Heaps algorithm

divide_and_conquer/heaps_algorithm.py

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+"""
+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,
+    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]]
+    """
+
+    if len(arr) <= 1:
+        return [arr]
+
+    res = []
+
+    def generate(k: int, arr: list):
+        if k == 1:
+            res.append(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))