Problem Description
You have numBottles water bottles that are initially full. You can exchange numExchange empty bottles for one full water bottle. The goal is to determine the maximum number of water bottles you can drink.
Key Insights
- Each time you drink from a full bottle, it becomes empty.
- You can exchange a certain number of empty bottles for additional full bottles.
- The process continues until you can no longer exchange empty bottles for full ones.
Space and Time Complexity
Time Complexity: O(log(numBottles)) - The number of exchanges decreases significantly with each round, making the process logarithmic in nature.
Space Complexity: O(1) - Only a few variables are used to keep track of counts.
Solution
The solution involves simulating the process of drinking water bottles and exchanging empty bottles for new ones. We start with the initial number of full bottles and repeatedly exchange empty bottles for new full ones until we can no longer make exchanges. The two main data structures used here are basic integer counters to track the number of full and empty bottles.