Given two integer X and Y, the task is compare X^Y and Y^X for large values of X and Y.
Examples:

Input: X = 2, Y = 3
Output: 2^3 < 3^2
2³ < 3²
Input: X = 4, Y = 5
Output: 4^5 > 5^4

Naive approach: A basic approach is to find the values X^Y and Y^X and compare them which can overflow as the values of X and Y can be large
Better approach: Taking log of both the equations, log(X^Y) = Y * log(X) and log(Y^X) = X * log(Y). Now, these values can be compared easily without overflows.
Below is the implementation of the above approach:

[GFGTABS] C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function to compare x^y and y^x
void compareVal(int x, int y)
{

 // Storing values OF x^y AND y^x
 long double a = y * log(x);
 long double b = x * log(y);

 // Comparing values
 if (a > b)
 cout << x << "^" << y << " > "
 << y << "^" << x;

 else if (a < b)
 cout << x << "^" << y << " < "
 << y << "^" << x;

 else if (a == b)
 cout << x << "^" << y << " = "
 << y << "^" << x;
}

// Driver code
int main()
{
 long double x = 4, y = 5;

 compareVal(x, y);

 return 0;
}

Java

// Java implementation of the approach
import java.util.*;

class GFG
{
 
// Function to compare x^y and y^x
static void compareVal(int x, int y)
{

 // Storing values OF x^y AND y^x
 double a = y * Math.log(x);
 double b = x * Math.log(y);

 // Comparing values
 if (a > b)
 System.out.print(x + "^" + y + " > " + 
 y + "^" + x);

 else if (a < b)
 System.out.print(x + "^" + y + " < " +
 y + "^" + x);

 else if (a == b)
 System.out.print(x + "^" + y + " = " +
 y + "^" + x );
}

// Driver code
public static void main(String[] args) 
{
 int x = 4, y = 5;

 compareVal(x, y);
}
} 

// This code is contributed by 29AjayKumar

Python3

# Python3 implementation of the approach 
from math import log

# Function to compare x^y and y^x 
def compareVal(x, y) :
 
 # Storing values OF x^y AND y^x
 a = y * log(x);
 b = x * log(y);
 
 # Comparing values
 if (a > b) :
 print(x, "^", y, ">", y, "^", x);
 
 elif (a < b) :
 print(x, "^", y, "<", y ,"^", x);

 elif (a == b) :
 print(x, "^", y, "=", y, "^", x); 

# Driver code 
if __name__ == "__main__" : 

 x = 4; y = 5; 

 compareVal(x, y); 

# This code is contributed by AnkitRai01

// C# implementation of the approach
using System;
class GFG
{
 
// Function to compare x^y and y^x
static void compareVal(double x, double y)
{

 // Storing values OF x^y AND y^x
 double a = y * Math.Log(x);
 double b = x * Math.Log(y);

 // Comparing values
 if (a > b)
 Console.Write (x + "^" + y + " > " + 
 y + "^" + x);

 else if (a < b)
 Console.Write (x + "^" + y + " < "+
 y + "^" + x);

 else if (a == b)
 Console.Write (x + "^" + y + " = " +
 y + "^" + x );
}

// Driver code
static public void Main ()
{
 double x = 4, y = 5;

 compareVal(x, y);
}
}

// This Code is contributed by ajit.

JavaScript

<script>
// Javascript implementation of the approach

// Function to compare x^y and y^x
function compareVal(x, y)
{

 // Storing values OF x^y AND y^x
 let a = y * Math.log(x);
 let b = x * Math.log(y);

 // Comparing values
 if (a > b)
 document.write(x + "^" + y + " > "
 + y + "^" + x);

 else if (a < b)
 document.write(x + "^" + y + " < "
 + y + "^" + x);

 else if (a == b)
 document.write(x + "^" + y + " = "
 + y + "^" + x);
}

// Driver code
 let x = 4, y = 5;

 compareVal(x, y);

</script>

[/GFGTABS]

Output

4^5 > 5^4

Time Complexity: O(1)
Auxiliary Space: O(1)

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