LintCode : Dices Sum 骰子求和

悠悠 2021-06-24 16:10 394阅读 0赞

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

Example  
Example 1:

Input: n = 1  
Output: \[\[1, 0.17\], \[2, 0.17\], \[3, 0.17\], \[4, 0.17\], \[5, 0.17\], \[6, 0.17\]\]  
Explanation: Throw a dice, the sum of the numbers facing up may be 1, 2, 3, 4, 5, 6, and the probability of each result is 0.17.  
Notice  
You do not care about the accuracy of the result, we will help you to output results.  
**代码：**  
有三个未知数：扔骰子次数，在当前次数上和的取值范围，当前次扔骰子可能出现的点数。

public class Solution {
        /**
         * @param n an integer
         * @return a list of Map.Entry<sum, probability>
         */
        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
            long[][] dp = new long[n+1][6*n+1];
            for(int i=1; i<=6; i++){
                dp[1][i] = 1;
            }
            
            for(int i=2; i<=n; i++){
                for(int j=i; j<=6*i; j++){
                    for(int k=1; k<=6&&k<=j; k++){
                        dp[i][j] = dp[i][j] + dp[i-1][j-k];
                    }
                }
            }
            
            double total = Math.pow(6,n);
            HashMap map = new HashMap<Integer,Double>();
            for(int i=n; i<=6*n; i++){
                map.put(i,dp[n][i]/total);
            }
            
            return new ArrayList<Map.Entry<Integer,Double>>(map.entrySet());
        }
    }

LintCode : Dices Sum 骰子求和

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