Heaps algorithm (#2475)

* heaps_algorithm: new algo

* typo

* correction doctest

* doctests: compare with itertools.permutations

* doctest: sorted instead of set

* doctest

* doctest

* rebuild

divide_and_conquer/heaps_algorithm.py

@@ -0,0 +1,56 @@
+"""
+Heap's 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 Heap's algorithm (recursive version),
+    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(k: int, arr: list):
+        if k == 1:
+            res.append(tuple(arr[:]))
+            return
+
+        generate(k - 1, arr)
+
+        for i in range(k - 1):
+            if k % 2 == 0:  # k is even
+                arr[i], arr[k - 1] = arr[k - 1], arr[i]
+            else:  # k is odd
+                arr[0], arr[k - 1] = arr[k - 1], arr[0]
+            generate(k - 1, arr)
+
+    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))