Buy three get one (a foreign company interview question)

Problem Description:

28 soldiers went to buy water, 3 empty bottles can be replaced by a bottle of water, ask the most to buy a few bottles of water can make all the soldiers drink water, and do not waste.

Problem Analysis:

The key to this problem is that 3 empty bottles of water will also produce empty bottles, and the first time to buy water bottles is not necessarily a 3 multiples. To understand this, the problem is solved.

If you purchase n bottles of water, then set F (n) as the number of bottles that can be given water, then:

F (n) = (N/3) + ((N/3) + (n%3)/3 + (((N/3) + (n%3)/3 + ((N/3) + (n%3)%3)/3 + ...

So the water we've actually obtained recently has n + f (n) bottles.

The code is as follows (Python implementation):

# Calculate How many extral bottles is free if you buy "num" bottles
def extrabottle (num):
    n = int (num)
    r = 0  While N/3! =
    0:
        # Calc Free bottle
        r = r + N/3
        # Calc Empty bottle number 
        # (empty ones of free bottle + empty ones of remainder)
        n = n/3 + n%3
    return r

def bottletobuy (num):
    i = Int (1) while
    TRUE:
 if (i + extrabottle (i) >= num):
           break
        i + = 1
    return i

print bottletobuy (28)

Last Answer: 19