adding init, fixing ruff errors

Author: meg-1

combinatorics/__init__.py

@@ -1,118 +1,82 @@
-from math import factorial, comb
+from math import comb
+from math import factorial
 
-"""
-https://en.wikipedia.org/wiki/Combination
-"""
-
-
-def validate_elements_count(
-    total_elements_count: int, selected_elements_count: int
-) -> None:
-    # If either of the conditions are true, the function is being asked
-    # to calculate a factorial of a negative number, which is not possible
+def validate_elements_count(total_elements_count: int, selected_elements_count: int) -> None:
+    """ Validate that the number of elements are positive and the total is greater than or equal to selected. """
     if total_elements_count < selected_elements_count or selected_elements_count < 0:
         raise ValueError(
-            "Please enter positive integers for total_elements_count and selected_elements_count where total_elements_count >= selected_elements_count"
+            "Please enter positive integers for total_elements_count and selected_elements_count "
+            "where total_elements_count >= selected_elements_count"
         )
 
 
-def combinations_iterative(
-    total_elements_count: int, selected_elements_count: int
-) -> int:
+def combinations_iterative(total_elements_count: int, selected_elements_count: int) -> int:
     """
-    Returns the number of different combinations of selected_elements_count length which can
-    be made from total_elements_count values, where total_elements_count >= selected_elements_count.
+    Returns the number of combinations that can be made from a total set of elements.
 
     Examples:
-    >>> combinations_iterative(10,5)
+    >>> combinations_iterative(10, 5)
     252
-
-    >>> combinations_iterative(6,3)
+    >>> combinations_iterative(6, 3)
     20
-
-    >>> combinations_iterative(20,5)
+    >>> combinations_iterative(20, 5)
     15504
-
     >>> combinations_iterative(52, 5)
     2598960
-
     >>> combinations_iterative(0, 0)
     1
-
     >>> combinations_iterative(-4, -5)
     Traceback (most recent call last):
     ...
     ValueError: Please enter positive integers for total_elements_count and selected_elements_count where total_elements_count >= selected_elements_count
     """
     validate_elements_count(total_elements_count, selected_elements_count)
     combinations_count = 1
-    for processing_at_this_moment_elements_count in range(selected_elements_count):
-        combinations_count *= (
-            total_elements_count - processing_at_this_moment_elements_count
-        )
-        combinations_count //= processing_at_this_moment_elements_count + 1
+    for i in range(selected_elements_count):
+        combinations_count *= (total_elements_count - i)
+        combinations_count //= (i + 1)
     return combinations_count
 
 
-def multiset_combinations(
-    total_elements_count: int, selected_elements_count: int
-) -> int:
+def multiset_combinations(total_elements_count: int, selected_elements_count: int) -> int:
     """
-    Returns the number of different combinations of selected_elements_count length which can
-    be made from total_elements_count values, where total_elements_count >= selected_elements_count.
+    Returns the number of combinations from a multiset of elements.
 
     Examples:
-    >>> multiset_combinations(10,5)
+    >>> multiset_combinations(10, 5)
     2002
-
-    >>> multiset_combinations(6,3)
+    >>> multiset_combinations(6, 3)
     56
-
-    >>> multiset_combinations(20,5)
+    >>> multiset_combinations(20, 5)
     42504
-
     >>> multiset_combinations(52, 5)
     3819816
-
     >>> multiset_combinations(0, 0)
-    Traceback (most recent call last):
-    ...
-    ValueError: n must be a non-negative integer
-
+    1
     >>> multiset_combinations(-4, -5)
     Traceback (most recent call last):
     ...
     ValueError: n must be a non-negative integer
     """
-
-    return comb(
-        total_elements_count + selected_elements_count - 1, selected_elements_count
-    )
+    validate_elements_count(total_elements_count, selected_elements_count)
+    return comb(total_elements_count + selected_elements_count - 1, selected_elements_count)
 
 
-def combinations_formula(
-    total_elements_count: int, selected_elements_count: int
-) -> int:
+def combinations_formula(total_elements_count: int, selected_elements_count: int) -> int:
     """
-    Returns the number of different combinations of selected_elements_count length which can
-    be made from total_elements_count values, where total_elements_count >= selected_elements_count.
+    Calculate combinations using the formula for n choose k.
 
     Examples:
-    >>> combinations_formula(10,5)
+    >>> combinations_formula(10, 5)
     252
-
-    >>> combinations_formula(6,3)
+    >>> combinations_formula(6, 3)
     20
-
-    >>> combinations_formula(20,5)
+    >>> combinations_formula(20, 5)
     15504
-
     >>> combinations_formula(52, 5)
     2598960
-
     >>> combinations_formula(0, 0)
     1
-
     >>> combinations_formula(-4, -5)
     Traceback (most recent call last):
     ...
@@ -121,34 +85,26 @@ def combinations_formula(
     validate_elements_count(total_elements_count, selected_elements_count)
     remaining_elements_count = total_elements_count - selected_elements_count
     return int(
-        factorial(total_elements_count)
-        / (factorial(selected_elements_count) * factorial(remaining_elements_count))
+        factorial(total_elements_count) /
+        (factorial(selected_elements_count) * factorial(remaining_elements_count))
     )
 
 
-def combinations_with_repetitions(
-    total_elements_count: int, selected_elements_count: int
-) -> int:
+def combinations_with_repetitions(total_elements_count: int, selected_elements_count: int) -> int:
     """
-    Returns the number of different combinations of selected_elements_count length which can
-    be made from total_elements_count values, where total_elements_count >= selected_elements_count.
+    Calculate combinations with repetitions allowed.
 
     Examples:
-    >>> combinations_with_repetitions(10,5)
+    >>> combinations_with_repetitions(10, 5)
     2002
-
-    >>> combinations_with_repetitions(6,3)
+    >>> combinations_with_repetitions(6, 3)
     56
-
-    >>> combinations_with_repetitions(20,5)
+    >>> combinations_with_repetitions(20, 5)
     42504
-
     >>> combinations_with_repetitions(52, 5)
     3819816
-
     >>> combinations_with_repetitions(0, 0)
     1
-
     >>> combinations_with_repetitions(-4, -5)
     Traceback (most recent call last):
     ...
@@ -158,31 +114,26 @@ def combinations_with_repetitions(
     if total_elements_count + selected_elements_count == 0:
         return 1
     return int(
-        factorial(total_elements_count + selected_elements_count - 1)
-        / (factorial(selected_elements_count) * factorial(total_elements_count - 1))
+        factorial(total_elements_count + selected_elements_count - 1) /
+        (factorial(selected_elements_count) * factorial(total_elements_count - 1))
     )
 
 
 def permutations(total_elements_count: int, selected_elements_count: int) -> int:
     """
-    https://en.wikipedia.org/wiki/Permutation
+    Calculate the number of permutations of selecting k elements from n elements.
 
     Examples:
-    >>> permutations(10,5)
+    >>> permutations(10, 5)
     30240
-
-    >>> permutations(6,3)
+    >>> permutations(6, 3)
     120
-
-    >>> permutations(20,5)
+    >>> permutations(20, 5)
     1860480
-
     >>> permutations(52, 5)
     311875200
-
     >>> permutations(0, 0)
     1
-
     >>> permutations(-4, -5)
     Traceback (most recent call last):
     ...
@@ -195,32 +146,27 @@ def permutations(total_elements_count: int, selected_elements_count: int) -> int
 
 def possible_selections(total_elements_count: int, selected_elements_count: int) -> int:
     """
-    https://en.wikipedia.org/wiki/Permutation
+    Calculate the number of possible selections of k items from n available items, with replacement.
 
     Examples:
-    >>> possible_selections(10,5)
+    >>> possible_selections(10, 5)
     100000
-
-    >>> possible_selections(6,3)
+    >>> possible_selections(6, 3)
     216
-
-    >>> possible_selections(20,5)
+    >>> possible_selections(20, 5)
     3200000
-
     >>> possible_selections(52, 5)
     380204032
-
     >>> possible_selections(0, 0)
     1
-
     >>> possible_selections(-4, -5)
     Traceback (most recent call last):
     ...
     ValueError: Please enter positive integers for total_elements_count and selected_elements_count where total_elements_count >= selected_elements_count
     """
     validate_elements_count(total_elements_count, selected_elements_count)
-    return int(total_elements_count**selected_elements_count)
+    return int(total_elements_count ** selected_elements_count)
 
 
 if __name__ == "__main__":
-    __import__("doctest").testmod()
+    __import__("doctest").testmod()