【最小生成树】洛谷 P3366 【模板】最小生成树
2021-04-15 18:29:00 # ACM

题链

$Kruskal$

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#include <bits/stdc++.h>
using namespace std;
#define MS 200009
#define ls rt<<1
#define rs rt<<1|1
#define LL long long
#define MAXN 0x3f3f3f3f

int n,m;
struct node{
	int u,v,val;
}p[MS];
int fa[MS];

int find(int x){
	if(x == fa[x]) return x;
	else return fa[x] = find(fa[x]);
}

void merge(int x,int y){
	fa[find(y)] = find(x);
}

bool cmp(node t1,node t2){
	return t1.val < t2.val;
}

int main() {
	ios::sync_with_stdio(false);
	cin >> n >> m;
	for(int i=1;i<=n;i++) fa[i] = i;
	for(int i=1;i<=m;i++){
		cin >> p[i].u >> p[i].v >> p[i].val;
	}
	sort(p+1,p+m+1,cmp);
	int ans = 0;
	for(int i=1;i<=m;i++){
		if(find(p[i].u) != find(p[i].v)){
			merge(p[i].u,p[i].v);
			ans += p[i].val;
		}
	}
	int flag = 1;
	for(int i=1;i<=n;i++){
		if(find(i) != find(1)) flag = 0;
	}
	if(flag) cout << ans << "\n";
	else cout << "orz\n";
	

	return 0;
}

$Prim$

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#include <bits/stdc++.h>
using namespace std;
#define MS 5009
#define ls rt<<1
#define rs rt<<1|1
#define LL long long
#define MAXN 0x3f3f3f3f

int n,m;
struct node{
	int to,val;
};
vector<node > vc[MS];
struct nod{
	int poi,val;
};
priority_queue<nod > Q;
int dis[MS];
int v[MS];

bool operator < (nod t1,nod t2){
	return t1.val > t2.val;
}

int main() {
	ios::sync_with_stdio(false);
	cin >> n >> m;
	for(int i=1;i<=m;i++){
		int u,v,w;
		cin >> u >> v >> w;
		vc[u].push_back({v,w});
		vc[v].push_back({u,w});
	}
	for(int i=1;i<=n;i++) dis[i] = MAXN;
	dis[1] = 0;
	Q.push({1,0});
	int ans = 0;
	while(!Q.empty()){
		nod x = Q.top();
		Q.pop();
		if(v[x.poi]) continue;
		v[x.poi] = 1;
		ans += x.val; // 答案 
		for(auto &it:vc[x.poi]){
			if(dis[it.to] > it.val){ // 相比 Dijkstra 少了源点到 x.poi 的距离 
				dis[it.to] = it.val;
				if(!v[it.to]){
					Q.push({it.to,dis[it.to]});
				}
			}
		}
	}
	cout << ans << "\n";
	

	return 0;
}

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