ZOJ 2562 More Divisors (n以内约数个数最多的最小数)

More Divisors

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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Everybody knows that we use decimal notation, i.e. the base of our notation is 10. Historians say that itis so because men have ten fingers. Maybe they are right. However, this is often not very convenient, tenhas only four divisors -- 1, 2, 5 and 10. Thus, fractions like 1/3, 1/4 or 1/6 have inconvenient decimalrepresentation. 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 12respectively. A good quiestion is: what is the number not exceeding n that has the greatest possiblenumber 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

题目链接：http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemId=1562

题目大意：求n以内约数个数最多的最小

题目分析：和前一题类似，暴搜即可

#include <cstdio>
#define ll long long
ll const INF = 1e16;
ll n, ans, ma;
int p[16] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47};

void DFS(int pos, ll val, ll num)
{
    if(val > n || pos > 14)
        return;
    if(num > ma || num == ma && val < ans)
    {
        ma = num;
        ans = val;
    }
    for(int i = 1; i <= 53; i++)
    {
        if(val > INF / p[pos])
            break;
        val *= p[pos];
        DFS(pos + 1, val, num * (i + 1));
    }
    return;
}

int main()
{
    while(scanf("%lld", &n) != EOF)
    {
        ma = 0;
        DFS(0, 1, 1);
        printf("%lld\n", ans);
    }
}