Given two integer numbers, X and Y. find the larger of X^Y and Y^X or determine if they are equal.
Examples:
Input : 2 3
Output : 3^2
We know 3^2 = 9 and 2^3 = 8.Input : 2 4
Output : Equal
A simple solution is to calculate x^y by looping for y times, but if the values of x and y is too large it will cause an overflow.
To solve the overflow problem, we can simplify the equation by taking the log.
log(x^y) = y* log(x)
Now, this equation will not cause overflow, and we can compare the two values directly.
C++
// C++ program to print greater of x^y and// y^x#include <bits/stdc++.h>using namespace std;void printGreater(double x, double y){ long double X = y * log(x); long double Y = x * log(y); if (abs(X - Y) < 1e-9) { cout << "Equal"; } else if (X > Y) { cout << x << "^" << y; } else { cout << y << "^" << x; }}int main(){ double x = 5, y = 8; printGreater(x, y); return 0;} |
Java
// Java program to print // greater of x^y and y^ximport java.io.*;class GFG{static void printGreater(int x, int y){ double X = y * Math.log(x); double Y = x * Math.log(y); if (Math.abs(X - Y) < 1e-9) { System.out.println("Equal"); } else if (X > Y) { System.out.println(x + "^" + y); } else { System.out.println(y + "^" + x); }}// Driver Codepublic static void main (String[] args) { int x = 5, y = 8; printGreater(x, y);}}// This code is contributed // by anuj_67. |
Python3
# Python3 program to print greater # of x^y and y^ximport mathdef printGreater(x, y): X = y * math.log(x); Y = x * math.log(y); if (abs(X - Y) < 1e-9): print("Equal"); elif (X > Y): print(x, "^", y); else: print(y, "^", x);# Driver Codex = 5;y = 8;printGreater(x, y);# This code is contributed by mits |
C#
// C# program to print // greater of x^y and y^xusing System;class GFG{static void printGreater(int x, int y){ double X = y * Math.Log(x); double Y = x * Math.Log(y); if (Math.Abs(X - Y) < 1e-9) { Console.WriteLine("Equal"); } else if (X > Y) { Console.WriteLine(x + "^" + y); } else { Console.WriteLine(y + "^" + x); }}// Driver Codepublic static void Main () { int x = 5, y = 8; printGreater(x, y);}}// This code is contributed // by anuj_67. |
PHP
<?php// PHP program to print greater // of x^y and y^xfunction printGreater($x, $y){ $X = $y * log($x); $Y = $x * log($y); if (abs($X - $Y) < 1e-9) { echo "Equal"; } else if ($X > $Y) { echo $x . "^" . $y; } else { echo $y . "^" . $x; }}// Driver Code$x = 5;$y = 8;printGreater($x, $y);// This code is contributed by mits?> |
Javascript
<script>// Javascript program to print greater of x^y and// y^xfunction printGreater(x, y){ let X = y * Math.log(x); let Y = x * Math.log(y); if (Math.abs(X - Y) < 1e-9) { document.write("Equal"); } else if (X > Y) { document.write(x + "^" + y); } else { document.write(y + "^" + x); }}// Driver Codelet x = 5, y = 8;printGreater(x, y);</script> |
Output:
5^8
Time complexity: O(1) because constant operations are being performed
Auxiliary space: O(1)
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