0667. Beautiful Arrangement II (M)

Beautiful Arrangement II (M)

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 <= 10^4.

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题意

对1-n这n个整数进行排列，使得到的序列相邻两个数字的差组成的集合中正好有k个不同的值。

思路

考虑这样一个问题，即给定n个整数形成一个排列，如何让相邻数字的差正好有n-1个不同的值。方法为头尾交叉插入，以 n=8 为例，依次插入 1、8、2、7、3、6、4、5，这样得到的差值分别为 7、6、5、4、3、2、1，满足条件。在此基础上解决原题：只要先找到k-1个不同的差值，剩下的数全升序或降序排列(即差值恒为1)就能满足有且仅有k个不同的差值。

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代码实现

Java

class Solution {
    public int[] constructArray(int n, int k) {
        int[] ans = new int[n];
        int left = 1, right = n;

        for (int i = 0; i < n; i++) {
            if (i < k) {
                ans[i] = i % 2 == 0 ? left++ : right--;
            } else {
                ans[i] = k % 2 == 0 ? right-- : left++;
            }
        }

        return ans;
    }
}