## Python, divide_and_conquer, heaps_algorithm_iterative.py

``````"""
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.
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))
``````