P2935

[USACO09JAN]Best Spot S

题目

约翰拥有P(1<=P<=500)个牧场.贝茜特别喜欢其中的F个.所有的牧场 由C(1 < C<=8000)条双向路连接，第i路连接着ai,bi，需要Ti(1<=Ti< 892)单 位时间来通过.

作为一只总想优化自己生活方式的奶牛，贝茜喜欢自己某一天醒来，到达所有那F个她喜欢的 牧场的平均需时最小.那她前一天应该睡在哪个牧场呢？请帮助贝茜找到这个最佳牧场.

此可见，牧场10到所有贝茜喜欢的牧场的平均距离最小，为最佳牧场.

输入

13 6 15
11
13
10
12
8
1
2 4 3
7 11 3
10 11 1
4 13 3
9 10 3
2 3 2
3 5 4
5 9 2
6 7 6
5 6 1
1 2 4
4 5 3
11 12 3
6 10 1
7 8 7

输出

10

点拨

根据题意，我们只需要求出这几个最喜爱的农场相对于每个点的距离，相加求最小值即可

对每个点要求最短路，时间复杂度为O(n^2*logn)

代码

#include <iostream>
#include <utility>
#include <queue>
using namespace std;
typedef long long ll;
#define fi(i, a, b) for (int i = a; i <= b; ++i)
#define fr(i, a, b) for (int i = a; i >= b; --i)
#define x first
#define y second
#define sz(x) ((int)(x).size())
#define pb push_back
using pii = pair<int, int>;
//#define DEBUG
int cnt = 1;
int head[505];
int dis[505][505];
int s[505];
int ans[505];
struct edge
{
    int e, w, next;
} edge[16005];
void add(int a, int b, int c)
{
    edge[cnt].e = b;
    edge[cnt].w = c;
    edge[cnt].next = head[a];
    head[a] = cnt++;
}
struct node
{
    int e, w;
    bool operator<(const node p) const
    {
        return w > p.w;
    }
};
int p, f, c;
void djstra(int s)
{
    priority_queue<node> pri;
    bool vis[505];
    fi(i, 0, p) vis[i] = false;
    pri.push({s, 0});
    while (!pri.empty())
    {
        node temp = pri.top();
        pri.pop();
        int x = temp.e, y = temp.w;
        vis[x] = true;
        // cout << x << endl;
        for (int j = head[x]; j != 0; j = edge[j].next)
        {
            int e = edge[j].e;
            int w = edge[j].w;
            // cout << e << " " << w << endl;
            // cout << dis[s][e] << endl;
            if (dis[s][e] >= dis[s][x] + w)
            {
                dis[s][e] = dis[e][s] = dis[s][x] + w;
                // cout << e << " " << dis[s][e] << " ";
                if(!vis[e])
                pri.push({e, dis[s][e]});
            }
        }
    }
    fi(i, 1, p) ans[i] += dis[s][i];
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
#ifdef DEBUG
    // freopen(D:\in.txt,r,stdin);
#endif
    cin >> p >> f >> c;
    fi(i, 1, f) cin >> s[i];
    fi(i, 1, p) fi(j, 1, p) dis[i][j] = 0x3f3f3f3f;
    fi(i, 1, p) dis[i][i] = 0;
    while (c--)
    {
        int a, b, c1;
        cin >> a >> b >> c1;
        add(a, b, c1);
        add(b, a, c1);
        dis[a][b] = dis[b][a] = c1;
    }
    // djstra(1);
    fi(i, 1, f)
    {
        djstra(s[i]);
    }
    double res[505];
    fi(i,1,p) res[i] = (double)ans[i]/f;
    // fi(i, 1, p) cout << res[i] << " ";
    // cout << endl;
    double minn = 0x3f3f3f;
    int minn1;
    fi(i,1,p){
        if(res[i] < minn){
            minn = res[i];
            minn1 = i;
        }
    }
    cout << minn1 << endl;
    return 0;
}