Beautiful Arrangement II

Problem

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

Solution

Two Pointers Solution: O(n) time

public class Solution {
    public int[] constructArray(int n, int k) {
        int[] res = new int[n];
        int left = 1, right = n;
        for (int i = 0; i < n; i++) {
            res[i] = k % 2 == 0 ? left++ : right--;
            if (k > 1) k--;
        }
        return res;
    }
}

Analysis

To construct an array with most various differences
We use two pointers left and right to put element inside
To get a new difference, we just need to use a different side
And we use k % 2 == 0 to change the side
Otherwise, we just use same side to guarantee the difference is same
As long as k > 1, we decrement it by 1