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最小生成树

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最小生成树

prim

稀疏图，采用邻接矩阵进行存储边之间的关系

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// prim 算法求最小生成树 

#include <cstdio>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>

#define INF 0x3f3f3f3f

using namespace std;

const int maxn = 505;

int a[maxn][maxn];

int vis[maxn],dist[maxn];

int n,m;

int u,v,w;

long long sum = 0;

int prim(int pos) {
	dist[pos] = 0;
	// 一共有 n 个点,就需要 遍历 n 次,每次寻找一个权值最小的点,记录其下标
	for(int i = 1; i <= n; i ++) {
		int cur = -1;
		for(int j = 1; j <= n; j ++) {
			if(!vis[j] && (cur == -1 || dist[j] < dist[cur])) {
				cur = j;
			}
		}
		// 这里需要提前终止
		if(dist[cur] >= INF) return INF;
		sum += dist[cur];
		vis[cur] = 1;
		for(int k = 1; k <= n; k ++) {
		    // 只更新还没有找到的最小权值
			if(!vis[k]) dist[k] = min(dist[k],a[cur][k]);
		}
	}
	return sum;
}

int main(void) {
	scanf("%d%d",&n,&m);
	memset(a,0x3f,sizeof(a));
	memset(dist,0x3f,sizeof(dist));
	for(int i = 1; i <= m; i ++) {
		scanf("%d%d%d",&u,&v,&w);
		a[u][v] = min(a[u][v],w);
		a[v][u] = min(a[v][u],w);
	}
	int value = prim(1);
	if(value >= INF) puts("impossible");
	else printf("%lld\n",sum);
	return 0;
}

kruskal

稠密图，采用邻接表进行存储边之间的关系

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// Kruskal 算法求最小生成树 

#include <cstdio>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

const int maxn = 2e5 + 10; 

struct node {
	int x,y,z;
}edge[maxn];

bool cmp(node a,node b) {
	return a.z < b.z;
}

int fa[maxn];

int n,m;

int u,v,w; 

long long sum;

int get(int x) {
	return x == fa[x] ? x : fa[x] = get(fa[x]);
}

int main(void) {
	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);
	}
	for(int i = 0; i <= n; i ++) {
		fa[i] = i;
	}
	sort(edge + 1,edge + 1 + m,cmp);
	// 每次加入一条最短的边
	for(int i = 1; i <= m; i ++) {
		int x = get(edge[i].x);
		int y = get(edge[i].y);
		if(x == y) continue;
		fa[y] = x;
		sum += edge[i].z;
	}
	int ans = 0;
	for(int i = 1; i <= n; i ++) {
		if(i == fa[i]) ans ++;
	}
	if(ans > 1) puts("impossible");
	else printf("%lld\n",sum);
	return 0;
}