反素数The Most Complex Number 搜索+剪枝

题目链接:http://acm.timus.ru/problem.aspx?space=1&num=1748、

1748. The Most Complex Number

Time limit: 1.0 second
Memory limit: 64 MB
Let us define a  complexity of an integer as the number of its divisors. Your task is to find the most complex integer in range from 1 to  n. If there are many such integers, you should find the minimal one.

Input

The first line contains the number of testcases  t (1 ≤  t ≤ 100). The  i-th of the following  t lines contains one integer  ni  (1 ≤  ni ≤ 10 18) .

Output

For each testcase output the answer on a separate line. The  i-th line should contain the most complex integer in range from 1 to  ni and its complexity, separated with space.

Sample

input output
5
1
10
100
1000
10000
1 1
6 4
60 12
840 32
7560 64

题意:给定一个数n  求0~n  中约数最多的数 输出者个数及其约数个数  由于数据比较大 需要剪枝

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
typedef unsigned long long ULL;
const ULL INF = ~0ULL;
ULL ans,n;
int best;
int p[16] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53};
void dfs(int dept,int lim,ULL tmp,int num)
{
    if(tmp>n)
        return ;
    if(num>best){
        best=num;
        ans=tmp;
    }
    if(num==best&&tmp<ans)
        ans=tmp;
    for(int i=1;i<=lim;i++){//剪枝
        if(n/p[dept]<tmp)
            break;
        dfs(dept+1,i,tmp*=p[dept],num*(i+1));
    }
}
int main()
{
    int cas;
    cin>>cas;
    while(cas--){
        cin>>n;
        best=0;
        ans=INF;
        dfs(0,60,1,1);
        cout<<ans<<" "<<best<<endl;
    }
    return 0;
}


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