Add: 1518. Water Bottles

Author: Sanajit Jana

TEMPLATE.md

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+# [<Question Title>](<Question Link>)
+
+## Question Description
+<Write the problem description in your own words or copy it from LeetCode. Keep it concise but clear.>
+
+---
+
+## Constraints
+- <Constraint 1>
+- <Constraint 2>
+- <Constraint 3>
+(Write the input limits, data ranges, and any conditions from the problem statement)
+
+---
+
+## Approach
+<Explain your step-by-step thought process.  
+Why this approach works.  
+Mention if you considered alternatives and why this one is better.>
+
+---
+
+## Dry Run
+Example Input: `<example input>`  
+
+Step-by-step execution:  
+- Step 1: <explain>  
+- Step 2: <explain>  
+- Step 3: <explain>  
+
+Final Answer = `<result>`
+
+---
+
+## Solution
+```java
+class Solution {
+    public <returnType> <methodName>(<parameters>) {
+        // your solution code here
+    }
+}
+```
+
+---
+
+## Time and Space Complexity
+- **Time Complexity:** O(<time analysis>)  
+- **Space Complexity:** O(<space analysis>)

problems/1518-water-bottles/README.md

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+# [1518. Water Bottles](https://leetcode.com/problems/water-bottles/?envType=daily-question&envId=2025-10-02)
+
+## Question Description
+There are numBottles water bottles that are initially full of water.  
+You can exchange numExchange empty water bottles from the market with one full water bottle.  
+
+The operation of drinking a full water bottle turns it into an empty bottle.  
+
+Given the two integers numBottles and numExchange, return the maximum number of water bottles you can drink.
+
+---
+
+## Constraints
+- 1 <= numBottles <= 100  
+- 2 <= numExchange <= 100  
+
+---
+
+## Approach
+We simulate the process step by step:  
+1. Drink all current bottles and increase the total count.  
+2. Track how many empty bottles are collected.  
+3. If empty bottles are enough for an exchange, convert them into new full bottles.  
+4. Continue until you cannot exchange anymore.  
+
+This works because each exchange is independent and only depends on the count of empty bottles at each step.
+
+---
+
+## Dry Run
+Example Input: numBottles = 9, numExchange = 3  
+
+Step-by-step execution:  
+- Start: count = 0, empty = 0, numBottles = 9  
+- Drink 9 bottles → count = 9, empty = 9  
+- Exchange 9/3 = 3 → numBottles = 3, empty = 0  
+- Drink 3 bottles → count = 12, empty = 3  
+- Exchange 3/3 = 1 → numBottles = 1, empty = 0  
+- Drink 1 bottle → count = 13, empty = 1  
+- Not enough bottles to exchange → Stop  
+
+Final Answer = 13  
+
+---
+
+## Solution
+```java
+class Solution {
+    public int numWaterBottles(int numBottles, int numExchange) {
+        int count = 0;
+        int empty = 0;
+        while (numBottles > 0) {
+            count += numBottles;
+            empty += numBottles;
+
+            numBottles = empty / numExchange;
+            empty = empty % numExchange;
+        }
+        return count;
+    }
+}
+```
+
+---
+
+## Time and Space Complexity
+- **Time Complexity:** O(numBottles) in the worst case, as we simulate exchanges until bottles run out.  
+- **Space Complexity:** O(1), using only a few variables.