AcWing 858. Prim算法求最小生成树(堆优化写法)

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AcWing 858. Prim算法求最小生成树(堆优化写法) 原题链接简单

作者：

发光二极管 , 2020-01-30 21:41:18 , 所有人可见 , 阅读 2936

17

6

给大家一个参考

#include <cstring>
#include <iostream>
#include <queue>
using namespace std;

const int MAXN = 510, MAXM = 2 * 1e5 + 10, INF = 0x3f3f3f3f;
typedef pair<int, int> PII;
int h[MAXM], e[MAXM], w[MAXM], ne[MAXM], idx;
bool vis[MAXN];
int n, m;

void add(int a, int b, int c) {
    e[idx] = b, w[idx] = c, ne[idx] = h[a], h[a] = idx ++ ;
}

int Prim()
{
    memset(vis, false, sizeof vis);
    int sum = 0, cnt = 0;
    priority_queue<PII, vector<PII>, greater<PII>> q;
    q.push({0, 1});

    while (!q.empty())
    {
        auto t = q.top();
        q.pop();
        int ver = t.second, dst = t.first;
        if (vis[ver]) continue;
        vis[ver] = true, sum += dst, ++cnt;

        for (int i = h[ver]; i != -1; i = ne[i])
        {
            int j = e[i];
            if (!vis[j]) {
                q.push({w[i], j});
            }
        }
    }

    if (cnt != n) return INF;
    return sum;
}

int main()
{
    cin >> n >> m;
    memset(h, -1, sizeof h);
    for (int i = 0; i < m; ++i)
    {
        int a, b, w;
        cin >> a >> b >> w;
        add(a, b, w);
        add(b, a, w);
    }

    int t = Prim();
    if (t == INF) cout << "impossible" << endl;
    else cout << t << endl; 
}

13 评论

2580 2023-02-23 21:13

为什么有人说优化了个寂寞，因为答主把每条边都进队了，和之前其实没啥区别，加一个dist数组会更好，加入堆中的起码要比之前更新的到生成树的距离要小这样就可以减少很多条边入堆

#include <cstring>
#include <iostream>
#include <queue>
using namespace std;

const int MAXN = 510, MAXM = 2 * 1e5 + 10, INF = 0x3f3f3f3f;
typedef pair<int, int> PII;
int h[MAXM], e[MAXM], w[MAXM], ne[MAXM], idx, d[MAXN];
bool vis[MAXN];
int n, m;

void add(int a, int b, int c) {
    e[idx] = b, w[idx] = c, ne[idx] = h[a], h[a] = idx ++ ;
}

int Prim()
{
    memset(vis, false, sizeof vis);
    memset(d, 0x3f, sizeof d);
    int sum = 0, cnt = 0;
    priority_queue<PII, vector<PII>, greater<PII>> q;
    q.push({0, 1});

    while (!q.empty())
    {
        auto t = q.top();
        q.pop();
        int ver = t.second, dst = t.first;
        if (vis[ver]) continue;
        vis[ver] = true, sum += dst, ++cnt;

        for (int i = h[ver]; i != -1; i = ne[i])
        {
            int j = e[i];
            if (!vis[j] && w[i] < d[j]) {
                d[j] = w[i];
                q.push({w[i], j});
            }
        }
    }

    if (cnt != n) return INF;
    return sum;
}

int main()
{
    scanf("%d%d", &n, &m);
    memset(h, -1, sizeof h);
    for (int i = 0; i < m; ++i)
    {
        int a, b, w;
        scanf("%d%d%d", &a, &b, &w);
        add(a, b, w);
        add(b, a, w);
    }

    int t = Prim();
    if (t == INF) cout << "impossible" << endl;
    else cout << t << endl; 
}