Water Bottles II - Solution & Explanation

This approach simulates the process of drinking water bottles and exchanging empty ones iteratively. We keep track of the number of full and empty bottles and perform exchanges as long as possible. In each iteration, all full bottles are consumed, and empty bottles are exchanged for new full bottles. Note that each time we perform an exchange, we increment the exchange rate by one, which affects the number of exchanges possible in future iterations.

This C code continuously drinks bottles by reducing the number of full bottles to zero in each iteration. It then calculates how many new full bottles can be obtained by exchanging empty bottles, and updates the exchange rate for future iterations.

This approach computes the total number of water bottles through a mathematical lens, given the initial bottle count and exchange rate. Instead of simulating each drink and exchange operation, it leverages mathematical calculation to determine the upper bound of bottles that can be consumed and exchanged within given rules and conditions.

In this method, while maintaining a count of total bottles drunk, we keep track of empty bottles, using integer division to calculate full bottles. The exchange rate is incremented at each step as per rules, and results calculated in fewer operations by concentrating on full/empty relationships.