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Find maximum among x^(y^2) or y^(x^2) where x and y are given

  • Difficulty Level : Basic
  • Last Updated : 02 Jun, 2021

Given X and Y whose values are greater than 2, the task is to find out which is maximum among 

x^(y^2) and y^(x^2) 

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Consider that either x is greater than y or y is greater than x. So, print 1 if x^(y^2) is greater or 2 if y^(x^2) is greater.
Examples: 
 

Input: X = 4, Y = 9
Output: 1

Input: X = 4, Y = 3
Output: 2

 



Approach: Assume 

*** QuickLaTeX cannot compile formula:
 

*** Error message:
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, then after taking ln on both sides and dividing by 

*** QuickLaTeX cannot compile formula:
 

*** Error message:
Error: Nothing to show, formula is empty

we can get 

*** QuickLaTeX cannot compile formula:
 

*** Error message:
Error: Nothing to show, formula is empty

.
Take 

*** QuickLaTeX cannot compile formula:
 

*** Error message:
Error: Nothing to show, formula is empty

. This function is monotonically decreasing for 

*** QuickLaTeX cannot compile formula:
 

*** Error message:
Error: Nothing to show, formula is empty

.
 

 

If x > y, then F(x) < F(y)

 

C++




// C++ program to find the greater value
#include <bits/stdc++.h>
using namespace std;
 
// Function to find maximum
bool findGreater(int x, int y)
{
    // Case 1
    if (x > y) {
       return false;
    }
 
    // Case 2
    else {
        return true;
    }
}
 
// Driver Code
int main()
{
    int x = 4;
    int y = 9;
 
    findGreater(x, y) ? cout << "1\n"
                      : cout << "2\n";
 
   return 0;
}

Java




// Java program to find
// the greater value
import java.io.*;
 
class GFG
{
 
// Function to find maximum
static boolean findGreater(int x,  
                           int y)
{
    // Case 1
    if (x > y)
    {
        return false;
    }
 
    // Case 2
    else
    {
        return true;
    }
}
 
// Driver Code
public static void main (String[] args)
{
    int x = 4;
    int y = 9;
     
    if(findGreater(x, y))
    System.out.println("1");
    else
    System.out.println("2");
}
}
 
// This code is contributed
// by inder_verma.

Python3




# Python3 program to find
# the greater value
 
# Function to find maximum
def findGreater(x, y):
     
    # Case 1
    if (x > y):
        return False;
 
    # Case 2
    else:
        return True;
 
# Driver Code
x = 4;
y = 9;
if(findGreater(x, y)):
    print("1");
else:
    print("2");
 
# This code is contributed
# by mits

C#




// C# program to find
// the greater value
using System;
 
class GFG
{
 
// Function to find maximum
static bool findGreater(int x,
                        int y)
{
    // Case 1
    if (x > y)
    {
        return false;
    }
 
    // Case 2
    else
    {
        return true;
    }
}
 
// Driver Code
public static void Main ()
{
    int x = 4;
    int y = 9;
     
    if(findGreater(x, y))
        Console.WriteLine("1");
    else
        Console.WriteLine("2");
}
}
 
// This code is contributed
// by inder_verma.

PHP




<?php
// PHP program to find the greater value
 
// Function to find maximum
function findGreater($x, $y)
{
    // Case 1
    if ($x > $y)
    {
        return false;
    }
 
    // Case 2
    else
    {
        return true;
    }
}
 
// Driver Code
$x = 4;
$y = 9;
if(findGreater($x, $y) == true)
    echo("1\n");
else
    echo("2\n");
 
// This code is contributed
// by inder_verma
?>

Javascript




<script>
 
// JavaScript program to find
// the greater value
 
 
// Function to find maximum
function findGreater(x,y)
{
    // Case 1
    if (x > y)
    {
        return false;
    }
 
    // Case 2
    else
    {
        return true;
    }
}
 
// Driver Code
var x = 4;
var y = 9;
 
if(findGreater(x, y))
document.write("1");
else
document.write("2");
 
 
// This code is contributed by 29AjayKumar
 
</script>
Output: 
1

 




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