题目:
Today, Osama gave Fadi an integer X, and Fadi was wondering about the minimum possible value of max(a,b) such that LCM(a,b) equals X. Both a and b should be positive integers.
LCM(a,b) is the smallest positive integer that is divisible by both a and b. For example, LCM(6,8)=24, LCM(4,12)=12, LCM(2,3)=6.
Of course, Fadi immediately knew the answer. Can you be just like Fadi and find any such pair?
Input
The first and only line contains an integer X (1≤X≤1012).
Output
Print two positive integers, a and b, such that the value of max(a,b) is minimum possible and LCM(a,b) equals X. If there are several possible such pairs, you can print any.
题意:给定一个数x,找出两个数a,b,使得LCM(a,b)= x;求满足条件并且使max(a,b)尽可能小的a和b。
这题乍一看有点懵,然后看了一下数据范围,发现可以暴力,所以写着试了一发,然后AC;
思路:
Xoxoxo首先判断x是否素数,如果是则输出1和它本身;如果不是,则进行枚举,枚举的复杂度是O(sqrt(n))。
#include<iostream>
#include<cmath>
#include<algorithm>
using namespace std;
#define ll long long
#define inf 0x3f3f3f3f
bool is_prim(ll x) {
ll m = sqrt(x);
for (ll i = 2; i <= m; i++) {
if (x % i == 0)
return false;
}
return true;
}
ll gcd(ll a, ll b) {
if (b == 0)
return a;
else
return gcd(b, a % b);
}
int main()
{
std::ios::sync_with_stdio(false);
std::cin.tie(0);
std::cout.tie(0);
ll x; cin >> x;
if (is_prim(x))
cout << "1 " << x << endl;
else {
ll maxn = 0;
for (ll i = 1; i <= sqrt(x); i++) {
if (x % i == 0) {
if (gcd(i, x / i) == 1)
maxn = i;
}
}
if (maxn)
cout << min(x / maxn, maxn) << " " << max(x / maxn, maxn) << endl;
else
cout << "1 " << x << endl;
}
return 0;
}