JosephusProblem.py

def JosephusProblemSimulator(n, debug=False):
  people = list(range(1, n+1))

  person = 1
  kill = False
  
  while len(people) > 1:
    if people.index(person) + 1 > len(people) - 1:
      nxtPerson = people[0]
    else:
      nxtPerson = people[people.index(person) + 1]

    if kill:
      people.remove(person)
      kill = False 
      if debug: print('killed', person) 
    else:
      if debug: print('skip', person , 'gonna kill', nxtPerson)
      kill = True

    if debug: print('--=>', people, '\n')
    person = nxtPerson

  return people[0]

def JosephusProblemFastCalc(n):
  return int((bin(n)[2:] + '1')[1:], 2)

print(JosephusProblemSimulator(41, True))
print(JosephusProblemFastCalc(41))

https://www.youtube.com/watch?v=uCsD3ZGzMgE