using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace HellWorld
{
class Program
{
public static void PrintSumProbabilityOfDices(int num)
{
int max = num*6;
int[,] arr = new int[num + 1,max + 1];
for (int i = 1; i <= 6;i++ )
{
arr[1, i] = 1;
}
for (int k = 2; k <= num;k++ )
{
for (int i = k; i <=6 * k;i++ )
{
for (int j = 1; j <= 6;j++ )
{
if(i>=j)
arr[k, i] += arr[k-1,i - j];
}
}
}
double total = Math.Pow((double)6, num);
for (int j = num; j <= max; j++)
{
double ratio = arr[6, j]/total;
Console.WriteLine("{0}:{1}",arr[6,j],ratio );
}
}
static void Main(string[] args)
{
PrintSumProbabilityOfDices(6);
Console.ReadLine();
}
}
}
状态转移方程
k表示骰子个数,n表示k个骰子的点数和
| - F(k-1, n-6) + F(k-1, n-5) + F(k-1, n-4) + F(k-1, n-3) + F(k-1, n-2) + F(k-1, n-1) | 对于 k > 0, k <= n <= 6*k
F(k, n) = |
|- 0 对于 n < k or n > 6*k
初始化k=1, F(1,1)=F(1,2)=F(1,3)=F(1,4)=F(1,5)=F(1,6)=1