Python/backtracking/all_combinations.py

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# -*- coding: utf-8 -*-
"""
In this problem, we want to determine all possible combinations of k
numbers out of 1 ... n. We use backtracking to solve this problem.
Time complexity: O(C(n,k)) which is O(n choose k) = O((n!/(k! * (n - k)!)))
"""
def generate_all_combinations(n: int, k: int) -> [[int]]:
"""
>>> generate_all_combinations(n=4, k=2)
[[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
"""
result = []
create_all_state(1, n, k, [], result)
return result
def create_all_state(increment, total_number, level, current_list, total_list):
if level == 0:
total_list.append(current_list[:])
return
for i in range(increment, total_number - level + 2):
current_list.append(i)
create_all_state(i + 1, total_number, level - 1, current_list, total_list)
current_list.pop()
def print_all_state(total_list):
for i in total_list:
print(*i)
if __name__ == '__main__':
n = 4
k = 2
total_list = generate_all_combinations(n, k)
print_all_state(total_list)