Problem : [Usaco2009 Jan]Best Spot

Problem : [Usaco2009 Jan]Best Spot

Time Limit: 1 Sec  Memory Limit: 128 MB
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Description

Bessie, always wishing to optimize her life, has realized that she really enjoys visiting F (1 <= F <= P) favorite pastures F_i of the P (1 <= P <= 500; 1 <= F_i <= P) total pastures (conveniently

numbered 1..P) that compose Farmer John's holdings.

Bessie knows that she can navigate the C (1 <= C <= 8,000) bidirectional cowpaths (conveniently numbered 1..C) that connect various pastures to travel to any pasture on the entire farm. Associated with each path P_i is a time T_i (1 <= T_i <= 892) to traverse that path (in either direction) and two path endpoints a_i and b_i (1 <= a_i <= P; 1 <= b_i <= P).

Bessie wants to find the number of the best pasture to sleep in so that when she awakes, the average time to travel to any of her F favorite pastures is minimized.

By way of example, consider a farm laid out as the map below shows, where *'d pasture numbers are favorites. The bracketed numbers are times to traverse the cowpaths.

            1*--[4]--2--[2]--3
                     |       |
                    [3]     [4]
                     |       |
                     4--[3]--5--[1]---6---[6]---7--[7]--8*
                     |       |        |         |
                    [3]     [2]      [1]       [3]
                     |       |        |         |
                    13*      9--[3]--10*--[1]--11*--[3]--12*

The following table shows distances for potential 'best place' of pastures 4, 5, 6, 7, 9, 10, 11, and 12:

      * * * * * * Favorites * * * * * *
 Potential      Pasture Pasture Pasture Pasture Pasture Pasture     Average
Best Pasture       1       8      10      11      12      13        Distance
------------      --      --      --      --      --      --      -----------
    4              7      16       5       6       9       3      46/6 = 7.67
    5             10      13       2       3       6       6      40/6 = 6.67
    6             11      12       1       2       5       7      38/6 = 6.33
    7             16       7       4       3       6      12      48/6 = 8.00
    9             12      14       3       4       7       8      48/6 = 8.00
   10             12      11       0       1       4       8      36/6 = 6.00 ** BEST
   11             13      10       1       0       3       9      36/6 = 6.00
   12             16      13       4       3       0      12      48/6 = 8.00

Input

第1行输入三个整数P，F C.之后F行每行输入一个整数表示一个贝茜喜欢的牧场．
之后C行每行输入三个整数ai，bi，Ti，描述一条路．

Output

一个整数，满足题目要求的最佳牧场．如果有多个答案，输出编号最小的

Sample Input

5 5
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

Sample Output

10

HINT

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#include<stdio.h>
#include<string.h>
class BestSpot {
	public:
		int g[501][501],p,f,c,l[501];
		void init() {
			scanf("%d %d %d",&p,&f,&c);
			memset(g,0x3f,sizeof(g));
			for(i=1; i<=f; i++)
				scanf("%d",&l[i]);
			for(i=1; i<=c; i++)
				scanf("%d %d %d",&u,&v,&w),g[u][v]=g[v][u]=w;
			for(i=1; i<=p; i++)
				g[i][i]=0;
		}
		void work() {
			for(k=1; k<=p; k++)
				for(i=1; i<=p; i++)
					for(j=1; j<=p; j++)
						if(g[i][k]+g[k][j]<g[i][j])
							g[i][j]=g[i][k]+g[k][j];
		}
		void print() {
			for(i=1; i<=p; i++) {
				sum=0;
				for(j=1; j<=f; j++)
					if(g[i][l[j]]!=0x3f3f3f3f)sum+=g[i][l[j]];
				if(sum<mn)
					mn=sum,ans=i;
			}
			printf("%d",ans);
		}
	private:
		int i,j,k,u,v,w,sum,ans,mn=0x7fffffff;
};
int main() {
	BestSpot Bessie;
	Bessie.init();
	Bessie.work();
	Bessie.print();
}