1518-Water Bottles

Optimized Bottle Exchange

Even though this is an easy solution i absoluetly loved this elegant solution that i thoough of.

Approach

In this optimized approach, we use math to gulp down as many bottles as possible before exchanging them for full ones. By maximizing each exchange, we ensure efficiency.

Steps

1. Start with a count of empty bottles consumed set to zero.
2. Continue until the number of full bottles is greater than the exchange rate:
   • Calculate the maximum number of full bottles we can gulp down in one go.
   • Add these to our consumed count.
   • Subtract the corresponding empty bottles from the total.
   • Exchange the empty bottles for new full ones.
3. Return the total number of bottles consumed, including any remaining full bottles.

Implementation

def num_water_bottles(numBottles: int, numExchange: int) -> int:
    consumedBottles = 0
    while numBottles >= numExchange:
        K = numBottles // numExchange
        consumedBottles += numExchange * K
        numBottles = numBottles - numExchange * K + K
    return consumedBottles + numBottles

Complexity

- Time: Efficient, logarithmic relative to the number of bottles.
- Space: Minimal, only requires a few variables.

Question Pattern Resembles

 - Greedy Approach:  You could say it is greedy but i wouldnt classify it as such overall i cant pinpoint it to any particular pattern. 

That reminds me Enjoy drinking responsibly and efficiently!