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Author: NamVr

2665-minimum-time-to-repair-cars/README.md

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+<p>You are given an integer array <code>ranks</code> representing the <strong>ranks</strong> of some mechanics. <font face="monospace">ranks<sub>i</sub></font> is the rank of the <font face="monospace">i<sup>th</sup></font> mechanic<font face="monospace">.</font> A mechanic with a rank <code>r</code> can repair <font face="monospace">n</font> cars in <code>r * n<sup>2</sup></code> minutes.</p>
+
+<p>You are also given an integer <code>cars</code> representing the total number of cars waiting in the garage to be repaired.</p>
+
+<p>Return <em>the <strong>minimum</strong> time taken to repair all the cars.</em></p>
+
+<p><strong>Note:</strong> All the mechanics can repair the cars simultaneously.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> ranks = [4,2,3,1], cars = 10
+<strong>Output:</strong> 16
+<strong>Explanation:</strong> 
+- The first mechanic will repair two cars. The time required is 4 * 2 * 2 = 16 minutes.
+- The second mechanic will repair two cars. The time required is 2 * 2 * 2 = 8 minutes.
+- The third mechanic will repair two cars. The time required is 3 * 2 * 2 = 12 minutes.
+- The fourth mechanic will repair four cars. The time required is 1 * 4 * 4 = 16 minutes.
+It can be proved that the cars cannot be repaired in less than 16 minutes.​​​​​
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> ranks = [5,1,8], cars = 6
+<strong>Output:</strong> 16
+<strong>Explanation:</strong> 
+- The first mechanic will repair one car. The time required is 5 * 1 * 1 = 5 minutes.
+- The second mechanic will repair four cars. The time required is 1 * 4 * 4 = 16 minutes.
+- The third mechanic will repair one car. The time required is 8 * 1 * 1 = 8 minutes.
+It can be proved that the cars cannot be repaired in less than 16 minutes.​​​​​
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= ranks.length &lt;= 10<sup>5</sup></code></li>
+	<li><code>1 &lt;= ranks[i] &lt;= 100</code></li>
+	<li><code>1 &lt;= cars &lt;= 10<sup>6</sup></code></li>
+</ul>

2665-minimum-time-to-repair-cars/solution.py

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+class Solution:
+    def repairCars(self, ranks: List[int], cars: int) -> int:
+        # The minimum possible time is 1,
+        # and the maximum possible time is when the slowest mechanic (highest rank) repairs all cars.
+        low, high = 1, cars * cars * ranks[0]
+
+        # Perform binary search to find the minimum time required.
+        while low < high:
+            mid = (low + high) // 2
+            cars_repaired = sum(int((mid / rank) ** 0.5) for rank in ranks)
+
+            # If the total cars repaired is less than required, increase the time.
+            if cars_repaired < cars:
+                low = mid + 1
+            else:
+                high = mid  # Otherwise, try a smaller time.
+
+        return low