prim求最小生成树

一直以来只会Kruskal

prim和dijkstra很像

只不过prim维护的是最短的边，而dijkstra维护的是最短的从起点到一个点的路径

同时prim要注意当前拓展的边是没有拓展过的

可以用堆优化

#include<bits/stdc++.h>
#define REP(i, a, b) for(register int i = (a); i < (b); i++)
#define _for(i, a, b) for(register int i = (a); i <= (b); i++)
using namespace std;

const int MAXN =  + ;
const int MAXM = 2e5 + ;

struct Edge{ int to, w, next; };
Edge e[MAXM << ];
int head[MAXN], d[MAXN], vis[MAXN], n, m, tot;

void AddEdge(int from, int to, int w)
{
    e[tot] = Edge{to, w, head[from]};
    head[from] = tot++;
}

void read(int& x)
{
    int f = ; x = ; char ch = getchar();
    while(!isdigit(ch)) { if(ch == '-') f = -; ch = getchar(); }
    while(isdigit(ch)) { x = x *  + ch - ''; ch = getchar(); }
    x *= f;
}

void prim()
{
    vis[] = ;
    _for(i, , n) d[i] = i ==  ?  : 1e9;
    for(int i = head[]; ~i; i = e[i].next)
    {
        int v = e[i].to;
        d[v] = min(d[v], e[i].w);
    }

    int ans = ;
    REP(k, , n)
    {
        int mint = 1e9, id;
        _for(i, , n)
            if(!vis[i] && d[i] < mint)
            {
                mint = d[i];
                id = i;
            }

        ans += mint;
        vis[id] = ;

        for(int i = head[id]; ~i; i = e[i].next)
        {
            int v = e[i].to;
            if(vis[v]) continue;
            d[v] = min(d[v], e[i].w);
        }
    }
    printf("%d\n", ans);
}

int main()
{
    memset(head, -, sizeof(head)); tot = ;
    read(n); read(m);
    _for(i, , m)
    {
        int u, v, w;
        read(u); read(v); read(w);
        AddEdge(u, v, w);
        AddEdge(v, u, w);
    }
    prim();
    return ;
}

堆优化版本

#include<bits/stdc++.h>
#define REP(i, a, b) for(register int i = (a); i < (b); i++)
#define _for(i, a, b) for(register int i = (a); i <= (b); i++)
using namespace std;

const int MAXN =  + ;
const int MAXM = 2e5 + ;

struct Edge{ int to, w, next; };
Edge e[MAXM << ];
int head[MAXN], d[MAXN], vis[MAXN], n, m, tot;

void AddEdge(int from, int to, int w)
{
    e[tot] = Edge{to, w, head[from]};
    head[from] = tot++;
}

void read(int& x)
{
    int f = ; x = ; char ch = getchar();
    while(!isdigit(ch)) { if(ch == '-') f = -; ch = getchar(); }
    while(isdigit(ch)) { x = x *  + ch - ''; ch = getchar(); }
    x *= f;
}

struct node
{
    int id, w;
    bool operator < (const node& rhs) const
    {
        return w > rhs.w;
    }
};
priority_queue<node> q;

void prim()
{
    vis[] = ;
    _for(i, , n) d[i] = i ==  ?  : 1e9;
    for(int i = head[]; ~i; i = e[i].next)
    {
        int v = e[i].to;
        d[v] = min(d[v], e[i].w);
    }
    _for(i, , n) q.push(node{i, d[i]});

    int ans = ;
    REP(k, , n)
    {
        int mint, id;
        while()
        {
            node x = q.top(); q.pop();
            if(vis[x.id]) continue;
            id = x.id, mint = x.w;
            break;
        }

        ans += mint;
        vis[id] = ;

        for(int i = head[id]; ~i; i = e[i].next)
        {
            int v = e[i].to;
            if(vis[v]) continue;
            if(d[v] > e[i].w)
            {
                d[v] = e[i].w;
                q.push(node{v, d[v]});
            }
        }
    }
    printf("%d\n", ans);
}

int main()
{
    memset(head, -, sizeof(head)); tot = ;
    read(n); read(m);
    _for(i, , m)
    {
        int u, v, w;
        read(u); read(v); read(w);
        AddEdge(u, v, w);
        AddEdge(v, u, w);
    }
    prim();
    return ;
}