//把n個骰子扔在地上，所有骰子朝上一面的點數之和為s。輸入n,打印出s的所有可能
//的值出現的概率。
#include "stdio.h"
#include "cmath"
#include "helper.h"
using namespace std;

//方法1：遞迴思路。把骰子分成兩堆，一堆1個，另一堆n-1個。
int diceSurface = 6;

void probabilityRecursively(int current, int sum,
	int* appearanceCount)
{
	if (current == 1)
		appearanceCount[sum]++;
	else
	{
		for (int i = 1; i <= diceSurface; ++i)
			probabilityRecursively(current - 1, i + sum, appearanceCount);
	}
}

void probability(int* appearanceCount, int n)
{
	for (int i = 1; i <= diceSurface; ++i)
		probabilityRecursively(n, i, appearanceCount);

}
void printAllProbability0(int n)
{
	if (n < 1)
		return;

	int maxSum = n * diceSurface;
	int* appearanceCount = new int[maxSum + 1]; //不會初始化為0

	for (int i = 0; i <= maxSum; i++)
		appearanceCount[i] = 0; //初始化

	probability(appearanceCount, n);

	int totalProbability = pow(diceSurface, n);
	for (int i = n; i <= maxSum; i++)
		printf("P(%d): %d/%d\n", i, appearanceCount[i], totalProbability);

	delete[] appearanceCount;
}


//兩個陣列交替進行，有點類似動態規劃的意思。
void printAllProbability1(int n)
{
	if (n < 1)
		return;

	int maxSum = n * diceSurface;
	int* appearanceCount[2];

	appearanceCount[0] = new int[maxSum + 1];
	appearanceCount[1] = new int[maxSum + 1];

	for (int i = 0; i <= maxSum; ++i)
	{
		appearanceCount[0][i] = 0;
		appearanceCount[1][i] = 0;
	}

	int flag = 0;
	for (int i = 1; i <= diceSurface; i++)
		appearanceCount[flag][i] = 1; 

	for (int k = 2; k <= n; ++k)
	{
		for (int i = 0; i < k; ++i)
			appearanceCount[1 - flag][i] = 0;

		for (int i = k; i <= maxSum; ++i)
		{
			appearanceCount[1 - flag][i] = 0;
			for (int j = 1; j <= i && j <= diceSurface; ++j)
				appearanceCount[1 - flag][i] += appearanceCount[flag][i - j];
		}
		flag = 1 - flag;
	}


	int totalProbability = pow(diceSurface, n);
	for (int i = n; i <= maxSum; i++)
		printf("P(%d): %d/%d\n", i, appearanceCount[flag][i], totalProbability);

	delete[] appearanceCount[0];
	delete[] appearanceCount[1];
}

int main()
{
	int n = 3;
	printAllProbability1(n);
	return 0;
}