count-total-number-of-colored-cells

java

python

python3

mysql

mssql

oraclesql

csharp

javascript

typescript

bash

swift

kotlin

dart

golang

ruby

scala

rust

racket

erlang

elixir

pythondata

postgresql

cangjie

Algorithms

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:

<ul>
	<li>At the first minute, color any arbitrary unit cell blue.</li>
	<li>Every minute thereafter, color blue every uncolored cell that touches a blue cell.</li>
</ul>

Below is a pictorial representation of the state of the grid after minutes 1, 2, and 3.
<img alt="" src="https://assets.leetcode.com/uploads/2023/01/10/example-copy-2.png" style="width: 500px; height: 279px;" />
Return the number of colored cells at the end of <code>n</code> minutes.

&nbsp;
Example 1:

<pre>
Input: n = 1
Output: 1
Explanation: After 1 minute, there is only 1 blue cell, so we return 1.
</pre>

Example 2:

<pre>
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. 
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 105</code></li>
</ul>

coloredCells

Count Total Number of Colored Cells

Minimum Cuts to Divide a Circle

minimum-cuts-to-divide-a-circle

分割圆的最少切割次数

Math

有一个无穷大的二维网格图，一开始所有格子都未染色。给你一个正整数&nbsp;<code>n</code>&nbsp;，表示你需要执行以下步骤&nbsp;<code>n</code>&nbsp;分钟：

<ul>
	<li>第一分钟，将 任一 格子染成蓝色。</li>
	<li>之后的每一分钟，将与蓝色格子相邻的 所有 未染色格子染成蓝色。</li>
</ul>

下图分别是 1、2、3 分钟后的网格图。
<img alt="" src="https://assets.leetcode.com/uploads/2023/01/10/example-copy-2.png" style="width: 500px; height: 279px;">
请你返回 <code>n</code>&nbsp;分钟之后 被染色的格子&nbsp;数目。

&nbsp;

示例 1：

<pre>输入：n = 1
输出：1
解释：1 分钟后，只有 1 个蓝色的格子，所以返回 1 。
</pre>

示例 2：

<pre>输入：n = 2
输出：5
解释：2 分钟后，有 4 个在边缘的蓝色格子和 1 个在中间的蓝色格子，所以返回 5 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= n &lt;= 105</code></li>
</ul>