n个骰子的点数
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把n个骰子扔在地上,所以骰子朝一面的点数之和为s。输入n,打印出s的所有可能的值出现的概率
#include <iostream>#include <math.h>using namespace std;int g_maxValue = 6;void Probability(int number, int current, int sum, int* Probabilities){if(current == 1){Probabilities[sum - number]++;}else{for(int i =1; i <= g_maxValue; i++)Probability(number, current-1, sum+i, Probabilities);}}void Probability(int number, int* Probabilities){for(int i = 1; i <= g_maxValue; i++){Probability(number, number, i, Probabilities);}}void printProbilites(int number){if(number < 1)return;int maxNum = number * g_maxValue;int* Probabilities = new int[maxNum - number +1];for(int i = number; i <= maxNum; i++)Probabilities[i - number] = 0 ;Probability(number, Probabilities);int total = pow((double)g_maxValue, number);for(int i= number; i <= maxNum; i++){double ratio = (double)Probabilities[i - number]/total;printf("%d: %e\n",i,ratio);}delete[] Probabilities;}// ====================方法二====================void PrintProbability_Solution2(int number){ if(number < 1) return; int* pProbabilities[2]; pProbabilities[0] = new int[g_maxValue * number + 1]; pProbabilities[1] = new int[g_maxValue * number + 1]; for(int i = 0; i < g_maxValue * number + 1; ++i) { pProbabilities[0][i] = 0; pProbabilities[1][i] = 0; } int flag = 0; for (int i = 1; i <= g_maxValue; ++i) pProbabilities[flag][i] = 1; for (int k = 2; k <= number; ++k) { for(int i = 0; i < k; ++i) pProbabilities[1 - flag][i] = 0; for (int i = k; i <= g_maxValue * k; ++i) { pProbabilities[1 - flag][i] = 0; for(int j = 1; j <= i && j <= g_maxValue; ++j) pProbabilities[1 - flag][i] += pProbabilities[flag][i - j]; } flag = 1 - flag; } double total = pow((double)g_maxValue, number); for(int i = number; i <= g_maxValue * number; ++i) { double ratio = (double)pProbabilities[flag][i] / total; printf("%d: %e\n", i, ratio); } delete[] pProbabilities[0]; delete[] pProbabilities[1];}
// ====================测试代码====================void Test(int n){ printf("Test for %d begins:\n", n); printf("Test for solution1\n"); printProbilites(n); printf("Test for solution2\n"); PrintProbability_Solution2(n); printf("\n");}int main(int argc, char* argv[]){ Test(1); Test(2); Test(3); Test(4); Test(11); Test(0); return 0;}
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