[problem3]欧拉

 

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

注意：用long long避免类型overflow。并注意到600851475143是奇数所以只能被奇数整除。思路：在求质因子的算法基础上记一下max就好了。

#include <iostream>
#include <cmath>
#include <ctime>
using namespace std;

//bool isPrime(long long val)
//{
//    long long limit = (long long)sqrt((double)val);
//
//    for(long long i = 3; i <= limit; i += 2)
//    {
//        if(val%i == 0)
//            return false;
//    }
//
//    return true;
//}

int _tmain(int argc, _TCHAR* argv[])
{
    long long theNum = 600851475143;

    // theNum can only be divided by odd number, 3, 5, 7, 9, etc.      
    int i = 3;
    clock_t start = clock();

    // By using below algorithm, it cost 2 milliseconds.
    
    int max = 0;
    while(theNum > 1)
    {
        if(theNum%i == 0)
        {            
            if(i > max)
                max = i;
            theNum /= i;
        }
        i += 2;
    }

    cout << max << endl;

    // By using this algorithm (mainly cost happens in isPrime function), it cost >1800 milliseconds.
    //while(true)
    //{
    //    if(theNum%i == 0)
    //    {
    //        long long val = theNum / i; // long long is a must to avoid overflow..
    //        if(isPrime(val))
    //        {
    //            cout << val << endl;
    //            break;
    //        }
    //    }

    //    i += 2;
    //}
    
    clock_t end = clock();
    double spentTime = difftime(end, start);
    cout << "spentTime: " << spentTime << endl;

    return 0;
}