Portal

Topic: Directionless graph with n points, n paths (n-1<m<=2*m), n points with some candy, some monsters, and point 1 with candy. When you start at 1:00 and ask for the expectation of finding the biggest candy, you are smart and know the map. When you first meet a monster, you have a chance to escape that point.

Idea: First, dfs records all the points connected with a point, and then traverses the monster points connected with a point connected block to update the maximum value.

#include <cstdio>
#include <queue>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <math.h>
#include <map>
#include <iterator>
#include <vector>
#include <set>
#include <bitset>
#include <stack>
#define ull unsigned long long
#define Mod(x) (x+mod)%mod
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define rep(i,a,b) for(int i=a;i<=b;i++)
#define mems(a,b) memset(a,b,sizeof(a))
using namespace std;
typedef long long ll;
const ll mod=1e9+7;;
const int N=1e5+5;
const double pi=acos(-1);
const int inf=0x3f3f3f3f;
const int M=50000+5;
int num;
int vi[N],vis[N],fi[N];
int ans[N],tot;
vector<int>ve[N];
void dfs(int u,int fa)
{
    vis[u]=1;
    num++;
    for(int i=0;i<ve[u].size();i++)
    {
        int v=ve[u][i];
        if(v==fa)
            continue;
        if(vi[v])
        {
            ans[tot++]=v;
            continue;
        }

        if(!vis[v])
        {
            dfs(v,u);
        }
    }
}
void dfs1(int u,int fa)
{
    if(vis[u]||vi[u])
        return;
    fi[u]=fa;
    num++;
    for(int i=0;i<ve[u].size();i++)
    {
        int v=ve[u][i];
        if(fi[v]==fa)
            continue;
        dfs1(v,fa);
    }
}
void init(int n)
{
    for(int i=0;i<=n;i++)
    {
        ve[i].clear();
        vi[i]=0;
        vis[i]=0;
        fi[i]=0;
    }
    num=0;
    tot=0;
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        int n,m,k;
        scanf("%d%d%d",&n,&m,&k);
        init(n);
        for(int i=1;i<=m;i++)
        {
            int a,b;
            scanf("%d%d",&a,&b);
            ve[a].push_back(b);
            ve[b].push_back(a);
        }
        for(int i=1;i<=k;i++)
        {
            int a;
            scanf("%d",&a);
            vi[a]=1;
        }
        dfs(1,-1);
        int ljt=num;
        double f=0.0;
        int v=0;
        for(int i=0;i<tot;i++)
        {
            num=0;
            for(int j=0;j<ve[ans[i]].size();j++)
            {
                dfs1(ve[ans[i]][j],++v);
//                printf("%d %d**\n",ve[ans[i]][j],num);
            }
            double ff=(double)num/ve[ans[i]].size();
//            printf("%d %d %d %.6f*\n",ans[i],num,ve[ans[i]].size(),ff);
            if(ff>f)
                f=ff;
        }
        printf("%.6f\n",ljt+f);
    }
}