) {
		auto [w, u] = Q.top();
		Q.pop();

		if (vis[u]) continue;
		vis[u] = true;
		ans += w;
		cnt ++;
		dis[u] = w;
		for (auto [v, d] : g[u]) {
			if (!vis[v]) {
				Q.push({d, v});
			}
		}
	}

	if (cnt != n) {
		cout << "orz\n";
	} else
		cout << ans << '\n';
    
	return 0;
}