2019ICPC邀请赛南昌A Attack 斯坦纳树

先对8个点整体做斯坦纳树，再求出每个状态的最小代价。再看每个状态是否属于独立的，即包含的点都是成对的，我们去更新这些独立的状态即可。

#include <cstdio>
#include <cstring>
#include <string>
#include <map>
#include <queue>
#include <iostream>
using namespace std;
const int MAXN = 40,MAXM = 2100;
queue <int> que;
string s1,s2;
map <string,int> mp;
bool inq[MAXN];
int head[MAXN],dis[MAXN][1 << 8],ans[1 << 8],spe[1 << 8],to[MAXM],nxt[MAXM],val[MAXM];
int cnt,n,m,s,t,inf;
void add(int x,int y,int v)
{
    nxt[++cnt] = head[x];
    to[cnt] = y;
    val[cnt] = v;
    head[x] = cnt;
}
void SPFA(int o)
{
    while(!que.empty())
    {
        int t = que.front();
        que.pop();
        inq[t] = false;
        for(int i = head[t];i;i = nxt[i])
        {
            if(dis[to[i]][o] > dis[t][o] + val[i])
            {
                dis[to[i]][o] = dis[t][o] + val[i];
                if(!inq[to[i]])
                {
                    inq[to[i]] = true;
                    que.push(to[i]);
                }
            }
        }
    }
}
void steiner_tree()
{
    for (int i = 0;i < (1 << 8);i++)
    {
        for (int j = 1;j <= n;j++)
        {
            for (int k = i;k;k = (k - 1) & i)
                dis[j][i] = min(dis[j][i],dis[j][k] + dis[j][i - k]);
            if (dis[j][i] != inf)
            {
                que.push(j);
                inq[j] = true;
            }
        }
        SPFA(i);
    }
}
bool check(int o)
{
    for (int i = 0;i <= 7;i += 2)
        if (((o >> i) & 1) ^ ((o >> (i + 1)) & 1))
            return false;
    return true;
}
int main()
{
    while (scanf("%d%d",&n,&m) > 0)
    {
        cnt = 0;
        memset(head,0,sizeof(head));
        memset(nxt,0,sizeof(nxt)); 
        memset(dis,0x1f,sizeof(dis));
        memset(ans,0x1f,sizeof(ans)); 
        inf = ans[0];
        int tv;
        string s1,s2;
        for (int i = 1;i <= n;i++)
        {
            cin >> s1;
            mp[s1] = i;
        }
        for (int i = 1;i <= m;i++)
        {
            cin >> s1 >> s2;
            scanf("%d",&tv);
            add(mp[s1],mp[s2],tv);
            add(mp[s2],mp[s1],tv);
        }
        for (int i = 1;i <= 8;i++)
        {
            cin >> s1;
            dis[mp[s1]][1 << (i - 1)] = 0;
        }
        steiner_tree();
        for (int i = 0;i < (1 << 8);i++)
        {
            spe[i] = check(i);
            for (int j = 1;j <= n;j++)
                ans[i] = min(ans[i],dis[j][i]); 
        }
        for (int i = 0;i < (1 << 8);i++)
            if (spe[i])
                for (int j = i;j;j = (j - 1) & i)
                    if (spe[j] && spe[i - j])
                        ans[i] = min(ans[i],ans[j] + ans[i - j]);
        printf("%d
",ans[(1 << 8) - 1]);
    }
    return 0;
}