Year 2118. Androids are in mass production for decades now, and they do all the work for humans. But androids have to go to school to be able to solve creative tasks. Just like humans before.
It turns out that high school struggles are not gone. If someone is not like others, he is bullied. Vasya-8800 is an economy-class android which is produced by a little-known company. His design is not perfect, his characteristics also could be better. So he is bullied by other androids.
One of the popular pranks on Vasya is to force him to compare xyxy with yxyx. Other androids can do it in milliseconds while Vasya's memory is too small to store such big numbers.
Please help Vasya! Write a fast program to compare xyxy with yxyx for Vasya, maybe then other androids will respect him.
On the only line of input there are two integers xx and yy (1≤x,y≤1091≤x,y≤109).
If xy<yxxy<yx, then print '<' (without quotes). If xy>yxxy>yx, then print '>' (without quotes). If xy=yxxy=yx, then print '=' (without quotes).
5 8
>
10 3
<
6 6
=
In the first example 58=5⋅5⋅5⋅5⋅5⋅5⋅5⋅5=39062558=5⋅5⋅5⋅5⋅5⋅5⋅5⋅5=390625, and 85=8⋅8⋅8⋅8⋅8=3276885=8⋅8⋅8⋅8⋅8=32768. So you should print '>'.
In the second example 103=1000<310=59049103=1000<310=59049.
In the third example 66=46656=6666=46656=66.
思路:
x^y 与 y^x 比较大小,由数据范围肯定不能乘算,所以可以变换一下 两边取对数 y*log(x) 与 x*log(y)比较 ,取对数结果要取long double 类型 !!!
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int main(){
std::ios::sync_with_stdio(false);
// std::cin.tie();
// std::cout.tie();
double a,b;
cin>>a>>b;
long double x,y;
x=b*log(a);
y=a*log(b);
// x=1/a*log(a); //上下两种都可以
// y=1/b*log(b);
if(x==y) {
cout<<"="<<endl;
return 0;
}
if(x<y) cout<<"<"<<endl;
else cout<<">"<<endl;
return 0;
}