本文主要是介绍【ProjectEuler】ProjectEuler_052(找出最小的正整数x，使得2x, 3x, 4x, 5x和6x都包含同样的数字)，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
#pragma once#include <windows.h>
#include <vector>
#include <set>using namespace std;class MoonMath
{
public:MoonMath(void);~MoonMath(void);//************************************// Method: IsInt// Access: public// Describe: 判断double值在epsilon的范围内是否很接近整数// 如1.00005在epsilon为0.00005以上就很接近整数// Parameter: double doubleValue 要判断的double值// Parameter: double epsilon 判断的精度，0 < epsilon < 0.5// Parameter: INT32 & intValue 如果接近，返回最接近的整数值// Returns: bool 接近返回true，否则返回false//************************************static bool IsInt(double doubleValue, double epsilon, INT32 &intValue);//************************************// Method: Sign// Access: public// Describe: 获取value的符号// Parameter: T value 要获取符号的值// Returns: INT32 正数、0和负数分别返回1、0和-1//************************************template <typename T>static INT32 Sign(T value);const static UINT32 MIN_PRIMER = 2; // 最小的素数//************************************// Method: IsPrimer// Access: public// Describe: 判断一个数是否是素数// Parameter: UINT32 num 要判断的数// Returns: bool 是素数返回true，否则返回false//************************************static bool IsPrimer(UINT32 num);//************************************// Method: IsIntegerSquare// Access: public static// Describe: 判断给定的数开平方后是否为整数// Parameter: UINT32 num// Returns: bool//************************************static bool IsIntegerSquare(UINT32 num);//************************************// Method: GetDiffPrimerFactorNum// Access: public static// Describe: 获取num所有的不同质因数// Parameter: UINT32 num// Returns: set<UINT32>//************************************static set<UINT32> MoonMath::GetDiffPrimerFactorNum(UINT32 num);//************************************// Method: GetDigitMap// Access: public// Describe: 获取num包含的数字map// Parameter: UINT32 num// Parameter: UINT16 & digitMap 返回的num的数字map，为2进制// Returns: bool 如果包含重复的数字，返回false，否则返回true//************************************static bool GetDigitMap(UINT32 num, UINT16 &digitMap);//************************************// Method: IsSameDigitNum// Access: public // Describe: 判断N个数字是否都是由相同的数字组成，每个数字都必须包含不同的数字// Parameter: const UINT32 nums[] N个数字组成的数组// Parameter: UINT32 numCount 数字个数// Returns: bool//************************************static bool IsNumsHaveSameDigit(const UINT32 nums[], UINT32 numCount);//************************************// Method: Factorial// Access: public // Describe: 获得n的阶乘// Parameter: UINT32 n// Returns: UINT32//************************************static UINT32 Factorial(UINT32 n);//************************************// Method: Combination// Access: public // Describe: 求(n,r)的组合// Parameter: UINT32 n// Parameter: UINT32 r// Returns: UINT32//************************************static UINT32 Combination(UINT32 n,UINT32 r);
};
#include "MoonMath.h"
#include <cmath>
#include <iostream>using namespace std;MoonMath::MoonMath(void)
{
}MoonMath::~MoonMath(void)
{
}template <typename T>
INT32 MoonMath::Sign(T value)
{if(value > 0){return 1;}else if(value == 0){return 0;}else{return -1;}
}bool MoonMath::IsInt(double doubleValue, double epsilon, INT32 &intValue)
{if(epsilon > 0.5 || epsilon < 0){return false;}if(INT32(doubleValue + epsilon) == INT32(doubleValue - epsilon)){return false;}INT32 value = INT32(doubleValue);intValue = (fabs(doubleValue - value) > 0.5) ? (value + MoonMath::Sign(doubleValue)) : (value) ;return true;
}bool MoonMath::IsPrimer(UINT32 num)
{if(num < MIN_PRIMER){return false;}if(num == MIN_PRIMER){return true;}// 判断是否能被2整除if((num & 1) == 0){return false;}UINT32 sqrtOfNum = (UINT32)sqrt((double)num); // num的2次方// 从MIN_PRIMER到sqrt(num)，如果任何数都不能被num整除，num是素数，否则不是for(UINT32 i = MIN_PRIMER + 1; i <= sqrtOfNum; i += 2){if(num % i == 0){return false;}}return true;
}bool MoonMath::IsIntegerSquare(UINT32 num)
{UINT32 qurtNum = (UINT32)sqrt((double)num);return (qurtNum * qurtNum) == num;
}set<UINT32> MoonMath::GetDiffPrimerFactorNum(UINT32 num)
{UINT32 halfNum = num / 2;set<UINT32> factors;for(UINT32 i = 2; i <= halfNum; ++i){if(!MoonMath::IsPrimer(i)){continue;}if(num % i == 0){factors.insert(i);while(num % i == 0){num /= i;}}}return factors;
}bool MoonMath::GetDigitMap(UINT32 num, UINT16 &digitMap)
{UINT32 digit = 0;digitMap = 0;while(num != 0){digit = num % 10;num /= 10;// 数字已存在，返回falseif(digitMap & (1 << digit)){return false;}digitMap |= (1 << digit);}return true;
}bool MoonMath::IsNumsHaveSameDigit(const UINT32 nums[], UINT32 numCount)
{UINT16 lastDigitMap = 0;UINT16 currDigitMap = 0;if(numCount < 2){return false;}if(!MoonMath::GetDigitMap(nums[0], lastDigitMap)){return false;}for(UINT32 i = 1; i < numCount; ++i){if(!MoonMath::GetDigitMap(nums[i], currDigitMap)){return false;}if(currDigitMap != lastDigitMap){return false;}}return true;
}UINT32 MoonMath::Factorial(UINT32 n)
{if(n <= 1){return 1;}UINT32 result = 1;for(UINT32 i = 2; i <= n; ++i){result *= i;}if (result==0){cout<<n<<endl;}return result;
}UINT32 MoonMath::Combination(UINT32 n, UINT32 r)
{// C(n,r)=n!/r!/(n-r)!=(r+1)*(r+2)*...*n/1/2/.../(n-r)UINT32 result=1;for (UINT32 i=r+1;i<=n;++i){result*=i;}UINT32 d=n-r;for (UINT32 i=2;i<=d;++i){result/=i;}return result;
}
// Permuted multiples
// Problem 52
// It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.
//
// Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits.
//
// 题目52：找出最小的正整数x，使得2x, 3x, 4x, 5x和6x都包含同样的数字。
// 125874和它的二倍，251748, 包含着同样的数字，只是顺序不同。
//
// 找出最小的正整数x，使得 2x, 3x, 4x, 5x, 和6x都包含同样的数字。#include <iostream>
#include <windows.h>
#include <ctime>
#include <assert.h>#include <MoonMath.h>using namespace std;// 打印时间等相关信息
class DetailPrinter
{
public:void Start();void End();DetailPrinter();private:LARGE_INTEGER timeStart;LARGE_INTEGER timeEnd;LARGE_INTEGER freq;
};DetailPrinter::DetailPrinter()
{QueryPerformanceFrequency(&freq);
}//************************************
// Method: Start
// Access: public
// Describe: 执行每个方法前调用
// Returns: void
//************************************
void DetailPrinter::Start()
{QueryPerformanceCounter(&timeStart);
}//************************************
// Method: End
// Access: public
// Describe: 执行每个方法后调用
// Returns: void
//************************************
void DetailPrinter::End()
{QueryPerformanceCounter(&timeEnd);cout << "Total Milliseconds is " << (double)(timeEnd.QuadPart - timeStart.QuadPart) * 1000 / freq.QuadPart << endl;const char BEEP_CHAR = '\007';cout << endl << "By GodMoon" << endl << __TIMESTAMP__ << BEEP_CHAR << endl;system("pause");
}/*************************解题开始*********************************///************************************
// Method: GetMulNum
// Access: public
// Describe: 获取num的倍数
// Parameter: UINT32 num
// Parameter: UINT32 mulNum[] 倍数存储位置，保存mulNumCount+1个num的倍数
// Parameter: UINT32 mulNumCount 最大倍数
// Returns: void
//************************************
void GetMulNum(UINT32 num, UINT32 mulNum[], UINT32 mulNumCount)
{for(UINT32 i = 1; i <= mulNumCount; ++i){mulNum[i - 1] = num * i;}
}void TestFun1()
{cout << "TestFun1 OK!" << endl;
}void F1()
{cout << "void F1()" << endl;// TestFun1();DetailPrinter detailPrinter;detailPrinter.Start();/*********************************算法开始*******************************/const UINT32 NUM_COUNT = 6;UINT32 mulNums[NUM_COUNT];UINT32 num;for(num = 1;; ++num){GetMulNum(num, mulNums, ARRAYSIZE(mulNums));if(MoonMath::IsNumsHaveSameDigit(mulNums, ARRAYSIZE(mulNums))){break;}}cout << "The smallest num is " << num << endl;/*********************************算法结束*******************************/detailPrinter.End();
}//主函数
int main()
{F1();return 0;
}/*
void F1()
The smallest num is 142857
Total Milliseconds is 32.823By GodMoon
Thu Mar 28 22:46:09 2013
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