/*

*

* 面试题43：n个骰子的点数

* 把n个骰子扔在地上，所有骰子朝上一面的点数之和为s。

* 输入n，打印出s的所有可能的值出现的概率。

*

*/

#include <iostream>

#include <cmath>

using namespace std;

const int max_val = ;

//核心，计算概率

//original为起始值，n个骰子起始值为n

//current为当前骰子个数

//骰子数之和

//和对应的次数

void probalility(int original, int current, int sum, int *probabilities)

{

    if (current == ) {

        probabilities[sum - original]++;

    }

    else{

        //每个骰子都有六种可能

        for (int i = ; i <= max_val; i++) {

            probalility(original, current - , i + sum, probabilities);

        }

    }

}

//计算概率

void probalility(int number, int *probabilities)

{

    for (int i = ; i <= max_val; i++) {

        probalility(number, number, i, probabilities);

    }

}

void PrintPrabability(int number)

{

    if (number < ) {

        return;

    }

    //申请空间

    int max_sum = number * max_val;

    int *probabilities = new int[max_sum];

    for (int i = number; i <= max_sum; i++) {

        probabilities[i] = ;

    }

    //计算可能的情况

    probalility(number, probabilities);

    //计算概率

    int total = pow(double(max_val), number);

    for (int i = number; i <= max_sum; i++) {

        double ratio = (double)probabilities[i - number] / total;

        cout << i << " " << ratio << endl;

    }

}