How to solve the Joseph problem?

Question

Python

def josephus1(ls, skip):
    skip -= 1
    idx = skip
    while len(ls) > 1:
        if idx+1 > len(ls):
            idx %= len(ls)
        print(ls.pop(idx),"выбывает")
        idx = (idx + skip) % len(ls)
        print(idx,"Это IDX")
    print('survivor: ', ls[0])

def josephus2(ls, skip):
    skip -= 1
    dead_num = 0
    while len(ls) > 1:
        dead_num = (dead_num+skip) % len(ls)
        print(ls.pop(dead_num),"выбывает")
    print('survivor: ', ls[0])


n = int(input('Введите количество человек:'))
m = int(input('Сколько человек посчитать?:'))
list_people = [i for i in range(1, n + 1)]
print(list_people)

josephus(list_people, m)

Natural numbers n, m are given. It is assumed that n people stand in a circle and get numbers, counting counterclockwise, 1, 2, ..., n. Then, starting from the first person, the m-th person is also counted counterclockwise (since people are standing in a circle, the first person is behind the n-th person). This person leaves the circle, after which, starting from the next one, the m-th person is counted again and so on until only one person remains from the whole circle. Determine his number.
I solved the problem, searched the Internet, found the first two algorithms - josephus1 and 2. Is there any other way to solve it more conveniently or are these better? I just figured it out for a long time, but I didn’t come up with a better one. I thought to make it through the counter so that each m value was deleted, but it didn’t work out, the wrong numbers were deleted there and I scored and deleted it.
And yet - how to adapt the algorithm to a different number of people that you consider? That is, first 5, then 3, then 7, well, you understand. Thanks in advance

Answer 1

See Graham, Knuth, Patashnik "Concrete Mathematics", World 2006, p 25