add Heap's algorithm

heaps.py

@@ -0,0 +1,35 @@
+# implementation based on https://en.wikipedia.org/wiki/Heap%27s_algorithm
+# Copyright Darío Clavijo 2024
+
+from sympy import factorial
+from sympy.combinatorics import Permutation
+
+def heaps(k, A):
+  if k == 1:
+    yield A
+  else:
+    for i  in range(0,  k):
+      yield from heap(k-1, A)
+      if k & 1 == 0:
+        A[i],A[k-1] = A[k-1],A[i]
+      else:
+        A[0],A[k-1] = A[k-1],A[0]
+
+
+def heaps_count_swaps(k, A):
+  c = 0
+  if k == 1:
+    return 0
+  else:
+    for i  in range(0,  k):
+      c += heaps_count_swaps(k-1, A)
+      if k & 1 == 0:
+        A[i],A[k-1] = A[k-1],A[i]
+      else:
+        A[0],A[k-1] = A[k-1],A[0]
+      c += 1
+  return c
+
+
+A038156 = lambda n: heaps_count_swaps(n, list(range(0,n)))
+