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

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  • Difficulty Level : Basic
  • Last Updated : 21 Sep, 2022
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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}}

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 x^y^2 > y^x^2, then after taking ln on both sides and dividing by (xy)^2 we can get ln(x)/(x^2) > ln(y)/(y^2).

Take F(x) = ln(x)/(x^2) . This function is monotonically decreasing for x > 2.

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

Time Complexity: O(1)

Auxiliary Space: O(1)


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