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Author: NamVr

3336-water-bottles-ii/README.md

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+<p>You are given two integers <code>numBottles</code> and <code>numExchange</code>.</p>
+
+<p><code>numBottles</code> represents the number of full water bottles that you initially have. In one operation, you can perform one of the following operations:</p>
+
+<ul>
+	<li>Drink any number of full water bottles turning them into empty bottles.</li>
+	<li>Exchange <code>numExchange</code> empty bottles with one full water bottle. Then, increase <code>numExchange</code> by one.</li>
+</ul>
+
+<p>Note that you cannot exchange multiple batches of empty bottles for the same value of <code>numExchange</code>. For example, if <code>numBottles == 3</code> and <code>numExchange == 1</code>, you cannot exchange <code>3</code> empty water bottles for <code>3</code> full bottles.</p>
+
+<p>Return <em>the <strong>maximum</strong> number of water bottles you can drink</em>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2024/01/28/exampleone1.png" style="width: 948px; height: 482px; padding: 10px; background: #fff; border-radius: .5rem;" />
+<pre>
+<strong>Input:</strong> numBottles = 13, numExchange = 6
+<strong>Output:</strong> 15
+<strong>Explanation:</strong> The table above shows the number of full water bottles, empty water bottles, the value of numExchange, and the number of bottles drunk.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2024/01/28/example231.png" style="width: 990px; height: 642px; padding: 10px; background: #fff; border-radius: .5rem;" />
+<pre>
+<strong>Input:</strong> numBottles = 10, numExchange = 3
+<strong>Output:</strong> 13
+<strong>Explanation:</strong> The table above shows the number of full water bottles, empty water bottles, the value of numExchange, and the number of bottles drunk.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= numBottles &lt;= 100 </code></li>
+	<li><code>1 &lt;= numExchange &lt;= 100</code></li>
+</ul>

3336-water-bottles-ii/solution.py

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+class Solution:
+    def maxBottlesDrunk(self, numBottles: int, numExchange: int) -> int:
+        a = 1
+        b = 2 * numExchange - 3
+        c = -2 * numBottles
+        delta = b * b - 4 * a * c
+        t = math.ceil((-b + math.sqrt(delta)) / (2 * a))
+        return numBottles + t - 1