[Leetcode] 667. Beautiful Arrangement II 解题报告

题目：

Given two integers n and k, you need to construct a list which contains n different 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.

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.

Note:

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

思路：

如果我们需要相邻两数的差距包括1,2, ..., k + 1 (<= n)个数，那么可以采用的策略是让这n个数的排列为：1，k+1，2，k，3，k-1，...。这样它们之间的差距就是k，k-1，k-2，..., 2，1，然后在后面追加其余的数即可。按照这个思路，我们可以写出如下的代码。

代码：

class Solution {
public:
    vector<int> constructArray(int n, int k) {
        int left = 1, right = k + 1;
        vector<int> ans;
        while (left <= right) {
            ans.push_back(left++);
            if (left <= right) {
                ans.push_back(right--);
            }
        }
        for (int i = k + 2; i <= n; ++i) {
            ans.push_back(i);
        }
        return ans;
    }
};