Water Bottles II

Problem Description

You are given two integers numBottles and numExchange. numBottles represents the number of full water bottles that you initially have. In one operation, you can perform one of the following operations:

• Drink any number of full water bottles turning them into empty bottles.
• Exchange numExchange empty bottles with one full water bottle. Then, increase numExchange by one.

Note that you cannot exchange multiple batches of empty bottles for the same value of numExchange.

Return the maximum number of water bottles you can drink.

Key Insights

• You can drink all the full bottles you have initially.
• Each time you exchange empty bottles for a full one, you can gain additional drinks.
• The value of numExchange increases with each successful exchange, allowing for more exchanges in the future.
• The process continues until you can no longer perform exchanges.

Space and Time Complexity

Time Complexity: O(n) where n is the number of bottles consumed, as each bottle may lead to an exchange. Space Complexity: O(1) as we are only using a constant amount of space for variables.

Solution

The solution involves simulating the drinking and exchanging process. We start with the initial number of full bottles and continuously drink them. For every batch of empty bottles, we check if we can exchange them for additional full bottles based on the current numExchange. After each exchange, we increment numExchange by one. This process continues until we can no longer perform any exchanges.

Code Solutions