+ problem 526

Author: fruit-in

Problemset/0526-Beautiful Arrangement/README.md

@@ -0,0 +1,51 @@
+# 526. Beautiful Arrangement
+Suppose you have `n` integers labeled `1` through `n`. A permutation of those `n` integers `perm` (**1-indexed**) is considered a **beautiful arrangement** if for every `i` (`1 <= i <= n`), **either** of the following is true:
+
+* `perm[i]` is divisible by `i`.
+* `i` is divisible by `perm[i]`.
+
+Given an integer `n`, return *the **number** of the **beautiful arrangements** that you can construct*.
+
+#### Example 1:
+<pre>
+<strong>Input:</strong> n = 2
+<strong>Output:</strong> 2
+<strong>Explanation:</strong>
+The first beautiful arrangement is [1,2]:
+    - perm[1] = 1 is divisible by i = 1
+    - perm[2] = 2 is divisible by i = 2
+The second beautiful arrangement is [2,1]:
+    - perm[1] = 2 is divisible by i = 1
+    - i = 2 is divisible by perm[2] = 1
+</pre>
+
+#### Example 2:
+<pre>
+<strong>Input:</strong> n = 1
+<strong>Output:</strong> 1
+</pre>
+
+#### Constraints:
+* `1 <= n <= 15`
+
+## Solutions (Rust)
+
+### 1. Solution
+```Rust
+impl Solution {
+    pub fn count_arrangement(n: i32) -> i32 {
+        Self::backtracking(n, 1, 0)
+    }
+
+    fn backtracking(n: i32, i: i32, bitmask: i32) -> i32 {
+        if i > n {
+            return 1;
+        }
+
+        (1..=n)
+            .filter(|p| (bitmask >> p) & 1 == 0 && (p % i == 0 || i % p == 0))
+            .map(|p| Self::backtracking(n, i + 1, bitmask | (1 << p)))
+            .sum()
+    }
+}
+```

Problemset/0526-Beautiful Arrangement/README_CN.md

@@ -0,0 +1,51 @@
+# 526. 优美的排列
+假设有从 1 到 n 的 n 个整数。用这些整数构造一个数组 `perm`（**下标从 1 开始**），只要满足下述条件 **之一** ，该数组就是一个 **优美的排列** ：
+
+* `perm[i]` 能够被 `i` 整除
+* `i` 能够被 `perm[i]` 整除
+
+给你一个整数 `n` ，返回可以构造的 **优美排列** 的 **数量** 。
+
+#### 示例 1:
+<pre>
+<strong>输入:</strong> n = 2
+<strong>输出:</strong> 2
+<strong>解释:</strong>
+第 1 个优美的排列是 [1,2]：
+    - perm[1] = 1 能被 i = 1 整除
+    - perm[2] = 2 能被 i = 2 整除
+第 2 个优美的排列是 [2,1]:
+    - perm[1] = 2 能被 i = 1 整除
+    - i = 2 能被 perm[2] = 1 整除
+</pre>
+
+#### 示例 2:
+<pre>
+<strong>输入:</strong> n = 1
+<strong>输出:</strong> 1
+</pre>
+
+#### 提示:
+* `1 <= n <= 15`
+
+## 题解 (Rust)
+
+### 1. 题解
+```Rust
+impl Solution {
+    pub fn count_arrangement(n: i32) -> i32 {
+        Self::backtracking(n, 1, 0)
+    }
+
+    fn backtracking(n: i32, i: i32, bitmask: i32) -> i32 {
+        if i > n {
+            return 1;
+        }
+
+        (1..=n)
+            .filter(|p| (bitmask >> p) & 1 == 0 && (p % i == 0 || i % p == 0))
+            .map(|p| Self::backtracking(n, i + 1, bitmask | (1 << p)))
+            .sum()
+    }
+}
+```

Problemset/0526-Beautiful Arrangement/Solution.rs

@@ -0,0 +1,16 @@
+impl Solution {
+    pub fn count_arrangement(n: i32) -> i32 {
+        Self::backtracking(n, 1, 0)
+    }
+
+    fn backtracking(n: i32, i: i32, bitmask: i32) -> i32 {
+        if i > n {
+            return 1;
+        }
+
+        (1..=n)
+            .filter(|p| (bitmask >> p) & 1 == 0 && (p % i == 0 || i % p == 0))
+            .map(|p| Self::backtracking(n, i + 1, bitmask | (1 << p)))
+            .sum()
+    }
+}

README.md

@@ -321,6 +321,7 @@
 [521][521l]  |[Longest Uncommon Subsequence I][521]                                                 |![rb]  ![rs]
 [524][524l]  |[Longest Word in Dictionary through Deleting][524]                                    |![py]
 [525][525l]  |[Contiguous Array][525]                                                               |![rb]  ![rs]
+[526][526l]  |[Beautiful Arrangement][526]                                                          |![rs]
 [528][528l]  |[Random Pick with Weight][528]                                                        |![rs]
 [529][529l]  |[Minesweeper][529]                                                                    |![rs]
 [530][530l]  |[Minimum Absolute Difference in BST][530]                                             |![py]
@@ -1667,6 +1668,7 @@
 [521]:Problemset/0521-Longest%20Uncommon%20Subsequence%20I/README.md#521-longest-uncommon-subsequence-i
 [524]:Problemset/0524-Longest%20Word%20in%20Dictionary%20through%20Deleting/README.md#524-longest-word-in-dictionary-through-deleting
 [525]:Problemset/0525-Contiguous%20Array/README.md#525-contiguous-array
+[526]:Problemset/0526-Beautiful%20Arrangement/README.md#526-beautiful-arrangement
 [528]:Problemset/0528-Random%20Pick%20with%20Weight/README.md#528-random-pick-with-weight
 [529]:Problemset/0529-Minesweeper/README.md#529-minesweeper
 [530]:Problemset/0530-Minimum%20Absolute%20Difference%20in%20BST/README.md#530-minimum-absolute-difference-in-bst
@@ -3013,6 +3015,7 @@
 [521l]:https://leetcode.com/problems/longest-uncommon-subsequence-i/
 [524l]:https://leetcode.com/problems/longest-word-in-dictionary-through-deleting/
 [525l]:https://leetcode.com/problems/contiguous-array/
+[526l]:https://leetcode.com/problems/beautiful-arrangement/
 [528l]:https://leetcode.com/problems/random-pick-with-weight/
 [529l]:https://leetcode.com/problems/minesweeper/
 [530l]:https://leetcode.com/problems/minimum-absolute-difference-in-bst/

README_CN.md

@@ -321,6 +321,7 @@
 [521][521l]  |[最长特殊序列 Ⅰ][521]                                     |![rb]  ![rs]
 [524][524l]  |[通过删除字母匹配到字典里最长单词][524]                   |![py]
 [525][525l]  |[连续数组][525]                                           |![rb]  ![rs]
+[526][526l]  |[优美的排列][526]                                         |![rs]
 [528][528l]  |[按权重随机选择][528]                                     |![rs]
 [529][529l]  |[扫雷游戏][529]                                           |![rs]
 [530][530l]  |[二叉搜索树的最小绝对差][530]                             |![py]
@@ -1667,6 +1668,7 @@
 [521]:Problemset/0521-Longest%20Uncommon%20Subsequence%20I/README_CN.md#521-最长特殊序列-i
 [524]:Problemset/0524-Longest%20Word%20in%20Dictionary%20through%20Deleting/README_CN.md#524-通过删除字母匹配到字典里最长单词
 [525]:Problemset/0525-Contiguous%20Array/README_CN.md#525-连续数组
+[526]:Problemset/0526-Beautiful%20Arrangement/README_CN.md#526-优美的排列
 [528]:Problemset/0528-Random%20Pick%20with%20Weight/README_CN.md#528-按权重随机选择
 [529]:Problemset/0529-Minesweeper/README_CN.md#529-扫雷游戏
 [530]:Problemset/0530-Minimum%20Absolute%20Difference%20in%20BST/README_CN.md#530-二叉搜索树的最小绝对差
@@ -3013,6 +3015,7 @@
 [521l]:https://leetcode.cn/problems/longest-uncommon-subsequence-i/
 [524l]:https://leetcode.cn/problems/longest-word-in-dictionary-through-deleting/
 [525l]:https://leetcode.cn/problems/contiguous-array/
+[526l]:https://leetcode.cn/problems/beautiful-arrangement/
 [528l]:https://leetcode.cn/problems/random-pick-with-weight/
 [529l]:https://leetcode.cn/problems/minesweeper/
 [530l]:https://leetcode.cn/problems/minimum-absolute-difference-in-bst/