Python Program pro nalezení faktoriálu čísla

The sections below show four ways to compute a factorial in Python — a for loop, an if-else version, recursion, and math.factorial() — plus the underlying algorithm and applications.

Faktoriál čísla pomocí smyčky

Let us take up the example of Python code that takes a positive integer as input to determine the factorial of positive integers. In the following code, the loop begins with one, and then it multiplies by each number that precedes the actual number whose factorial is to be determined.

Následující Python code illustrates the factorial function using a loop.

Python kód:

print ("Input a number")
factorialIP = int (input ())
ffactor23 = 1
for j in range (1, factorialIP+1):
   ffactor23 = ffactor23 * j
print ("The factorial of the number is “, ffactor23)

Výstup:

Input a number
4
The factorial of the number is 24

Výše Python program takes the input of positive numbers only, and it does not have a check of negative numbers in it. In this program, the factor is 1 when j is equal to 1. When j is 2, the factor is multiplied with 2, and it will do the action till j comes at 4 to arrive at 24.

Faktoriál čísla pomocí příkazu IF…else

Následující Python code illustrates the factorial function using a function. Unlike the loop version, this program also checks for negative numbers before computing the factorial.

V předchozím Python code, the check for negative numbers was not applied, making the factorial function incomplete and prone to deliver an error message if negative numbers are given as an input.

In the given code, the loop begins with one and multiplies by each preceding number, and the function also validates the input for negative numbers.

Python kód:

print("Enter a number for the purpose of determining factorial")
factorialIP = int(input())
def factorial(factorialIP):
   if factorialIP < 0:
     print ('Factorial does not exist')
     factor=0
     return factor
   elif factorialIP == 0:
     factor=1
     return factor
     print(factor)
   else:
     factor = 1
     for j in range (1, factorialIP+1):
       factor = factor * j
     return factor
  print ("The factorial of the number is ", factorial(factorialIP))

Výstup:

1) Enter a number to determine factorial
   -4
   Factorial does not exist
   The factorial of the number is 0

2) Enter a number to determine factorial
   4
   Factorial does not exist
   The factorial of the number is 24

Toto Python program accepts positive numbers and adds a check for negative numbers using the if and else statement, correctly returning 24 for an input of 4.

Faktoriál čísla pomocí rekurze

Následující Python code illustrates the factorial function using recursion. In this example, a recursive function that takes a positive integer as input determines the factorial number.

Python kód:

print("Enter a number for the purpose of determining factorial")
def factorial(num2):
  if num2 < 0:
    return 'Factorial does not exist'
  elif num2 == 0:
     return 1
  else:
     return num2 * factorial(num2-1)
number1 = int(input())
print("The factorial of the number is",factorial(number1))

Výstup:

Enter a number for the purpose of determining factorial
4
The factorial of the number is 24

The recursion can be explained as a concept wherein the function invoked in the Python module can call itself again and again. It runs until the Python condition present in the module is satisfied, wherein the function invoked is passed with a value.

Ve výše uvedeném Python program, the function def factorial keeps calling itself recursively until and unless the number reaches zero. Once the number reaches zero, it initializes the number as 1, ending the recursion.

Factorial of a Number using math.factorial()

Následující Python code illustrates the factorial function using math.factorial(), which can be used by importing the math module.

This function does not accept negative integers, and it throws a value error when float numbers are provided.

Python kód:

print("Enter a number for computing factorial")
import math
number1 = int(input())
print("The factorial is as computed comes out to be ")
print(math.factorial(number1))

Výstup:

Enter a number for computing factorial
4
The factorial, as computed, comes out to be 24

Algoritmus pro faktoriální program v Python

Vezměme si příklad, který ilustruje koncept faktoriálu.

For determination of factorial 5, follow these steps:

5! = 5 x (5-1) x (5-2) x (5-3) x (5-4)
5! =120

Tady, 5! je vyjádřen jako 120.

Následující diagram pomáhá pochopit algoritmus výpočtu faktoriálu a v tomto případě si vezměme příklad faktoriálu 4!

Algoritmus s obrázkovým příkladem faktoriálu 4!

Aplikace faktoriálu v Python

Faktoriál čísla má širokou úroveň aplikací v matematice. Zde jsou důležité aplikace Python:

• Python helps in computation, followed with print factorial in faster and more efficient terms than other available programming languages.
• Jedno Python code is easily understandable and can be replicated across different platforms, and the factorial Python program can be incorporated in several mathematical model-building assignments.

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