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++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# 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

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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. 

chevron_right


Output:

4^5 > 5^4

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : AnkitRai01, jit_t, 29AjayKumar

Article Tags :
Practice Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.