POJ2139 Six Degrees of Cowvin Bacon 【Floyd】
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Six Degrees of Cowvin Bacon
Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 3131 Accepted: 1455
Description
The cows have been making movies lately, so they are ready to play a variant of the famous game "Six Degrees of Kevin Bacon".
The game works like this: each cow is considered to be zero degrees of separation (degrees) away from herself. If two distinct cows have been in a movie together, each is considered to be one 'degree' away from the other. If a two cows have never worked together but have both worked with a third cow, they are considered to be two 'degrees' away from each other (counted as: one degree to the cow they've worked with and one more to the other cow). This scales to the general case.
The N (2 <= N <= 300) cows are interested in figuring out which cow has the smallest average degree of separation from all the other cows. excluding herself of course. The cows have made M (1 <= M <= 10000) movies and it is guaranteed that some relationship path exists between every pair of cows.
The game works like this: each cow is considered to be zero degrees of separation (degrees) away from herself. If two distinct cows have been in a movie together, each is considered to be one 'degree' away from the other. If a two cows have never worked together but have both worked with a third cow, they are considered to be two 'degrees' away from each other (counted as: one degree to the cow they've worked with and one more to the other cow). This scales to the general case.
The N (2 <= N <= 300) cows are interested in figuring out which cow has the smallest average degree of separation from all the other cows. excluding herself of course. The cows have made M (1 <= M <= 10000) movies and it is guaranteed that some relationship path exists between every pair of cows.
Input
* Line 1: Two space-separated integers: N and M
* Lines 2..M+1: Each input line contains a set of two or more space-separated integers that describes the cows appearing in a single movie. The first integer is the number of cows participating in the described movie, (e.g., Mi); the subsequent Mi integers tell which cows were.
* Lines 2..M+1: Each input line contains a set of two or more space-separated integers that describes the cows appearing in a single movie. The first integer is the number of cows participating in the described movie, (e.g., Mi); the subsequent Mi integers tell which cows were.
Output
* Line 1: A single integer that is 100 times the shortest mean degree of separation of any of the cows.
Sample Input
4 23 1 2 32 3 4
Sample Output
100
Hint
[Cow 3 has worked with all the other cows and thus has degrees of separation: 1, 1, and 1 -- a mean of 1.00 .]
Source
USACO 2003 March Orange
#include <stdio.h>#include <stdlib.h>#include <string.h>#include <iostream>#include <algorithm>#include <queue>using namespace std;typedef long long LL;#define maxn 302#define inf 0x3f3f3f3fint G[maxn][maxn], N, M;int sta[maxn];void Floyd(){ int i, j, k; for(k = 1; k <= N; ++k) for(i = 1; i <= N; ++i) for(j = 1; j <= N; ++j) if(G[i][k] + G[k][j] < G[i][j]) G[i][j] = G[i][k] + G[k][j]; }int main() { // freopen("stdin.txt", "r", stdin); int i, j, num, ans = inf; memset(G, 0x3f, sizeof(G)); scanf("%d%d", &N, &M); for(i = 1; i <= N; ++i) G[i][0] = G[i][i] = 0; while(M--) { scanf("%d", &num); for(i = 0; i < num; ++i) { scanf("%d", sta + i); for(j = 0; j < i; ++j) G[sta[i]][sta[j]] = G[sta[j]][sta[i]] = 1; } } Floyd(); for(i = 1; i <= N; ++i) { for(j = 1; j <= N; ++j) G[i][0] += G[i][j]; if(ans > G[i][0]) ans = G[i][0]; } printf("%d\n", ans * 100 / (N - 1)); return 0;}
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