# 667. Beautiful Arrangement II

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.

# Solution

Approach 1: generate a sequence -- find how by going through some examples.

# Code (Python)

Approach 1:

class Solution:
    def constructArray(self, n: int, k: int) -> List[int]:
        # idea: 
        # [1, n, 2, n-1, 3, n-2 ...] for a construction when k = n - 1
        # [1, 2, 3, ..., n] for a construction when k = 1
        # now construct by [1, k + 1, 2, k, 3, k - 1, ...] + [k + 2, k + 3, ..., n]
        result = []
        start, end = 1, k + 1
        while start < end:
            result.append(start)
            result.append(end)
            start += 1
            end -= 1
        if start == end:
            result.append(start)
        for i in range(k + 2, n + 1):
            result.append(i)
        return result

# Code (C++)

Approach 1:

Approach 2: