zoj2562--More Divisors(反素数模板)

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Everybody knows that we use decimal notation, i.e. the base of our notation is 10. Historians say that it is so because men have ten fingers. Maybe they are right. However, this is often not very convenient, ten has only four divisors -- 1, 2, 5 and 10. Thus, fractions like 1/3, 1/4 or 1/6 have inconvenient decimal representation. In this sense the notation with base 12, 24, or even 60 would be much more convenient.

The main reason for it is that the number of divisors of these numbers is much greater -- 6, 8 and 12 respectively. A good quiestion is: what is the number not exceeding n that has the greatest possible number of divisors? This is the question you have to answer.

Input:

The input consists of several test cases, each test case contains a integer n (1 <= n <= 10¹⁶).

Output:

For each test case, output positive integer number that does not exceed n and has the greatest possible number of divisors in a line. If there are several such numbers, output the smallest one.

Sample Input:

10
20
100

Sample Output:

6
12
60

从反素数的定义中可以看出两个性质：

（1）一个反素数的所有质因子必然是从2开始的连续若干个质数，因为反素数是保证约数个数为的这个数尽量小

（2）同样的道理，如果，那么必有

#include <cstdio>
#define LL long long
LL maxsum , bestnum , n ;
LL pri[20]={2,3,5,7,11,13,17,19,23,29,31,37,39,41,43,47,53};  

void f(LL num,LL k,LL sum,LL limit)
{
    LL i , temp ;
    if( sum > maxsum )
    {
        maxsum = sum ;
        bestnum = num ;
    }
    if( sum == maxsum && bestnum > num )
        bestnum = num ;
    if(k == 20) return ;
    temp = num ;
    for(i = 1 ; i <= limit ; i++)
    {
        if( temp*pri[k] > n )
            break;
        temp = temp*pri[k] ;
        f(temp,k+1,sum*(i+1),i);
    }
    return ;
}
int main()
{
    while(scanf("%lld", &n)!=EOF)
    {
        bestnum = maxsum = -1 ;
        f(1,0,1,50);
        printf("%lld\n", bestnum);
    }
}

zoj2562--More Divisors(反素数模板)

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原文地址：http://blog.csdn.net/winddreams/article/details/39323479