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47 lines
1.2 KiB
Python
47 lines
1.2 KiB
Python
"""
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In this problem, we want to determine all possible combinations of k
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numbers out of 1 ... n. We use backtracking to solve this problem.
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Time complexity: O(C(n,k)) which is O(n choose k) = O((n!/(k! * (n - k)!)))
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"""
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from typing import List
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def generate_all_combinations(n: int, k: int) -> List[List[int]]:
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"""
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>>> generate_all_combinations(n=4, k=2)
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[[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
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"""
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result: List[List[int]] = []
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create_all_state(1, n, k, [], result)
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return result
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def create_all_state(
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increment: int,
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total_number: int,
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level: int,
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current_list: List[int],
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total_list: List[List[int]],
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) -> None:
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if level == 0:
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total_list.append(current_list[:])
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return
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for i in range(increment, total_number - level + 2):
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current_list.append(i)
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create_all_state(i + 1, total_number, level - 1, current_list, total_list)
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current_list.pop()
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def print_all_state(total_list: List[List[int]]) -> None:
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for i in total_list:
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print(*i)
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if __name__ == "__main__":
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n = 4
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k = 2
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total_list = generate_all_combinations(n, k)
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print_all_state(total_list)
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