# Comparing X^Y and Y^X for very large values of X and Y

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`

Time Complexity: O(1)

Auxiliary Space: O(1)

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