Mathematical puzzle to train the programmer's brain Q04 Carving a stick

Problem summary

Cut a bar of length n by m people to make 1 cm units. However, only one person can cut at a time. How many steps will it take?

Code The version I tried without thinking about anything for the time being. The policy is "cut from the longest"

def cutbar(length, member):
    bar = [length]
    step = 0
    while bar != [1]*len(bar): #End if all lengths are 1
        for i in range(min(member, len(bar))):
            piece = bar.pop(0) #lead(=Maximum value)Take out
            if piece == 1:
                break
            else:
                cut1 = round(piece/2)
                cut2 = piece - cut1
                bar += [cut1, cut2]
        bar.sort(reverse=True) #Sort in descending order
        step += 1
    return step

print(cutbar(20, 3))
print(cutbar(100, 5))

With a comeback

It's smarter to do it recursively. Most of the code below is for sale in the text, but ...

#Q04 Carving a stick
#Using recursion

def cutbars(length, member, pieces): #Initial length of bar, number of people, current number of bar pieces
    if pieces >= length: #Finished cutting
        return 0
    elif pieces < member: #Cut all bar pieces uniformly
        return 1 + cutbars(length, member, pieces * 2)
    else: #Cut only the sticks for members
        return 1 + cutbars(length, member, pieces + member)
    
print(cutbars(20, 3 ,1))
print(cutbars(100, 5, 1))