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)
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