doctest all_combinations.py

backtracking/all_combinations.py

@@ -12,6 +12,8 @@
 
 def combination_lists(n: int, k: int) -> list[list[int]]:
  """
+ Generates all possible combinations of k numbers out of 1 ... n using itertools.
+
  >>> combination_lists(n=4, k=2)
  [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
  """
@@ -20,6 +22,8 @@ def combination_lists(n: int, k: int) -> list[list[int]]:
 
 def generate_all_combinations(n: int, k: int) -> list[list[int]]:
  """
+ Generates all possible combinations of k numbers out of 1 ... n using backtracking.
+
  >>> generate_all_combinations(n=4, k=2)
  [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
  >>> generate_all_combinations(n=0, k=0)
@@ -34,6 +38,14 @@ def generate_all_combinations(n: int, k: int) -> list[list[int]]:
  ValueError: n must not be negative
  >>> generate_all_combinations(n=5, k=4)
  [[1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 4, 5], [1, 3, 4, 5], [2, 3, 4, 5]]
+ >>> generate_all_combinations(n=3, k=3)
+ [[1, 2, 3]]
+ >>> generate_all_combinations(n=3, k=1)
+ [[1], [2], [3]]
+ >>> generate_all_combinations(n=1, k=0)
+ [[]]
+ >>> generate_all_combinations(n=1, k=1)
+ [[1]]
  >>> from itertools import combinations
  >>> all(generate_all_combinations(n, k) == combination_lists(n, k)
  ... for n in range(1, 6) for k in range(1, 6))
@@ -56,6 +68,28 @@ def create_all_state(
  current_list: list[int],
  total_list: list[list[int]],
 ) -> None:
+ """
+ Helper function to recursively build all combinations.
+
+ >>> create_all_state(1, 4, 2, [], result := [])
+ >>> result
+ [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
+ >>> create_all_state(1, 3, 3, [], result := [])
+ >>> result
+ [[1, 2, 3]]
+ >>> create_all_state(2, 2, 1, [1], result := [])
+ >>> result
+ [[1, 2]]
+ >>> create_all_state(1, 0, 0, [], result := [])
+ >>> result
+ [[]]
+ >>> create_all_state(1, 4, 0, [1, 2], result := [])
+ >>> result
+ [[1, 2]]
+ >>> create_all_state(5, 4, 2, [1, 2], result := [])
+ >>> result
+ []
+ """
  if level == 0:
  total_list.append(current_list[:])
  return