Heaps algorithm iterative (#2505)

* heap's algorithm iterative

* doctest

* doctest

* rebuild

divide_and_conquer/heaps_algorithm_iterative.py

@@ -0,0 +1,60 @@
+"""
+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))