Fix factorial issues (TheAlgorithms#5496)

* updating DIRECTORY.md

* pass integer to `math.factorial` in `project_euler/problem_015`

* remove duplicated factorial function

* updating DIRECTORY.md

* Update maths/factorial_iterative.py

Co-authored-by: Christian Clauss <[email protected]>

* Update factorial_iterative.py

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Christian Clauss <[email protected]>

Author: 3 people

DIRECTORY.md

@@ -75,6 +75,7 @@
   * [Morse Code](https://github.com/TheAlgorithms/Python/blob/master/ciphers/morse_code.py)
   * [Onepad Cipher](https://github.com/TheAlgorithms/Python/blob/master/ciphers/onepad_cipher.py)
   * [Playfair Cipher](https://github.com/TheAlgorithms/Python/blob/master/ciphers/playfair_cipher.py)
+  * [Polybius](https://github.com/TheAlgorithms/Python/blob/master/ciphers/polybius.py)
   * [Porta Cipher](https://github.com/TheAlgorithms/Python/blob/master/ciphers/porta_cipher.py)
   * [Rabin Miller](https://github.com/TheAlgorithms/Python/blob/master/ciphers/rabin_miller.py)
   * [Rail Fence Cipher](https://github.com/TheAlgorithms/Python/blob/master/ciphers/rail_fence_cipher.py)
@@ -453,7 +454,6 @@
   * [Eulers Totient](https://github.com/TheAlgorithms/Python/blob/master/maths/eulers_totient.py)
   * [Extended Euclidean Algorithm](https://github.com/TheAlgorithms/Python/blob/master/maths/extended_euclidean_algorithm.py)
   * [Factorial Iterative](https://github.com/TheAlgorithms/Python/blob/master/maths/factorial_iterative.py)
-  * [Factorial Python](https://github.com/TheAlgorithms/Python/blob/master/maths/factorial_python.py)
   * [Factorial Recursive](https://github.com/TheAlgorithms/Python/blob/master/maths/factorial_recursive.py)
   * [Factors](https://github.com/TheAlgorithms/Python/blob/master/maths/factors.py)
   * [Fermat Little Theorem](https://github.com/TheAlgorithms/Python/blob/master/maths/fermat_little_theorem.py)
@@ -565,6 +565,7 @@
 
 ## Other
   * [Activity Selection](https://github.com/TheAlgorithms/Python/blob/master/other/activity_selection.py)
+  * [Check Strong Password](https://github.com/TheAlgorithms/Python/blob/master/other/check_strong_password.py)
   * [Date To Weekday](https://github.com/TheAlgorithms/Python/blob/master/other/date_to_weekday.py)
   * [Davisb Putnamb Logemannb Loveland](https://github.com/TheAlgorithms/Python/blob/master/other/davisb_putnamb_logemannb_loveland.py)
   * [Dijkstra Bankers Algorithm](https://github.com/TheAlgorithms/Python/blob/master/other/dijkstra_bankers_algorithm.py)
@@ -952,6 +953,7 @@
   * [Reverse Words](https://github.com/TheAlgorithms/Python/blob/master/strings/reverse_words.py)
   * [Split](https://github.com/TheAlgorithms/Python/blob/master/strings/split.py)
   * [Upper](https://github.com/TheAlgorithms/Python/blob/master/strings/upper.py)
+  * [Wildcard Pattern Matching](https://github.com/TheAlgorithms/Python/blob/master/strings/wildcard_pattern_matching.py)
   * [Word Occurrence](https://github.com/TheAlgorithms/Python/blob/master/strings/word_occurrence.py)
   * [Word Patterns](https://github.com/TheAlgorithms/Python/blob/master/strings/word_patterns.py)
   * [Z Function](https://github.com/TheAlgorithms/Python/blob/master/strings/z_function.py)

maths/factorial_iterative.py

@@ -1,8 +1,11 @@
-# factorial of a positive integer -- https://en.wikipedia.org/wiki/Factorial
+"""Factorial of a positive integer -- https://en.wikipedia.org/wiki/Factorial
+"""
 
 
-def factorial(n: int) -> int:
+def factorial(number: int) -> int:
     """
+    Calculate the factorial of specified number (n!).
+
     >>> import math
     >>> all(factorial(i) == math.factorial(i) for i in range(20))
     True
@@ -14,17 +17,27 @@ def factorial(n: int) -> int:
     Traceback (most recent call last):
         ...
     ValueError: factorial() not defined for negative values
+    >>> factorial(1)
+    1
+    >>> factorial(6)
+    720
+    >>> factorial(0)
+    1
     """
-    if n != int(n):
+    if number != int(number):
         raise ValueError("factorial() only accepts integral values")
-    if n < 0:
+    if number < 0:
         raise ValueError("factorial() not defined for negative values")
     value = 1
-    for i in range(1, n + 1):
+    for i in range(1, number + 1):
         value *= i
     return value
 
 
 if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
     n = int(input("Enter a positive integer: ").strip() or 0)
     print(f"factorial{n} is {factorial(n)}")

maths/factorial_python.py

@@ -26,7 +26,7 @@ def solution(n: int = 20) -> int:
     """
     n = 2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,
     # 2, 3,...
-    k = n / 2
+    k = n // 2
 
     return int(factorial(n) / (factorial(k) * factorial(n - k)))