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66 lines
1.8 KiB
Python
66 lines
1.8 KiB
Python
"""
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The sum-of-subsetsproblem states that a set of non-negative integers, and a
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value M, determine all possible subsets of the given set whose summation sum
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equal to given M.
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Summation of the chosen numbers must be equal to given number M and one number
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can be used only once.
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"""
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from typing import List
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def generate_sum_of_subsets_soln(nums: List[int], max_sum: int) -> List[List[int]]:
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result: List[List[int]] = []
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path: List[int] = []
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num_index = 0
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remaining_nums_sum = sum(nums)
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create_state_space_tree(nums, max_sum, num_index, path, result, remaining_nums_sum)
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return result
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def create_state_space_tree(
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nums: List[int],
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max_sum: int,
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num_index: int,
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path: List[int],
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result: List[List[int]],
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remaining_nums_sum: int,
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) -> None:
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"""
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Creates a state space tree to iterate through each branch using DFS.
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It terminates the branching of a node when any of the two conditions
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given below satisfy.
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This algorithm follows depth-fist-search and backtracks when the node is not
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branchable.
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"""
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if sum(path) > max_sum or (remaining_nums_sum + sum(path)) < max_sum:
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return
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if sum(path) == max_sum:
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result.append(path)
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return
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for num_index in range(num_index, len(nums)):
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create_state_space_tree(
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nums,
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max_sum,
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num_index + 1,
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path + [nums[num_index]],
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result,
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remaining_nums_sum - nums[num_index],
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)
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"""
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remove the comment to take an input from the user
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print("Enter the elements")
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nums = list(map(int, input().split()))
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print("Enter max_sum sum")
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max_sum = int(input())
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"""
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nums = [3, 34, 4, 12, 5, 2]
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max_sum = 9
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result = generate_sum_of_subsets_soln(nums, max_sum)
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print(*result)
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