# Six Degrees of Cowvin Bacon (POJ 2139)

A shortest path problem, we need to calculate out shortest distance between each pair of cows, then for each cow we caculate its average distance to other cows and at last preserve the lowest value.

import java.io.*;
import java.util.*;

public class SixDegreesOfCowvinBacon {
private static int INF = 10000000;
private static void solve(int[][] dist) {
int N = dist.length;

for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
for (int k = 0; k < N; k++) {
dist[i][j] = Math.min(dist[i][j], dist[i][k] + dist[k][j]);
}
}
}

int minsum = INF;

for (int i = 0; i < N; i++) {
int sum = 0;
for (int j = 0; j < N; j++) {
sum += dist[i][j];
}

minsum = Math.min(minsum, sum);
}

System.out.println(minsum * 100 / (N - 1));
}

public static void main(String[] args) throws IOException {

int N = Integer.parseInt(str[0]), M = Integer.parseInt(str[1]);

int[][] dist = new int[N][N];
for (int i = 0; i < N; i++) {
Arrays.fill(dist[i], INF);
dist[i][i] = 0;
}

for (int i = 0; i < M; i++) {
int[] cows = new int[str.length];

for (int j = 1; j < str.length; j++) {
cows[j] = Integer.parseInt(str[j]) - 1;
}

for (int j = 1; j < cows.length; j++) {
for (int k = j + 1; k < cows.length; k++) {
dist[cows[j]][cows[k]] = 1;
dist[cows[k]][cows[j]] = 1;
}
}
}

solve(dist);
}
}