Sync LeetCode submission Runtime - 0 ms (100.00%), Memory - 17.8 MB (48.12%)

Author: jimit105

2649-count-total-number-of-colored-cells/README.md

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+<p>There exists an infinitely large two-dimensional grid of uncolored unit cells. You are given a positive integer <code>n</code>, indicating that you must do the following routine for <code>n</code> minutes:</p>
+
+<ul>
+	<li>At the first minute, color <strong>any</strong> arbitrary unit cell blue.</li>
+	<li>Every minute thereafter, color blue <strong>every</strong> uncolored cell that touches a blue cell.</li>
+</ul>
+
+<p>Below is a pictorial representation of the state of the grid after minutes 1, 2, and 3.</p>
+<img alt="" src="https://assets.leetcode.com/uploads/2023/01/10/example-copy-2.png" style="width: 500px; height: 279px;" />
+<p>Return <em>the number of <strong>colored cells</strong> at the end of </em><code>n</code> <em>minutes</em>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 1
+<strong>Output:</strong> 1
+<strong>Explanation:</strong> After 1 minute, there is only 1 blue cell, so we return 1.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 2
+<strong>Output:</strong> 5
+<strong>Explanation:</strong> After 2 minutes, there are 4 colored cells on the boundary and 1 in the center, so we return 5. 
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
+</ul>

2649-count-total-number-of-colored-cells/solution.py

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+# Approach 2: Math
+
+# Time: O(1)
+# Space: O(1)
+
+class Solution:
+    def coloredCells(self, n: int) -> int:
+        return 1 + 4 * (n - 1) * n // 2
+