Kruskal && Prim模板

1. Kruskal(并查集模板)：

/*
	Kruskal：并查集实现，记录两点和距离，按距离升序排序，O (ElogE)
*/
struct Edge	{
	int u, v, w;
	bool operator < (const Edge &r) const {
		return w < r.w;
	}
}edge[E];
sort (edge+1, edge+1+m);
if (!uf.same (x, y))	uf.Union (x, y), ans += w;

2. Prim：

O (n ^ 2)：

/*
	Prim：Dijkstra思想，邻接矩阵实现，适合稠密图, O (n ^ 2)
	不连通返回-1，或返回最小生成树长度(MST)
*/
int Prim(int s)	{
	memset (vis, false, sizeof (vis));
	memset (d, INF, sizeof (d));	d[s] = 0;
	int ret = 0;
	for (int i=1; i<=n; ++i)	{
		int mn = INF, u = -1;
		for (int i=1; i<=n; ++i)	{
			if (!vis[i] && d[i] < mn)	mn = d[u=i];
		}
		if (u == -1)	return -1;
		vis[u] = true;	ret += d[u];
		for (int i=1; i<=n; ++i)	{
			if (!vis[i] && d[i] > w[u][i])	{
				d[i] = w[u][i];
			}
		}
	}
	return ret;
}

O (ElogV)：

/*
	Prim：Dijkstra思想，优先队列优化，适合稀疏图，O (ElogV)
	不连通返回-1，或返回最小生成树长度(MST)
*/
int Prim(int s)	{
	memset (vis, false, sizeof (vis));
	memset (d, INF, sizeof (d));
	priority_queue<Edge> Q;
	for (int i=head[s]; ~i; i=edge[i].nex)	{
		int v = edge[i].v, w = edge[i].w;
		if (d[v] > w)	{
			d[v] = w;	Q.push (Edge (v, d[v]));
		}
	}
	vis[s] = true;	d[s] = 0;	int ret = 0;
	while (!Q.empty ())	{
		int u = Q.top ().v;	Q.pop ();
		if (vis[u])	continue;
		vis[u] = true;	ret += d[u];
		for (int i=head[u]; ~i; i=edge[i].nex)	{
			int v = edge[i].v, w = edge[i].w;
			if (!vis[v] && d[v] > w)	{
				d[v] = w;	Q.push (Edge (v, d[v]));
			}
		}
	}
	return ret;
}