adding my solution to 1518

problems/1518/jeremymanning.md

@@ -1,11 +1,45 @@
 # [Problem 1518: Water Bottles](https://leetcode.com/problems/water-bottles)
 
 ## Initial thoughts (stream-of-consciousness)
+- There's almost certainly an analytic solution to this problem-- something like (number of bottles) + (log (base exchange rate) number of bottles) + 1...but probably not *quite* that simple
+- The naive solution would be to do something like:
+    - keep a running total of the number of bottles that have been drunk
+    - then, until there are fewer than `numExchange` bottles left:
+        - exchange as many bottles as possible and add that to the total
+        - update the number of remaining bottles
+- If `numExchange` was 1, we'd get an infinite loop, but it looks like this isn't allowed (`2 <= numExchange <= 100`)
+
 
 ## Refining the problem, round 2 thoughts
+- I'll start by implementing the naive solution.  Given the problem specification (maximum `numBottles` is 100, minimum `numExchange` is 2), I don't think we'll run out of compute time...
+- Updating the number of remaining bottles should work as follows:
+    - Exchange whatever we can.  The number of bottles now in our collection is `availableBottles // numExchange`
+    - Also track what's left over (`availableBottles % numExchange`)
 
 ## Attempted solution(s)
 ```python
-class Solution:  # paste your code here!
-    ...
+class Solution:
+    def numWaterBottles(self, numBottles: int, numExchange: int) -> int:        
+        drinkableTotal = numBottles
+        bottlesAvailable = numBottles
+
+        while bottlesAvailable >= numExchange:
+            nextExchange = bottlesAvailable // numExchange
+            drinkableTotal += nextExchange
+
+            bottlesAvailable %= numExchange
+            bottlesAvailable += nextExchange
+
+        return drinkableTotal
 ```
+- All given test cases pass
+- Other test cases:
+    - `numBottles = 100, numExchange = 2`: passes
+    - `numBottles = 100, numExchange = 3`: passes
+    - `numBottles = 100, numExchange = 4`: passes
+    - `numBottles = 48, numExchange = 7`: passes
+- Seems ok...submitting...
+
+![Screenshot 2024-07-06 at 11 47 50 PM](https://github.com/ContextLab/leetcode-solutions/assets/9030494/66a9540c-5afc-4cd4-9652-6e8aa99ab59d)
+
+Slow, but I'll take it-- solved!