POJ 3071 Football

Football

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 2366		Accepted: 1191

Description

Consider a single-elimination football tournament involving 2ⁿ teams, denoted 1, 2, …, 2ⁿ. In each round of the tournament, all teams still in the tournament are placed in a list in order of increasing index. Then, the first team in the list plays the second team, the third team plays the fourth team, etc. The winners of these matches advance to the next round, and the losers are eliminated. After n rounds, only one team remains undefeated; this team is declared the winner.

Given a matrix P = [p_ij] such that p_ij is the probability that team i will beat team j in a match determine which team is most likely to win the tournament.

Input

The input test file will contain multiple test cases. Each test case will begin with a single line containing n (1 ≤ n ≤ 7). The next 2ⁿ lines each contain 2ⁿ values; here, the jth value on the ith line represents p_ij. The matrix P will satisfy the constraints that p_ij = 1.0 − p_ji for all i ≠ j, and p_ii = 0.0 for all i. The end-of-file is denoted by a single line containing the number −1. Note that each of the matrix entries in this problem is given as a floating-point value. To avoid precision problems, make sure that you use either the double data type instead of float.

Output

The output file should contain a single line for each test case indicating the number of the team most likely to win. To prevent floating-point precision issues, it is guaranteed that the difference in win probability for the top two teams will be at least 0.01.

Sample Input

2
0.0 0.1 0.2 0.3
0.9 0.0 0.4 0.5
0.8 0.6 0.0 0.6
0.7 0.5 0.4 0.0
-1

Sample Output

2
題目大意：輸入n，總共有2^n支球隊，每支球隊打敗其餘球隊的機率經過矩陣輸入，求奪冠機率最大的球隊是哪支球隊。
解題方法：機率DP。

#include <stdio.h>
#include <iostream>
#include <string.h>
using namespace std;

int main()
{
    double p[200][200];
    double dp[200][200];//dp[i][j]表明第i輪比賽中j勝出的機率
    int n;
    while(scanf("%d", &n) != EOF && n != -1)
    {
        memset(dp, 0, sizeof(dp));
        for (int i = 0; i < 1 << n; i++)
        {
            for (int j = 0; j < 1 << n; j++)
            {
                scanf("%lf", &p[i][j]);
            }
        }
        for (int i = 0; i < 1 << n; i++)
        {
            dp[0][i] = 1;
        }
        for (int i = 1; i <= n; i++)//總共有n輪比賽
        {
            for (int j = 0; j < (1 << n); j++)
            {
                int t = j / (1 << (i - 1));
                t ^= 1;
                for (int k = t * (1 << (i - 1)); k < t * (1 << (i - 1)) + (1 << (i - 1)); k++)
                {
                    dp[i][j] += dp[i - 1][j] * dp[i - 1][k] * p[j][k];
                }
            }
        }
        double temp = 0.0;
        int ans;
        for (int i = 0; i < 1 << n; i++)
        {
            if (dp[n][i] > temp)
            {
                temp = dp[n][i];
                ans = i;
            }
        }
        printf("%d\n", ans + 1);
    }
    return 0;
}