Water Bottles

main.md

Question

Approach

I start by drinking all the initial bottles, keeping track of empties. While I have enough empties to exchange for a full one, I perform the exchange, drink those, and update my empty count. I continue until I can no longer exchange.

Implementation

class Solution:
    def numWaterBottles(self, numBottles: int, numExchange: int) -> int:
        total = numBottles
        empty = numBottles
        
        while empty >= numExchange:
            new_full = empty // numExchange  
            total += new_full
            empty = empty % numExchange + new_full 
        
        return total

Complexities

• Time: O(log(numBottles)) (since bottles shrink with each exchange)
• Space: O(1)