UVA 1151 Buy or Build （最小生成树）

先求出原图的最小生成树，然后枚举买哪些套餐，把一个套餐内的点相互之间边权为0，直接用并查集缩点。正确性是基于一个贪心，

在做Kruskal算法是，对于没有进入最小生成树的边，排序在它前面的边不会减少。

边比较多，用prim求最小生成树，效果比Kruskal好，枚举套餐的时候在用Kruskal。

prim和dijkstra的区别在于点距离的定义。

#include<bits/stdc++.h>
using namespace std;
const int maxn = 1005;
int n,q;

int C[9];
vector<int> Buy[9];
#define PB push_back

int x[maxn],y[maxn];
#define squ(x) ((x)*(x))

int dist(int a,int b) { return squ(x[a]-x[b])+squ(y[a]-y[b]); }

struct Edge
{
    int u,v,w;
    Edge(){}
    Edge(int u,int v,int w):u(u),v(v),w(w){}
    bool operator < (const Edge& x) const {
        return w > x.w;
    }
}edges[maxn];

bool EdgeLess(const Edge &x,const Edge &y) { return x.w < y.w; }

int ecnt;

int d[maxn];
bool done[maxn];
const int INF = 0x3f3f3f3f;

int Prim()
{
    fill(d,d+n,INF);
    fill(done,done+n,0);
    ecnt = 0;
    priority_queue<Edge> q;
    q.push(Edge(-1,0,0)); // dummy edge
    int tot = d[0] = 0;
    while(q.size()){
        Edge x = q.top(); q.pop();
        if(done[x.v]) continue;
        edges[ecnt++] = x;
        tot += x.w;
        done[x.v] = true;
        for(int i = 1; i < n; i++){
            if(done[i]) continue;
            int cost = dist(x.v,i);
            if(d[i]>cost){
                d[i] = cost;
                q.push(Edge(x.v,i,cost));
            }
        }
    }
    return tot;
}

int pa[maxn];
int Find(int x) { return x==pa[x]?x:pa[x]=Find(pa[x]); }
void Union(int a,int b,int &cnt)
{
    int s1 = Find(a),s2 = Find(b);
    if(s1 != s2){
        pa[s1] = s2; cnt--;
    }
}

int Kruskal(int cnt)
{
    if(!cnt) return 0;
    int ans = 0;
    for(int i = 1; i < ecnt; i++){
        Edge &e = edges[i];
        int s1 = Find(e.u), s2 = Find(e.v);
        if(s1 != s2) { ans += e.w; pa[s1] = s2; cnt--; if(!cnt) return ans; }

    }
    return ans;
}

int main()
{
    //freopen("in.txt","r",stdin);
    int T; scanf("%d",&T);
    while(T--){
        scanf("%d%d",&n,&q);
        for(int i = 0; i < q; i++){
            int t; scanf("%d%d",&t,C+i);
            Buy[i].clear();
            while(t--) {
                int c; scanf("%d",&c);
                Buy[i].PB(c-1);
            }
        }
        for(int i = 0; i < n; i++){
            scanf("%d%d",x+i,y+i);
        }
        int ans = Prim();
        sort(edges+1,edges+ecnt,EdgeLess);

        for(int mask = 1,M = 1<<q; mask < M; mask++){
            for(int i = 0; i < n; i++) pa[i] = i;
            int tot = 0,cnt = n-1;

            for(int i = 0; i < q; i++){
                if(mask&1<<i){
                    tot += C[i];
                    for(int j = 1; j < Buy[i].size(); j++) {
                         Union(Buy[i][0],Buy[i][j],cnt);
                    }
                }
            }

            tot += Kruskal(cnt);
            ans = min(ans,tot);
        }
        printf("%d
",ans);
        if(T) putchar('
');
    }
    return 0;
}