For some fixed N, an array A is beautiful if it is a permutation of the integers 1, 2, ..., N, such that:

For every i < j, there is no k with i < k < j such that A[k] * 2 = A[i] + A[j].

Given N, return any beautiful array A. (It is guaranteed that one exists.)

Example 1:

Input: 4
Output: [2,1,4,3]
 

Example 2:

Input: 5
Output: [3,1,2,5,4]

Note:

• 1 <= N <= 1000

對於某些固定的 N，如果數組 A 是整數 1, 2, ..., N 組成的排列，使得：

對於每個 i < j，都不存在 k 滿足 i < k < j 使得 A[k] * 2 = A[i] + A[j]。

那麽數組 A 是漂亮數組。

給定 N，返回任意漂亮數組 A（保證存在一個）。

示例 1：

輸入：4
輸出：[2,1,4,3]

示例 2：

輸入：5
輸出：[3,1,2,5,4]

提示：

• 1 <= N <= 1000

16ms

 1 class Solution {
 2     func beautifulArray(_ N: Int) -> [Int] {
 3         var a:[Int] = [Int](repeating: 0,count: N)
 4         dfs(1, 0, N, &a,0)
 5         for i in 0..<N
 6         {
 7             a[i] += 1
 8         }
 9         return a
10     }
11     //深度優先搜索。DFS即Depth First Search.
 
12     //對每一個可能的分支路徑深入到不能再深入為止，而且每個節點只能訪問一次
13     func dfs(_ d:Int,_ m:Int,_ n: Int,_ a:inout [Int],_ off:Int) -> Int
14     {
15         var off = off
16         if m >= n {return off}
17         if m + d >= n
18         {
19             a[off] = m
20             off += 1
21             return off
22         }
23         for i in 0..<2
24         {
25             off = dfs(d*2, m+d*i, n, &a, off)
26         }
27         return off
28     }
29 }

[Swift Weekly Contest 108]LeetCode932. 漂亮數組 | Beautiful Array