// 程序员面试题精选100题(43)-n个骰子的点数.cpp : 定义控制台应用程序的入口点。//#include "stdafx.h"#include <iostream>#include <math.h>#include <windows.h>using namespace std;//////////////////////////////////////////////////////////////////////////int g_maxValue = 6;void SumProbabilityOfDices(int original, int current, int value, int tempSum, int* pProbabilities){if(current == 1){int sum = value + tempSum;pProbabilities[sum - original]++;}else{for(int i = 1; i <= g_maxValue; ++i){int sum = value + tempSum;SumProbabilityOfDices(original, current - 1, i, sum, pProbabilities);}}} void SumProbabilityOfDices(int number, int* pProbabilities){for(int i = 1; i <= g_maxValue; ++i)SumProbabilityOfDices(number, number, i, 0, pProbabilities);}void PrintSumProbabilityOfDices_1(int number){if(number < 1)return;int maxSum = number * g_maxValue;int* pProbabilities = new int[maxSum - number + 1];for(int i = number; i <= maxSum; ++i)pProbabilities[i - number] = 0;SumProbabilityOfDices(number, pProbabilities);int total = pow((double)g_maxValue, number);double sum1=0;for(int i = number; i <= maxSum; ++i){double ratio = (double)pProbabilities[i - number] / total;//printf("%d: %lf\n", i, ratio);//cout<<i<<":"<<ratio<<" ";cout<<i<<":"<<pProbabilities[i - number]<<" ";sum1+=ratio;}cout<<"sum is equal to "<<sum1<<endl;cout<<"total is equal to "<<total<<endl;delete[] pProbabilities;}///////////////////////////////////////////////////////////////////////////void PrintSumProbabilityOfDices_2(int number){double* pProbabilities[2];pProbabilities[0] = new double[g_maxValue * number + 1];pProbabilities[1] = new double[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 = 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);double ifone=0;for(int i = number; i <= g_maxValue * number; ++i){double ratio = pProbabilities[flag][i] / total;ifone+=ratio;//?printf("%d: %f\n", i, ratio);cout<<i<<":"<<pProbabilities[flag][i]<<" ";}cout<<" all the probabilities is "<<ifone<<endl;delete[] pProbabilities[0];//local , here is rightdelete[] pProbabilities[1];}//////////////////////////////////////////////////////////////////////////void PrintSumProbabilityOfDices_myself(int n)// all by myself without looking the answer, actually is the idea of the second method,but is seems that the second answer is wrong somewhere{//?HANDLE hHeap1,hHeap2,hHeap3;int *dicesArr = NULL;dicesArr = new int[n*7+1];//int[n*6+1]; here i made a so stupid mistake which takes me nearly 4 hour to handle,all the notes parts are my attempts to correct my program, indeed, I learn a little thing //hHeap1 = HeapCreate(HEAP_GENERATE_EXCEPTIONS,0x1000,0xffff);//dicesArr = (int*)HeapAlloc(hHeap1,HEAP_NO_SERIALIZE, sizeof(int)*(7*n+1));//Number of bytes to be allocated.that is means that if dicesArr access out of range HeapFree is wrongint *dicesSum = NULL;dicesSum = new int[n*7+1];//hHeap2 = HeapCreate(HEAP_GENERATE_EXCEPTIONS,0x1000,0xffff);//dicesSum = (int*)HeapAlloc(hHeap2,HEAP_NO_SERIALIZE, sizeof(int)*(7*n+1));//hHeap3 = HeapCreate(HEAP_GENERATE_EXCEPTIONS,0x1000,0xffff);double *problility = NULL;problility = new double[7*n+1];//problility = (double*)HeapAlloc(hHeap3,HEAP_NO_SERIALIZE, sizeof(double)*(7*n+1));// Fuck!, so easy a sentence really takes me more than 3 hoursfor (int i=0;i<=n*6;i++){dicesArr[i]=0;dicesSum[i]=0;}for (int i=1;i<=6;i++){dicesArr[i]=1;dicesSum[i]=dicesSum[i-1]+dicesArr[i];}for (int k=2;k<=n;k++){for (int i=k;i<=7*k/2;i++)//dicesArr[0] dicesSum[0] is always 1{if(i-k>=6){dicesArr[i]=dicesSum[i-1]-dicesSum[i-1-6];}else{dicesArr[i]=dicesSum[i-1];}dicesArr[7*k-i]=dicesArr[i];}for (int j=k;j<=7*k;j++){if (j==k){dicesSum[j]=1;}elsedicesSum[j]=dicesSum[j-1]+dicesArr[j];}/*for (int i=k;i<=6*k;i++){cout<<dicesArr[i]<<":";cout<<dicesSum[i]<<" ";}cout<<endl;*/}double sum=0;long int sumint=0;for (int j=n;j<=6*n;j++){problility[j] = dicesArr[j]/pow(6.0,n);sumint+=dicesArr[j];sum+=problility[j];//cout<<j<<":"<<problility[j]<<" ";cout<<j<<":"<<dicesArr[j]<<" ";}cout<<"sum is "<<sum<<endl;cout<<sumint<<" is equal to "<<pow(6.0,n)<<endl;/**/if (dicesArr!=NULL){delete[] dicesArr;//HeapFree(hHeap1,0,dicesArr);// here is noticeable when the dicesArr = NULL;//dicesArr = NULL; 居然不报错 dicesArr[] = NULL; 报错}//new分配的内存是从堆上的来的，而局部变量都是从栈上得到内存。每个模块都有一个与之相绑定的堆和一个栈，//其两个的大小都可以通过编译器选项指定。所以楼主的new是从dll的堆上分，delete是从应用程序的堆上撤，根本不是同一个堆上，所以出错。if (dicesSum!=NULL){delete[] dicesSum;//here is wrong even in the local function,but in the above functions both are right,why????//HeapFree(hHeap2,0,dicesSum);dicesSum = NULL;}if (problility!=NULL){delete[] problility;//HeapFree(hHeap3,0,problility);problility = NULL;}}//////////////////////////////////////////////////////////////////////////int _tmain(int argc, _TCHAR* argv[]){int n;cin>>n;PrintSumProbabilityOfDices_1(n);//PrintSumProbabilityOfDices_2(n);cout<<"what?"<<endl;PrintSumProbabilityOfDices_myself(n);system("pause");return 0;}
