Contar números factoriales en un rango dado

Un número F es un número factorial si existe algún entero I >= 0 tal que F = I! (es decir, F es factorial de I). Ejemplos de números factoriales son 1, 2, 6, 24, 120,…. 
Escriba un programa que tome como entrada dos enteros largos ‘bajo’ y ‘alto’ donde 0 < bajo < alto y encuentre el conteo de números factoriales en el intervalo cerrado [bajo, alto]. 
Ejemplos: 

Input: 0 1 
Output: 1 //Reason: Only factorial number is 1 

Input: 12 122 
Output: 2 // Reason: factorial numbers are 24, 120 

Input: 2 720 
Output: 5 // Factorial numbers are: 2, 6, 24, 120, 720 

1) Encuentra el primer factorial que sea mayor o igual a bajo . Sea este factorial x! (factorial de x) y el valor de este factorial sea ‘fact’
2) Siga incrementando x, y siga actualizando ‘fact’ mientras fact es menor o igual que high . Cuente el número de veces que se ejecuta este ciclo.
3) Devuelva el conteo calculado en el paso 2.
A continuación se muestra la implementación del algoritmo anterior. Gracias a Kartik por sugerir la siguiente solución. 
 

// C++ Program to count factorial numbers in given range
#include <iostream>
using namespace std;
 
int countFact(int low, int high)
{
    // Find the first factorial number 'fact' greater than or
    // equal to 'low'
    int fact = 1, x = 1;
    while (fact < low)
    {
        fact = fact*x;
        x++;
    }
 
    // Count factorial numbers in range [low, high]
    int res = 0;
    while (fact <= high)
    {
        res++;
        fact = fact*x;
        x++;
    }
 
    // Return the count
    return res;
}
 
// Driver program to test above function
int main()
{
    cout << "Count is " << countFact(2, 720);
    return 0;
}

// Java Program to count factorial
// numbers in given range
 
class GFG
{
    static int countFact(int low, int high)
    {
        // Find the first factorial number
        // 'fact' greater than or equal to 'low'
        int fact = 1, x = 1;
        while (fact < low)
        {
            fact = fact * x;
            x++;
        }
     
        // Count factorial numbers
        // in range [low, high]
        int res = 0;
        while (fact <= high)
        {
            res++;
            fact = fact * x;
            x++;
        }
     
        // Return the count
        return res;
    }
     
    // Driver code
    public static void main (String[] args)
    {
        System.out.print("Count is "
                         + countFact(2, 720));
    }
}
 
// This code is contributed by Anant Agarwal.

# Python3 Program to count factorial
# numbers in given range
 
def countFact(low,high):
 
    # Find the first factorial number
    # 'fact' greater than or
    # equal to 'low'
    fact = 1
    x = 1
    while (fact < low):
     
        fact = fact * x
        x += 1
     
  
    # Count factorial numbers
    # in range [low, high]
    res = 0
    while (fact <= high):
     
        res += 1
        fact = fact * x
        x += 1
     
  
    # Return the count
    return res
 
# Driver code
 
print("Count is ", countFact(2, 720))
 
# This code is contributed
# by Anant Agarwal.

// C# Program to count factorial
// numbers in given range
using System;
 
public class GFG
{
     
    // Function to count factorial
    static int countFact(int low, int high)
    {
         
        // Find the first factorial number numbers
        // 'fact' greater than or equal to 'low'
        int fact = 1, x = 1;
        while (fact < low)
        {
            fact = fact * x;
            x++;
        }
     
        // Count factorial numbers
        // in range [low, high]
        int res = 0;
        while (fact <= high)
        {
            res++;
            fact = fact * x;
            x++;
        }
     
        // Return the count
        return res;
    }
     
    // Driver code
    public static void Main ()
    {
        Console.Write("Count is " + countFact(2, 720));
    }
}
 
// This code is contributed by Sam007

<?php
// PHP Program to count factorial
// numbers in given range
function countFact($low, $high)
{
    // Find the first factorial
    // number 'fact' greater
    // than or equal to 'low'
    $fact = 1; $x = 1;
    while ($fact < $low)
    {
        $fact = $fact * $x;
        $x++;
    }
 
    // Count factorial numbers
    // in range [low, high]
    $res = 0;
    while ($fact <= $high)
    {
        $res++;
        $fact = $fact * $x;
        $x++;
    }
 
    // Return the count
    return $res;
}
 
// Driver Code
echo "Count is " , countFact(2, 720);
 
// This code is contributed by ajit
?>

<script>
// Javascript Program to count factorial
// numbers in given range
function countFact(low, high)
{
 
    // Find the first factorial
    // number 'fact' greater
    // than or equal to 'low'
    let fact = 1;
    let x = 1;
    while (fact < low)
    {
        fact = fact * x;
        x++;
    }
 
    // Count factorial numbers
    // in range [low, high]
    let res = 0;
    while (fact <= high)
    {
        res++;
        fact = fact * x;
        x++;
    }
 
    // Return the count
    return res;
}
 
// Driver Code
document.write("Count is " + countFact(2, 720));
 
// This code is contributed by _saurabh_jaiswal
</script>

Producción : 

Count is 5

Complejidad temporal: aproximadamente igual a O(K) donde K es el mayor devisor de alto y no es igual a alto.

Complejidad del espacio auxiliar:  O(1).

Este artículo es una contribución de Shivam. Escriba comentarios si encuentra algo incorrecto o si desea compartir más información sobre el tema tratado anteriormente.