heaps.py

# 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 heaps(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)))

def a(n):
  m=0
  L = list(range(0,n))
  for p in heaps(len(L),L):
    m = max(m,Permutation(p).rank())
  return m


def a(n):
  m=0
  L = list(range(0,n))
  for p in heaps(len(L),L):
    m = Permutation(p).rank()
  return m



print([a(n) for n in range(0,10)])