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‎Problemset/1411-Number of Ways to Paint N × 3 Grid/README.md

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# 1411. Number of Ways to Paint N × 3 Grid
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You have a `grid` of size `n x 3` and you want to paint each cell of the grid with exactly one of the three colors: **Red**, **Yellow**, or **Green** while making sure that no two adjacent cells have the same color (i.e., no two cells that share vertical or horizontal sides have the same color).
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Given `n` the number of rows of the grid, return *the number of ways* you can paint this `grid`. As the answer may grow large, the answer **must be** computed modulo <code>10<sup>9</sup> + 7</code>.
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#### Example 1:
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![](https://assets.leetcode.com/uploads/2020/03/26/e1.png)
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<pre>
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<strong>Input:</strong> n = 1
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<strong>Output:</strong> 12
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<strong>Explanation:</strong> There are 12 possible way to paint the grid as shown.
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</pre>
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#### Example 2:
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<pre>
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<strong>Input:</strong> n = 5000
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<strong>Output:</strong> 30228214
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</pre>
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#### Constraints:
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* `n == grid.length`
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* `1 <= n <= 5000`
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## Solutions (Rust)
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### 1. Solution
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```Rust
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impl Solution {
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pub fn num_of_ways(n: i32) -> i32 {
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let mut x = 6;
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let mut y = 6;
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for _ in 1..n {
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x = (x + y) % 1_000_000_007 * 2 % 1_000_000_007;
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y = (x + y) % 1_000_000_007;
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}
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(x + y) % 1_000_000_007
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}
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}
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```

‎Problemset/1411-Number of Ways to Paint N × 3 Grid/README_CN.md

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# 1411. 给 N x 3 网格图涂色的方案数
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你有一个 `n x 3` 的网格图 `grid` ，你需要用 **红，黄，绿** 三种颜色之一给每一个格子上色，且确保相邻格子颜色不同（也就是有相同水平边或者垂直边的格子颜色不同）。
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给你网格图的行数 `n` 。
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请你返回给 `grid` 涂色的方案数。由于答案可能会非常大，请你返回答案对 `10^9 + 7` 取余的结果。
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#### 示例 1:
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<pre>
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<strong>输入:</strong> n = 1
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<strong>输出:</strong> 12
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<strong>解释:</strong> 总共有 12 种可行的方法：
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<img src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/04/12/e1.png">
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</pre>
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#### 示例 2:
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<pre>
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<strong>输入:</strong> n = 2
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<strong>输出:</strong> 54
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</pre>
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#### 示例 3:
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<pre>
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<strong>输入:</strong> n = 3
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<strong>输出:</strong> 246
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</pre>
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#### 示例 4:
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<pre>
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<strong>输入:</strong> n = 7
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<strong>输出:</strong> 106494
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</pre>
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#### 示例 5:
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<pre>
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<strong>输入:</strong> n = 5000
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<strong>输出:</strong> 30228214
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</pre>
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#### 提示:
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* `n == grid.length`
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* `grid[i].length == 3`
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* `1 <= n <= 5000`
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## 题解 (Rust)
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### 1. 题解
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```Rust
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impl Solution {
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pub fn num_of_ways(n: i32) -> i32 {
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let mut x = 6;
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let mut y = 6;
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for _ in 1..n {
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x = (x + y) % 1_000_000_007 * 2 % 1_000_000_007;
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y = (x + y) % 1_000_000_007;
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}
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(x + y) % 1_000_000_007
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}
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}
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```

‎Problemset/1411-Number of Ways to Paint N × 3 Grid/Solution.rs

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impl Solution {
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pub fn num_of_ways(n: i32) -> i32 {
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let mut x = 6;
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let mut y = 6;
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for _ in 1..n {
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x = (x + y) % 1_000_000_007 * 2 % 1_000_000_007;
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y = (x + y) % 1_000_000_007;
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}
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(x + y) % 1_000_000_007
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}
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}

‎README.md

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[1408][1408l]|[String Matching in an Array][1408] |![rs]
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[1409][1409l]|[Queries on a Permutation With Key][1409] |![rb]&nbsp;&nbsp;![rs]&nbsp;&nbsp;![kt]
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[1410][1410l]|[HTML Entity Parser][1410] |![rs]
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[1411][1411l]|[Number of Ways to Paint N × 3 Grid][1411] |![rs]
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[1413][1413l]|[Minimum Value to Get Positive Step by Step Sum][1413] |![rs]
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[1414][1414l]|[Find the Minimum Number of Fibonacci Numbers Whose Sum Is K][1414] |![rb]&nbsp;&nbsp;![rs]
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[1415][1415l]|[The k-th Lexicographical String of All Happy Strings of Length n][1415] |![py]&nbsp;&nbsp;![rb]
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[1408]:Problemset/1408-String%20Matching%20in%20an%20Array/README.md#1408-string-matching-in-an-array
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[1409]:Problemset/1409-Queries%20on%20a%20Permutation%20With%20Key/README.md#1409-queries-on-a-permutation-with-key
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[1410]:Problemset/1410-HTML%20Entity%20Parser/README.md#1410-html-entity-parser
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[1411]:Problemset/1411-Number%20of%20Ways%20to%20Paint%20N%20×%203%20Grid/README.md#1411-number-of-ways-to-paint-n-3-grid
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[1413]:Problemset/1413-Minimum%20Value%20to%20Get%20Positive%20Step%20by%20Step%20Sum/README.md#1413-minimum-value-to-get-positive-step-by-step-sum
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[1414]:Problemset/1414-Find%20the%20Minimum%20Number%20of%20Fibonacci%20Numbers%20Whose%20Sum%20Is%20K/README.md#1414-find-the-minimum-number-of-fibonacci-numbers-whose-sum-is-k
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[1415]:Problemset/1415-The%20k-th%20Lexicographical%20String%20of%20All%20Happy%20Strings%20of%20Length%20n/README.md#1415-the-k-th-lexicographical-string-of-all-happy-strings-of-length-n
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[1408l]:https://leetcode.com/problems/string-matching-in-an-array/
37003702
[1409l]:https://leetcode.com/problems/queries-on-a-permutation-with-key/
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[1410l]:https://leetcode.com/problems/html-entity-parser/
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[1411l]:https://leetcode.com/problems/number-of-ways-to-paint-n-3-grid/
37023705
[1413l]:https://leetcode.com/problems/minimum-value-to-get-positive-step-by-step-sum/
37033706
[1414l]:https://leetcode.com/problems/find-the-minimum-number-of-fibonacci-numbers-whose-sum-is-k/
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[1415l]:https://leetcode.com/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/

‎README_CN.md

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[1408][1408l]|[数组中的字符串匹配][1408] |![rs]
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[1409][1409l]|[查询带键的排列][1409] |![rb]&nbsp;&nbsp;![rs]&nbsp;&nbsp;![kt]
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[1410][1410l]|[HTML 实体解析器][1410] |![rs]
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[1411][1411l]|[给 N x 3 网格图涂色的方案数][1411] |![rs]
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[1413][1413l]|[逐步求和得到正数的最小值][1413] |![rs]
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[1414][1414l]|[和为 K 的最少斐波那契数字数目][1414] |![rb]&nbsp;&nbsp;![rs]
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[1415][1415l]|[长度为 n 的开心字符串中字典序第 k 小的字符串][1415] |![py]&nbsp;&nbsp;![rb]
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[1408]:Problemset/1408-String%20Matching%20in%20an%20Array/README_CN.md#1408-数组中的字符串匹配
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[1409]:Problemset/1409-Queries%20on%20a%20Permutation%20With%20Key/README_CN.md#1409-查询带键的排列
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[1410]:Problemset/1410-HTML%20Entity%20Parser/README_CN.md#1410-html-实体解析器
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[1411]:Problemset/1411-Number%20of%20Ways%20to%20Paint%20N%20×%203%20Grid/README_CN.md#1411-给-n-x-3-网格图涂色的方案数
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[1413]:Problemset/1413-Minimum%20Value%20to%20Get%20Positive%20Step%20by%20Step%20Sum/README_CN.md#1413-逐步求和得到正数的最小值
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[1414]:Problemset/1414-Find%20the%20Minimum%20Number%20of%20Fibonacci%20Numbers%20Whose%20Sum%20Is%20K/README_CN.md#1414-和为-k-的最少斐波那契数字数目
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[1415]:Problemset/1415-The%20k-th%20Lexicographical%20String%20of%20All%20Happy%20Strings%20of%20Length%20n/README_CN.md#1415-长度为-n-的开心字符串中字典序第-k-小的字符串
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[1408l]:https://leetcode.cn/problems/string-matching-in-an-array/
37003702
[1409l]:https://leetcode.cn/problems/queries-on-a-permutation-with-key/
37013703
[1410l]:https://leetcode.cn/problems/html-entity-parser/
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[1411l]:https://leetcode.cn/problems/number-of-ways-to-paint-n-3-grid/
37023705
[1413l]:https://leetcode.cn/problems/minimum-value-to-get-positive-step-by-step-sum/
37033706
[1414l]:https://leetcode.cn/problems/find-the-minimum-number-of-fibonacci-numbers-whose-sum-is-k/
37043707
[1415l]:https://leetcode.cn/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/

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