leetcode premium，【leetcode】667. Beautiful Arrangement II

題目如下：

Given two integers?n?and?k, you need to construct a list which contains?ndifferent positive integers ranging from?1?to?n?and obeys the following requirement:?
Suppose this list is [a1, a2, a3, ... , an], then the list [|a1?- a2|, |a2?- a3|, |a3?- a4|, ... , |an-1?- an|] has exactly?k?distinct integers.

If there are multiple answers, print any of them.

Example 1:

Input: n = 3, k = 1
Output: [1, 2, 3]
Explanation: The [1, 2, 3] has three different positive integers ranging from 1 to 3, and the [1, 1] has exactly 1 distinct integer: 1.

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leetcode premium、Example 2:

Input: n = 3, k = 2
Output: [1, 3, 2]
Explanation: The [1, 3, 2] has three different positive integers ranging from 1 to 3, and the [2, 1] has exactly 2 distinct integers: 1 and 2.

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Note:

1. The?n?and?k?are in the range 1 <= k < n <= 104.

解題思路：感覺自己對“給定一個條件，輸出對應排列”這一類型的題目比較沒有思路。本題的解法我也是想了很久才想出來。以[1,2,3,4,5,6]為例，當前k是等于1的；假設要k=2,只需要把6插入到頭部[6,1,2,3,4,5]即可。而如果要k=3,那么把6插入到1的后面，變成[1,6,2,3,4,5]。接下來就是遞推了，記插入6的位置為inx，要使得k=4，只要在k=2的基礎上把最后一個元素插入到inx+2的位置；同理，如果是k=5，就在k=3的基礎上操作。

代碼如下：

class Solution(object):def constructArray(self, n, k):""":type n: int:type k: int:rtype: List[int]"""res = [i for i in range(1,n+1)]inx = 0if k % 2 == 1:inx = 1else:res.insert(0, res.pop(-1))k -= 1inx += 2while k > 1:res.insert(inx,res.pop(-1))inx += 2k -= 2return res

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