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 <bits/stdc++.h>using namespace std;// Function to compare x^y and y^xvoid 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 codeint main(){ long double x = 4, y = 5; compareVal(x, y); return 0;} |
Java
// Java implementation of the approachimport java.util.*;class GFG{ // Function to compare x^y and y^xstatic 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 codepublic 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 approachusing System;class GFG{ // Function to compare x^y and y^xstatic 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 codestatic 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^xfunction 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> |
Output:
4^5 > 5^4
Time Complexity: O(1)
Auxiliary Space: O(1)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
