【ProjectEuler】ProjectEuler_026

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本文探讨了如何在1至1000的范围内找到具有最长循环小数位数的数，通过计算1除以不同整数后的循环小数长度，最终确定了1/983为具有982位循环小数的数。

// Problem 26
// 13 September 2002
//
// A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
//
// 1/2	= 	0.5
// 1/3	= 	0.(3)
// 1/4	= 	0.25
// 1/5	= 	0.2
// 1/6	= 	0.1(6)
// 1/7	= 	0.(142857)
// 1/8	= 	0.125
// 1/9	= 	0.(1)
// 1/10	= 	0.1
// Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
//
// Find the value of d  1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.

#include <iostream>
#include <windows.h>
#include <vector>
using namespace std;

// 获取下一位小数，用remaindNum/num
// 余数保存在remaindNum中
int GetDivisor(int &remaindNum, int num)
{
    remaindNum *= 10;

    int result = remaindNum / num;
    remaindNum = remaindNum % num;
    return result;
}

vector<int> decimalNumVec;		//保存小数位数
vector<int> remainderNumVec;	//保存余数，位置与上面的保存小数的位置相同

// 检测是否成功获取到循环，如果余数和小数都相同，则表示找到了循环，返回循环位数
// 没有获取到循环返回0
int check(int inDecimalNum, int inRemainderNum)
{
    int length = decimalNumVec.size();

    for(int i = 0; i < length; i++)
    {
        if(inDecimalNum == decimalNumVec[i] && inRemainderNum == remainderNumVec[i])
        {
            return length - i - 1;		//循环位数
        }
    }

    return 0;
}

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

    LARGE_INTEGER timeStart, timeEnd, freq;
    QueryPerformanceFrequency(&freq);
    QueryPerformanceCounter(&timeStart);

    const int MAX_NUM = 1000;

    int decimalNum = 0, remaindNum = 0;		//获取当前数的小数位和余数
    int currentLength = 0;					//获取当前数的小数循环长度
    int maxLength = 0, maxNum = 0;			//获取小数循环最长的长度和那个数

    for(int i = 1; i <= MAX_NUM; i++)
    {
        decimalNumVec.clear();
        remainderNumVec.clear();

        remaindNum = 10;			//初始化

        while((currentLength = check(decimalNum, remaindNum)) == 0)
        {
            decimalNum = GetDivisor(remaindNum, i);

            //记录小数位和余数
            decimalNumVec.push_back(decimalNum);
            remainderNumVec.push_back(remaindNum);
        }

        if(currentLength > maxLength)
        {
            maxLength = currentLength;
            maxNum = i;
        }
    }

    cout << "在1-" << MAX_NUM << "里，拥有最长循环小数单元的数是" << maxNum << "，1/" << maxNum << "是" << maxLength << "位循环小数" << endl;

    QueryPerformanceCounter(&timeEnd);
    cout << "Total Milliseconds is " << (double)((double)(timeEnd.QuadPart - timeStart.QuadPart) * 1000 / (double)freq.QuadPart) << endl;
}

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

/*
void F1()
在1-1000里，拥有最长循环小数单元的数是983，1/983是982位循环小数
Total Milliseconds is 2831.6

By GodMoon
*/