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"""

In the Combination Sum problem, we are given a list consisting of distinct integers.

We need to find all the combinations whose sum equals to target given.

We can use an element more than one.

Time complexity(Average Case): O(n!)

Constraints:

1 <= candidates.length <= 30

2 <= candidates[i] <= 40

All elements of candidates are distinct.

1 <= target <= 40

"""

def backtrack(

candidates: list, path: list, answer: list, target: int, previous_index: int

) -> None:

"""

A recursive function that searches for possible combinations. Backtracks in case

of a bigger current combination value than the target value.

Parameters

----------

previous_index: Last index from the previous search

target: The value we need to obtain by summing our integers in the path list.

answer: A list of possible combinations

path: Current combination

candidates: A list of integers we can use.

"""

if target == 0:

answer.append(path.copy())

else:

for index in range(previous_index, len(candidates)):

if target >= candidates[index]:

path.append(candidates[index])

backtrack(candidates, path, answer, target - candidates[index], index)

path.pop(len(path) - 1)

def combination_sum(candidates: list, target: int) -> list:

"""

>>> combination_sum([2, 3, 5], 8)

[[2, 2, 2, 2], [2, 3, 3], [3, 5]]

>>> combination_sum([2, 3, 6, 7], 7)

[[2, 2, 3], [7]]

>>> combination_sum([-8, 2.3, 0], 1)

Traceback (most recent call last):

...

RecursionError: maximum recursion depth exceeded

"""

path = [] # type: list[int]

answer = [] # type: list[int]

backtrack(candidates, path, answer, target, 0)

return answer

def main() -> None:

print(combination_sum([-8, 2.3, 0], 1))

if __name__ == "__main__":

import doctest

doctest.testmod()

main()

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