667. Beautiful Arrangement II

LeetCode 667. Beautiful Arrangement II

Description

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.

Tags

Array

Solution

We first append number [1, k+1] to the result array from two ends of the interval toward the middle interchangeably, to construct the first k-1 distinct integers. Then, we leave the remaining numbers [k+2, n] in the result for the last one distinct interger (which is 1).

Complexity

• Time complexity: $O(n)$

• Space complexity: $O(n)$

Code

func constructArray(n int, k int) []int {
	l, r, ans := 1, k+1, make([]int, 0, n)
	for l <= r {
		ans = append(ans, l)
		l++
		if l <= r {
			ans = append(ans, r)
			r--
		}
	}
	for i := k + 2; i <= n; i++ {
		ans = append(ans, i)
	}
	return ans
}

Reference

1. Beautiful Arrangement II解题报告