update: 2579. Count Total Number of Colored Cells

Author: JuneLin2001

docs/LeetCode/2579. Count Total Number of Colored Cells/README.mdx

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+---
+title: 2579. Count Total Number of Colored Cells
+description: There exists an infinitely large two-dimensional grid of uncolored unit cells. You are given a positive integer n, indicating that you must do the following routine for n minutes
+keywords: [LeetCode, 2579. Count Total Number of Colored Cells, Medium,Math]
+---
+
+# [{frontMatter.title}](https://leetcode.com/problems/count-total-number-of-colored-cells)
+:::danger Medium
+:::
+
+import Tabs from "@theme/Tabs";
+import TabItem from "@theme/TabItem";
+
+<Tabs>
+  <TabItem value="description" label="題目描述" default>
+    ## Description
+There exists an infinitely large two-dimensional grid of uncolored unit cells. You are given a positive integer n, indicating that you must do the following routine for n minutes:
+
+At the first minute, color any arbitrary unit cell blue.
+Every minute thereafter, color blue every uncolored cell that touches a blue cell.
+Below is a pictorial representation of the state of the grid after minutes 1, 2, and 3.  
+
+![](https://assets.leetcode.com/uploads/2023/01/10/example-copy-2.png)
+
+Return the number of colored cells at the end of n minutes.
+
+
+#### Example 1:
+Input: n = 1  
+Output: 1  
+Explanation: After 1 minute, there is only 1 blue cell, so we return 1.  
+
+#### Example 2:
+Input: n = 2  
+Output: 5  
+Explanation: After 2 minutes, there are 4 colored cells on the boundary and 1 in the center, so we return 5. 
+
+
+## Constraints:
+```
+1 <= n <= 105
+```
+  </TabItem>
+<TabItem value="solution" label="解答">
+   ## Solution
+```js
+/**
+ * @param {number} n
+ * @return {number}
+ */
+var coloredCells = function (n) {
+  return 2 * n * (n - 1) + 1;
+};
+
+```
+  </TabItem>
+</Tabs>
+
+
+## 解題思路
+看了 Discussion 提到這題其實是個數學問題，套公式就能寫出時間複雜度空間複雜度皆為 O(1) 的完美答案
+## 心得
+窩...數學好爛...

docs/LeetCode/2579. Count Total Number of Colored Cells/solution.js

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+/**
+ * @param {number} n
+ * @return {number}
+ */
+var coloredCells = function (n) {
+  return 2 * n * (n - 1) + 1;
+};