mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-05 02:40:16 +00:00
bc8df6de31
* [pre-commit.ci] pre-commit autoupdate updates: - [github.com/astral-sh/ruff-pre-commit: v0.2.2 → v0.3.2](https://github.com/astral-sh/ruff-pre-commit/compare/v0.2.2...v0.3.2) - [github.com/pre-commit/mirrors-mypy: v1.8.0 → v1.9.0](https://github.com/pre-commit/mirrors-mypy/compare/v1.8.0...v1.9.0) * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
67 lines
1.7 KiB
Python
67 lines
1.7 KiB
Python
"""
|
|
The sum-of-subsetsproblem 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_soln(nums: list[int], max_sum: int) -> list[list[int]]:
|
|
result: list[list[int]] = []
|
|
path: list[int] = []
|
|
num_index = 0
|
|
remaining_nums_sum = sum(nums)
|
|
create_state_space_tree(nums, max_sum, num_index, path, result, remaining_nums_sum)
|
|
return result
|
|
|
|
|
|
def create_state_space_tree(
|
|
nums: list[int],
|
|
max_sum: int,
|
|
num_index: int,
|
|
path: list[int],
|
|
result: list[list[int]],
|
|
remaining_nums_sum: int,
|
|
) -> None:
|
|
"""
|
|
Creates a state space tree to iterate through each branch using DFS.
|
|
It terminates the branching of a node when any of the two conditions
|
|
given below satisfy.
|
|
This algorithm follows depth-fist-search and backtracks when the node is not
|
|
branchable.
|
|
|
|
"""
|
|
if sum(path) > max_sum or (remaining_nums_sum + sum(path)) < max_sum:
|
|
return
|
|
if sum(path) == max_sum:
|
|
result.append(path)
|
|
return
|
|
for index in range(num_index, len(nums)):
|
|
create_state_space_tree(
|
|
nums,
|
|
max_sum,
|
|
index + 1,
|
|
[*path, nums[index]],
|
|
result,
|
|
remaining_nums_sum - nums[index],
|
|
)
|
|
|
|
|
|
"""
|
|
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())
|
|
|
|
"""
|
|
nums = [3, 34, 4, 12, 5, 2]
|
|
max_sum = 9
|
|
result = generate_sum_of_subsets_soln(nums, max_sum)
|
|
print(*result)
|