Prim算法

算法原理

代码实现

#include <iostream>
#include <cstring>
#include <algorithm>

using namespace std;

const int N = 510, INF = 0x3f3f3f3f;

int n, m;
int g[N][N];
int dist[N];
bool st[N];

int prim()
{
    memset(dist, 0x3f, sizeof dist);

    int res = 0;
    for(int i = 0; i < n; i ++)
    {
        //一种找出最小边的写法，很巧妙，可用于dijkstra prim
        int t = -1;//存储最小的边的节点
        for(int j = 1; j <= n; j ++)
            if(!st[j] && (t == -1 || dist[t] > dist[j]))
                t = j;//第一次 t为1

        if(i && dist[t] == INF) return INF;
        if(i) res += dist[t];

        for(int j = 1; j <= n; j ++) dist[j] = min(dist[j], g[t][j]);//更新所有点到1的距离，t为1

        st[t] = true;
    }
    return res;
}

int main()
{
    cin >> n >> m;

    memset(g, 0x3f, sizeof g);

    while(m --)
    {
        int a, b, c;
        cin >> a >> b >> c;
        g[a][b] = g[b][a] = min(g[a][b], c);
    }

    int t = prim();

    if(t == INF) puts("impossible");
    else printf("%d\n", t);

    return 0;
}

作者：coderhu1
链接：https://www.acwing.com/activity/content/code/content/643891/
来源：AcWing
著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。

Kruskal算法

算法原理

代码实现

#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

const int N = 100010, M = 200010, INF = 0x3f3f3f3f;

int n, m;
int p[N];

struct Edge
{
    int a, b, w;

    bool operator< (const Edge &W)const
    {
        return w < W.w;
    }
}edges[M];

int find(int x)
{
    if (p[x] != x) p[x] = find(p[x]);
    return p[x];
}

int kruskal()
{
    sort(edges, edges + m);

    for (int i = 1; i <= n; i ++ ) p[i] = i;    // 初始化并查集

    int res = 0, cnt = 0;
    for (int i = 0; i < m; i ++ )
    {
        int a = edges[i].a, b = edges[i].b, w = edges[i].w;

        a = find(a), b = find(b);
        if (a != b)
        {
            p[a] = b;
            res += w;
            cnt ++ ;
        }
    }

    if (cnt < n - 1) return INF;
    return res;
}

int main()
{
    scanf("%d%d", &n, &m);

    for (int i = 0; i < m; i ++ )
    {
        int a, b, w;
        scanf("%d%d%d", &a, &b, &w);
        edges[i] = {a, b, w};
    }

    int t = kruskal();

    if (t == INF) puts("impossible");
    else printf("%d\n", t);

    return 0;
}

作者：yxc
链接：https://www.acwing.com/activity/content/code/content/48773/
来源：AcWing
著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。