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Comparing X^Y and Y^X for very large values of X and Y
• Last Updated : 03 May, 2021

Given two integer X and Y, the task is compare XY and YX 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 XY and YX 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(XY) = Y * log(X) and log(YX) = X * log(Y). Now, these values can be compared easily without overflows.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``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#

 `// 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

 ``
Output:
`4^5 > 5^4`

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