題目描述

Description
Throw n dices, the sum of the dices’ faces is S. Given n, find the all possible value of S along with its probability.

• You do not care about the accuracy of the result, we will help you to output results.

Example
Given n = 1, return [ [1, 0.17], [2, 0.17], [3, 0.17], [4, 0.17], [5, 0.17], [6, 0.17]].

思路

看到這題，首先想到的就是動態規劃了，二維陣列記錄概率，然後用公式來求解：
n是骰子數量，a是點數，f(n,a)指的是n個骰子點數為a的概率
有了公式就很方便進行求解了

• 第一層迴圈，表示骰子數量
• 第二層迴圈，表示點數
• 第三層迴圈，用來計算概率

程式碼

public List<Map.Entry<Integer, Double>> dicesSum(int n) {
        // Write your code here
        // Ps. new AbstractMap.SimpleEntry<Integer, Double>(sum, pro)
 

        // to create the pair
        List<Map.Entry<Integer, Double>> result = new ArrayList<>();
        double[][] dp = new double[n + 1][n * 6 + 1];
        for (int i = 1; i < 7; i++) {
            dp[1][i] = 1.0 / 6;
        }
        for (int i = 2; i <= n; i++) {
            for
 
 (int j = i; j <= 6 * i; j++) {
                for (int m = 1; m <= 6; m++) {
                    if (j > m) {
                        dp[i][j] += dp[i - 1][j - m];
                    }
                }
                dp[i][j] /= 6.0;
            }
        }
        for (int i = n; i <= 6 * n; ++i) {
            result.add(new AbstractMap.SimpleEntry<>(i, dp[n][i]));
        }
        return result;
    }