n個骰子的點數之和的機率

n個骰子的點數。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，列印出S的所有可能的值出現的機率。

思想：F(n,s) = F(n-1,s-6)+F(n-1,s-5)+F(n-1,s-4)+F(n-1,s-3)+F(n-1,s-2)+F(n-1,s-1);

#include <stdio.h>#include <stdlib.h>#include <string.h>int power(int base,unsigned int n){if(n==0) return 1;if(n==1) return base;int half=power(base,n>>1);return ((n & 1) == 1 ? base : 1) * half * half;}//遞迴int F(int n, int s){if(s<n || s>6*n) return 0;if(n==1) return 1;//if(s==n || s==6*n) return 1;elsereturn F(n-1,s-6)+F(n-1,s-5)+F(n-1,s-4)+F(n-1,s-3)+F(n-1,s-2)+F(n-1,s-1);}void listDiceProbability(int n){int i=0;unsigned int nTotal=power(6,n);for(i=n;i<=6*n;i++){printf("P(s=%d) = %d/%d\n",i,F(n,i),nTotal);}}//非遞迴void pr_probabilityOfDices(unsigned int N){const unsigned int MAX = 12;int i=0,size=0,s,n;if (N > MAX){printf("too big!\n");return;}// new arrayint **f=malloc(sizeof(int *)*(N+1));for(i=1;i<N+1;i++){size=sizeof(int)*(6*i+1);f[i]=(int *)malloc(size);memset(f[i],0,size);}//initfor(i=1;i<=6;i++){f[1][i]=1;}//updatefor(n=2;n<N+1;n++){for(s=n;s<=(n*6);s++){f[n][s]=0;for(i=1;i<=6;i++)if(s-i>=n-1 && s-i <= 6*(n-1))f[n][s]+=f[n-1][s-i];}}unsigned int ntotal=power(6,N);for(i=N;i<6*N+1;i++){printf("p(s=%d) = %d/%d \n",i,f[N][i],ntotal);}//free arrayfor(i=1;i<N+1;i++)free(f[i]);free(f);}//同上void PrintSumProbabilityOfDices(unsigned int N){const unsigned int MAX=12;  //max number of dicesif(N>MAX){printf("Overflow!\n");return;};unsigned int a[MAX+1][6*MAX+1];unsigned int n,s,i;memset(a,0,sizeof(a));for(s=1;s<=6;s++)a[1][s]=1;for(n=2;n<=N;n++)for(s=n;s<=6*n;s++){a[n][s]=0;for(i=1;i<=6 && i<s;i++)a[n][s]+=a[n-1][s-i];}unsigned int nTotal=power(6,N);for(i=N;i<=6*N;i++){printf("P(s=%d) = %d/%d\n",i,a[N][i],nTotal);}}int main(void){puts("***********");listDiceProbability(3);puts("***********");pr_probabilityOfDices(3);return 0;}