学步园

#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);

    //************************************
    // 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);
};

#include "MoonMath.h"
#include <cmath>

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)
{
    // 0和1不是素数
    if(num <= 1)
    {
        return false;
    }

    UINT32 sqrtOfNum = (UINT32)sqrt((double)num); // num的2次方

    // 从2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 = 2; i <= sqrtOfNum; ++i)
    {
        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;
}

// Prime permutations
//     Problem 49
//     The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
//
//     There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
//
//     What 12-digit number do you form by concatenating the three terms in this sequence?

#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:    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
// Returns:   bool              如果包含重复的数字，返回false，否则返回true
//************************************
bool 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false
        if(digitMap & (1 << digit) == 1)
        {
            return false;
        }

        digitMap |= (1 << digit);
    }

    return true;
}

//************************************
// 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: UINT32 num1
// Parameter: UINT32 num2
// Returns:   bool
//************************************
bool IsSameDigitNum(const UINT32 nums[], UINT32 numCount)
{
    UINT16 lastDigitMap = 0;
    UINT16 currDigitMap = 0;

    if(numCount <= 2)
    {
        return false;
    }

    if(!GetDigitMap(nums[0], lastDigitMap))
    {
        return false;
    }

    for(UINT32 i = 1; i < numCount; ++i)
    {
        if(!GetDigitMap(nums[i], currDigitMap))
        {
            return false;
        }

        if(currDigitMap != lastDigitMap)
        {
            return false;
        }
    }

    return true;
}


void TestFun1()
{


    cout << "Test OK!" << endl;
}

void F1()
{
    cout << "void F1()" << endl;

    // TestFun1();

    DetailPrinter detailPrinter;
    detailPrinter.Start();

    /*********************************算法开始*******************************/
    const UINT32 START_NUM = 1000;
    const UINT32 END_NUM = 9999;
    const UINT32 SKIP_NUM=1487;     // 排除已有的数字

    UINT32 maxAddNum = 0;
    UINT32 nums[3];
    bool notFound = true;
    UINT32 addNum;
    UINT32 num;

    for(num = START_NUM; num <= END_NUM && notFound; ++num)
    {
        maxAddNum = (END_NUM - num) / 2;
        nums[0] = num;

        if(!MoonMath::IsPrimer(num))
        {
            continue;
        }

        if (num==SKIP_NUM)
        {
            continue;
        }

        for(addNum = 1; addNum <= maxAddNum; ++addNum)
        {
            nums[1] = num + addNum;
            nums[2] = num + addNum * 2;

            if(IsSameDigitNum(nums, ARRAYSIZE(nums))
                    && MoonMath::IsPrimer(nums[1])
                    && MoonMath::IsPrimer(nums[2]))
            {
                notFound = false;
                break;
            }
        }
    }

    cout << "The 12-digit number is " << nums[0] << nums[1] << nums[2] << endl;

    /*********************************算法结束*******************************/

    detailPrinter.End();
}

//主函数
int main()
{
    F1();
    return 0;
}

/*
void F1()
The 12-digit number is 296962999629
Total Milliseconds is 202.389

By GodMoon
Wed Mar 13 20:54:30 2013
*/