Program to compare m^n and n^m

Last Updated : 20 Dec, 2022

Given two positive integers m and n, the task is to write a program that checks whether m^n is greater than, less than, or equal to n^m.

Examples :

Input: m = 3, n = 10
Output: m^n > n^m
Explanation : 3^10=59049 which is greater than 10^3=1000

Input: m = 987654321, n = 123456987
Output: m^n < n^m

A naive approach is to compute m^n and n^m, which causes overflow when m and n are very large.
An efficient approach is to solve this problem using log.

Given LHS = m^n and RHS = n^m.
After taking log on both sides, LHS = n*log(m) and RHS = m*log(n)
Then compare the LHS and RHS.

C++

// CPP program to compare which is greater 
// m^n or n^m  
#include <bits/stdc++.h>
using namespace std;
 
// function to compare m^n and n^m 
void check(unsigned long long m, unsigned long long int n)
    {
        // m^n 
        double RHS = m * (double)log(n);
         
        // n^m 
        double LHS = n * (double)log(m); 
         
        if ( LHS > RHS )
            cout << "m^n > n^m";
             
        else if ( LHS < RHS )
            cout << "m^n < n^m";
             
        else
            cout << "m^n = n^m";
    }
 
// Drivers Code 
int main() {
     
    unsigned long long m = 987654321, n = 123456987;
     
    // function call to compare m^n and n^m
    check(m, n);
     
    return 0;
}

Java

// Java program to compare which 
// is greater m^n or n^m 
import java .io.*;
 
class GFG
{
// function to compare
// m^n and n^m 
static void check(long m, long n)
{
    // m^n 
    double RHS = m * (double)Math.log(n);
     
    // n^m 
    double LHS = n * (double)Math.log(m); 
     
    if (LHS > RHS)
        System.out.print("m^n > n^m");
         
    else if (LHS < RHS)
    System.out.print("m^n < n^m");
         
    else
        System.out.print("m^n = n^m");
}
 
// Driver Code 
static public void main (String[] args)
{
    long m = 987654321, n = 123456987;
 
    // function call to 
    // compare m^n and n^m
    check(m, n);
}
}
 
// This code is contributed by anuj_67.

Python3

# Python3 program to compare 
# which is greater m^n or n^m 
import math
 
# function to compare
# m^n and n^m 
def check( m, n):
     
    # m^n 
    RHS = m * math.log(n);
     
    # n^m 
    LHS = n * math.log(m); 
     
    if (LHS > RHS):
        print("m^n > n^m");
         
    elif (LHS < RHS):
        print("m^n < n^m");
         
    else:
        print("m^n = n^m");
 
# Driver Code 
m = 987654321; 
n = 123456987;
 
# function call to 
# compare m^n and n^m
check(m, n);
 
# This code is contributed by mits

C#

// C# program to compare which  
// is greater m^n or n^m 
using System;
 
class GFG
{
// function to compare
// m^n and n^m 
static void check(ulong m, ulong n)
{
    // m^n 
    double RHS = m * (double)Math.Log(n);
     
    // n^m 
    double LHS = n * (double)Math.Log(m); 
     
    if (LHS > RHS)
        Console.Write("m^n > n^m");
         
    else if (LHS < RHS)
    Console.Write("m^n < n^m");
         
    else
        Console.Write("m^n = n^m");
}
 
// Driver Code 
static public void Main ()
{
    ulong m = 987654321, n = 123456987;
 
    // function call to 
    // compare m^n and n^m
    check(m, n);
 
}
}
 
// This code is contributed by anuj_67.

PHP

<?php
// PHP program to compare  
// which is greater m^n or n^m 
 
// function to compare
// m^n and n^m 
function check( $m, $n)
{
    // m^n 
    $RHS = $m * log($n);
     
    // n^m 
    $LHS = $n * log($m); 
     
    if ( $LHS > $RHS )
        echo "m^n > n^m";
         
    else if ( $LHS < $RHS )
    echo "m^n < n^m";
         
    else
        echo "m^n = n^m";
}
 
// Driver Code 
$m = 987654321; 
$n = 123456987;
 
// function call to 
// compare m^n and n^m
check($m, $n);
 
// This code is contributed by anuj_67.
?>

Javascript

<script>
 
// javascript program to compare which
// is greater m^n or n^m
 
// function to compare
// m^n and n^m
 
function check( m,  n)
{
    // m^n
    var RHS = m * Math.log(n);
       
    // n^m
    var LHS = n * Math.log(m); 
       
    if (LHS > RHS){
        document.write("m^n > n^m");
    }
    else if (LHS < RHS) {
    document.write("m^n < n^m");
    }
           
    else {
        document.write("m^n = n^m");
    }
}
   
// Driver Code
 
     var m = 987654321 ;  
     var n = 123456987;
   
    // function call to
    // compare m^n and n^m
    check(m, n);
     
</script>