Find larger of x^y and y^x

Given two integer numbers, X and Y. find the larger of X^Y and Y^X or determine if they are equal.
Examples:

Input : 2 3
Output : 3^2
We know 3^2 = 9 and 2^3 = 8.

Input : 2 4
Output : Equal

A simple solution is to calculate x^y by looping for y times, but if the values of x and y is too large it will cause an overflow. 
To solve the overflow problem, we can simplify the equation by taking the log. 
log(x^y) = y* log(x) 
Now, this equation will not cause overflow, and we can compare the two values directly.  

C++

// C++ program to print greater of x^y and
// y^x
#include <bits/stdc++.h>
using namespace std;

void printGreater(double x, double y)
{
    long double X = y * log(x);
    long double Y = x * log(y);
    if (abs(X - Y) < 1e-9) {
        cout << "Equal";
    }
    else if (X > Y) {
        cout << x << "^" << y;
    }
    else {
        cout << y << "^" << x;
    }
}

int main()
{
    double x = 5, y = 8;
    printGreater(x, y);
    return 0;
}

Java

// Java program to print
// greater of x^y and y^x
import java.io.*;

class GFG
{
static void printGreater(int x,
                         int y)
{
    double X = y * Math.log(x);
    double Y = x * Math.log(y);
    if (Math.abs(X - Y) < 1e-9)
    {
        System.out.println("Equal");
    }
    else if (X > Y)
    {
        System.out.println(x + "^" + y);
    }
    else
    {
        System.out.println(y + "^" + x);
    }
}

// Driver Code
public static void main (String[] args)
{
    int x = 5, y = 8;
    printGreater(x, y);
}
}

// This code is contributed
// by anuj_67.

Python3

# Python3 program to print greater
# of x^y and y^x
import math

def printGreater(x, y):

    X = y * math.log(x);
    Y = x * math.log(y);
    if (abs(X - Y) < 1e-9):
        print("Equal");
    elif (X > Y):
        print(x, "^", y);
    else:
        print(y, "^", x);

# Driver Code
x = 5;
y = 8;
printGreater(x, y);

# This code is contributed by mits

C#

// C# program to print
// greater of x^y and y^x
using System;

class GFG
{
static void printGreater(int x,
                          int y)
{
    double X = y * Math.Log(x);
    double Y = x * Math.Log(y);
    if (Math.Abs(X - Y) < 1e-9)
    {
        Console.WriteLine("Equal");
    }
    else if (X > Y)
    {
        Console.WriteLine(x +
                          "^" + y);
    }
    else
    {
        Console.WriteLine(y +
                          "^" + x);
    }
}

// Driver Code
public static void Main ()
{
    int x = 5, y = 8;
    printGreater(x, y);
}
}

// This code is contributed
// by anuj_67.

PHP

<?php
// PHP program to print greater
// of x^y and y^x
function printGreater($x, $y)
{
    $X = $y * log($x);
    $Y = $x * log($y);
    if (abs($X - $Y) < 1e-9)
    {
        echo "Equal";
    }
    else if ($X > $Y)
    {
        echo $x . "^" . $y;
    }
    else
    {
        echo $y . "^" . $x;
    }
}

// Driver Code
$x = 5;
$y = 8;
printGreater($x, $y);

// This code is contributed by mits
?>

Javascript

<script>

// Javascript program to print greater of x^y and
// y^x


function printGreater(x, y)
{
    let X = y * Math.log(x);
    let Y = x * Math.log(y);
    if (Math.abs(X - Y) < 1e-9) {
        document.write("Equal");
    }
    else if (X > Y) {
        document.write(x + "^" + y);
    }
    else {
        document.write(y + "^" + x);
    }
}

// Driver Code

let x = 5, y = 8;
printGreater(x, y);


</script>

Output:

5^8

Time complexity: O(1) because constant operations are being performed
Auxiliary space: O(1)