mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-05 02:40:16 +00:00
61 lines
1.6 KiB
Python
61 lines
1.6 KiB
Python
|
"""
|
||
|
|
Heap's (iterative) algorithm returns the list of all permutations possible from a list.
|
||
|
|
It minimizes movement by generating each permutation from the previous one
|
||
|
|
by swapping only two elements.
|
||
|
|
More information:
|
||
|
|
https://en.wikipedia.org/wiki/Heap%27s_algorithm.
|
||
|
|
"""
|
||
|
|
|
||
|
|
|
||
|
|
def heaps(arr: list) -> list:
|
||
|
|
"""
|
||
|
|
Pure python implementation of the iterative Heap's algorithm,
|
||
|
|
returning all permutations of a list.
|
||
|
|
>>> heaps([])
|
||
|
|
[()]
|
||
|
|
>>> heaps([0])
|
||
|
|
[(0,)]
|
||
|
|
>>> heaps([-1, 1])
|
||
|
|
[(-1, 1), (1, -1)]
|
||
|
|
>>> heaps([1, 2, 3])
|
||
|
|
[(1, 2, 3), (2, 1, 3), (3, 1, 2), (1, 3, 2), (2, 3, 1), (3, 2, 1)]
|
||
|
|
>>> from itertools import permutations
|
||
|
|
>>> sorted(heaps([1,2,3])) == sorted(permutations([1,2,3]))
|
||
|
|
True
|
||
|
|
>>> all(sorted(heaps(x)) == sorted(permutations(x))
|
||
|
|
... for x in ([], [0], [-1, 1], [1, 2, 3]))
|
||
|
|
True
|
||
|
|
"""
|
||
|
|
|
||
|
|
if len(arr) <= 1:
|
||
|
|
return [tuple(arr)]
|
||
|
|
|
||
|
|
res = []
|
||
|
|
|
||
|
|
def generate(n: int, arr: list):
|
||
|
|
c = [0] * n
|
||
|
|
res.append(tuple(arr))
|
||
|
|
|
||
|
|
i = 0
|
||
|
|
while i < n:
|
||
|
|
if c[i] < i:
|
||
|
|
if i % 2 == 0:
|
||
|
|
arr[0], arr[i] = arr[i], arr[0]
|
||
|
|
else:
|
||
|
|
arr[c[i]], arr[i] = arr[i], arr[c[i]]
|
||
|
|
res.append(tuple(arr))
|
||
|
|
c[i] += 1
|
||
|
|
i = 0
|
||
|
|
else:
|
||
|
|
c[i] = 0
|
||
|
|
i += 1
|
||
|
|
|
||
|
|
generate(len(arr), arr)
|
||
|
|
return res
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == "__main__":
|
||
|
|
user_input = input("Enter numbers separated by a comma:\n").strip()
|
||
|
|
arr = [int(item) for item in user_input.split(",")]
|
||
|
|
print(heaps(arr))
|