Add tests and cleanup sum_of_subsets algorithm (#12746)

* Add tests and cleanup sum_of_subsets algorithm.

* Update sum_of_subsets.py

* Update sum_of_subsets.py

* Update sum_of_subsets.py

* Update sum_of_subsets.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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---------

Co-authored-by: Maxim Smolskiy <[email protected]>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: 3 people

backtracking/sum_of_subsets.py

@@ -1,16 +1,26 @@
 """
-The sum-of-subsetsproblem states that a set of non-negative integers, and a
+The sum-of-subsets problem states that a set of non-negative integers, and a
 value M, determine all possible subsets of the given set whose summation sum
 equal to given M.
 
 Summation of the chosen numbers must be equal to given number M and one number
 can be used only once.
 """
 
-from __future__ import annotations
 
+def generate_sum_of_subsets_solutions(nums: list[int], max_sum: int) -> list[list[int]]:
+    """
+    The main function. For list of numbers 'nums' find the subsets with sum
+    equal to 'max_sum'
+
+    >>> generate_sum_of_subsets_solutions(nums=[3, 34, 4, 12, 5, 2], max_sum=9)
+    [[3, 4, 2], [4, 5]]
+    >>> generate_sum_of_subsets_solutions(nums=[3, 34, 4, 12, 5, 2], max_sum=3)
+    [[3]]
+    >>> generate_sum_of_subsets_solutions(nums=[3, 34, 4, 12, 5, 2], max_sum=1)
+    []
+    """
 
-def generate_sum_of_subsets_soln(nums: list[int], max_sum: int) -> list[list[int]]:
     result: list[list[int]] = []
     path: list[int] = []
     num_index = 0
@@ -34,7 +44,21 @@ def create_state_space_tree(
     This algorithm follows depth-fist-search and backtracks when the node is not
     branchable.
 
+    >>> path = []
+    >>> result = []
+    >>> create_state_space_tree(
+    ...     nums=[1],
+    ...     max_sum=1,
+    ...     num_index=0,
+    ...     path=path,
+    ...     result=result,
+    ...     remaining_nums_sum=1)
+    >>> path
+    []
+    >>> result
+    [[1]]
     """
+
     if sum(path) > max_sum or (remaining_nums_sum + sum(path)) < max_sum:
         return
     if sum(path) == max_sum:
@@ -51,16 +75,7 @@ def create_state_space_tree(
         )
 
 
-"""
-remove the comment to take an input from the user
-
-print("Enter the elements")
-nums = list(map(int, input().split()))
-print("Enter max_sum sum")
-max_sum = int(input())
+if __name__ == "__main__":
+    import doctest
 
-"""
-nums = [3, 34, 4, 12, 5, 2]
-max_sum = 9
-result = generate_sum_of_subsets_soln(nums, max_sum)
-print(*result)
+    doctest.testmod()