1023: Pong’s Birds（概率）

1023: Pong’s Birds

时间限制: 1 Sec  内存限制: 128 MB
提交: 94  解决: 21
[提交][状态][讨论版]

题目描述

In order to train his birds, Pong is holding a competition for them. (He have birds, does he?) He have 2n birds,
so he want to hold elimination series. Literally, if n = 2 and he has 4 birds identified as 1,2,3,4, he would first hold competition for 1 and 2, 3 and 4, the one fails would be eliminated and then he holds competition for the winners. 
According to his long observation, for each pair of birds he knows the probability to win for each bird, and he want to know the probability of each bird to be the final winner.

输入

For the first row there is an integer T(T ≤ 100), which is the number of test cases.
For each case , first row is an integer n(1 ≤ n ≤ 7), for the next 2n rows , each row has 2n real numbers as the probability to win for the i-th when competed to j-th bird. It is promised that for each i, j p[i][j] + p[j][i] = 1 and p[i][i] = 0;

输出

For each case you should output a line with 2n real numbers, which is the probability of i-th bird be the final winner. Rounded to 3 decimal places.
Make sure to output a space character after each number, to prevent the Presentation Error.

样例输入

1
1
0 0.5
0.5 0

样例输出

0.500 0.500

提示

求队伍夺冠概率，画图找下规律递推，

#include <bits/stdc++.h>
using namespace std;

const int MAXN = (1 << 7) + 5;
double p[MAXN][MAXN];
double dp[8][MAXN];//dp[i][j]表示第i轮j队伍出线概率

int main()
{
    int t;
    int n;
    int n2;
    int i, j, k;
    int grp;
    for (j = 0; j < MAXN; ++j) {
        dp[0][j] = 1;
    }
    scanf("%d", &t);
    while (t--) {
        scanf("%d", &n);
        n2 = 1 << n;
        for (i = 0; i < n2; ++i) {
            for (j = 0; j < n2; ++j) {
                scanf("%lf", &p[i][j]);
            }
        }

        for (i = 1; i <= n; ++i) {
            for (j = 0; j < n2; ++j) {
                grp = j / (1 << (i - 1));//
                grp ^= 1;//奇偶互换
                dp[i][j] = 0;
                for (k = grp << (i - 1); k < ((grp + 1) << (i - 1)); ++k) {
                    dp[i][j] += dp[i - 1][j] * dp[i - 1][k] * p[j][k];
                }
            }
        }

        for (i = 0; i < n2 - 1; ++i) {
            printf("%.3lf ", dp[n][i]);
        }
        printf("%.3lf
", dp[n][n2 - 1]);
    }
    return 0;
}

记忆化搜索

#include <bits/stdc++.h>
using namespace std;

const int MAXN = (1 << 7) + 5;
double p[MAXN][MAXN];
double dp[8][MAXN];//dp[i][j]表示第i轮j队伍出线概率

double dfs(int i, int j)
{
    if (i == 0) {
        return 1;
    }
    if (dp[i][j] >= 0) {
        //printf("%lf
", dp[i][j]);
        return dp[i][j];
    }
    int k;
    int grp;
    grp = j / (1 << (i - 1));//
    grp ^= 1;//奇偶互换
    dp[i][j] = 0;
    for (k = grp << (i - 1); k < ((grp + 1) << (i - 1)); ++k) {
        dp[i][j] += dfs(i - 1, j) * dfs(i - 1, k) * p[j][k];
    }
    return dp[i][j];
}

int main()
{
    int t;
    int n;
    int n2;
    int i, j, k;
    int grp;
    scanf("%d", &t);
    while (t--) {
        scanf("%d", &n);
        n2 = 1 << n;
        for (i = 0; i < n2; ++i) {
            for (j = 0; j < n2; ++j) {
                scanf("%lf", &p[i][j]);
            }
        }
        
        //memset(dp, -1, sizeof(dp));//不能使用
        for (i = 1; i <= n; ++i) {
            for (j = 0; j < n2; ++j) {
                dp[i][j] = -1;
            }
        }

        for (i = 0; i < n2 - 1; ++i) {
            printf("%.3lf ", dfs(n, i));
        }
        printf("%.3lf
", dfs(n, n2 - 1));
    }
    return 0;
}