Dados dos enteros positivos m y n , la tarea es escribir un programa que verifique si m^n es mayor, menor o igual que n^m.
Ejemplos:
Entrada: m = 3, n = 10
Salida: m^n > n^m
Explicación: 3^10=59049 que es mayor que 10^3=1000
Entrada: m = 987654321, n = 123456987
Salida: m^n < n ^ m
Un enfoque ingenuo es calcular m^n y n^m, lo que provoca un desbordamiento cuando m y n son muy grandes.
Un enfoque eficiente es resolver este problema usando log .
Dado LHS = m^n y RHS = n^m.
Después de tomar log en ambos lados, LHS = n*log(m) y RHS = m*log(n)
Luego compare LHS y 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>
Producción :
m^n < n^m