How do I approach solving the Beautiful Arrangement II problem?

Start by using a mathematical approach that alternates between the smallest and largest values to construct the array. This ensures distinct values while maintaining the required length.

What is the expected time complexity for this problem?

The time complexity is O(n) since the array is constructed in a linear pass, with no extra loops or nested iterations.

Can the Beautiful Arrangement II problem have multiple valid solutions?

Yes, multiple valid solutions are possible as long as the arrangement satisfies the condition of having exactly k distinct integers.

How can I optimize my solution for space complexity?

Optimize space by using in-place array construction with two pointers or a greedy approach, avoiding extra data structures.

What are common pitfalls to avoid when solving this problem?

Avoid overcomplicating the solution with unnecessary steps or failing to account for edge cases like incorrect repetition of integers.

#667

Medium

auto_awesome数组·数学

LeetCode 题解工作台

优美的排列 II

给你两个整数 n 和 k ，请你构造一个答案列表 answer ，该列表应当包含从 1 到 n 的 n 个不同正整数，并同时满足下述条件：假设该列表是 answer = [a 1 , a 2 , a 3 , ... , a n ] ，那么列表 [|a 1 - a 2 |, |a 2 - a 3 |…

数组数学

题目描述

给你两个整数 n 和 k ，请你构造一个答案列表 answer ，该列表应当包含从 1 到 n 的 n 个不同正整数，并同时满足下述条件：

假设该列表是 answer = [a₁, a₂, a₃, ... , a_n] ，那么列表 [|a₁ - a₂|, |a₂ - a₃|, |a₃ - a₄|, ... , |a_n-1 - a_n|] 中应该有且仅有 k 个不同整数。

返回列表 answer 。如果存在多种答案，只需返回其中 任意一种 。

示例 1：

输入：n = 3, k = 1
输出：[1, 2, 3]
解释：[1, 2, 3] 包含 3 个范围在 1-3 的不同整数，并且 [1, 1] 中有且仅有 1 个不同整数：1

示例 2：

输入：n = 3, k = 2
输出：[1, 3, 2]
解释：[1, 3, 2] 包含 3 个范围在 1-3 的不同整数，并且 [2, 1] 中有且仅有 2 个不同整数：1 和 2

提示：

1 <= k < n <= 10⁴

lightbulb

解题思路

方法一：构造

先按照 1, n, 2, n-1, 3,... 构造答案数据 ans 的前 $k$ 个数，共产生 $k-1$ 个不同的整数。然后根据 $k$ 的奇偶性确定从哪个数开始构造下一个数。

时间复杂度 $O(n)$ ，忽略答案数组的空间消耗，空间复杂度 $O(1)$ 。

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class Solution:
    def constructArray(self, n: int, k: int) -> List[int]:
        l, r = 1, n
        ans = []
        for i in range(k):
            if i % 2 == 0:
                ans.append(l)
                l += 1
            else:
                ans.append(r)
                r -= 1
        for i in range(k, n):
            if k % 2 == 0:
                ans.append(r)
                r -= 1
            else:
                ans.append(l)
                l += 1
        return ans

speed

复杂度分析

指标	值
时间	O(n)
空间	O(1)

psychology

面试官常问的追问

外企场景

question_mark
The candidate should demonstrate a solid understanding of how to manipulate arrays using mathematical methods.
question_mark
Look for the candidate's ability to optimize both time and space complexity, focusing on an efficient O(n) solution.
question_mark
Check if the candidate can identify and avoid common pitfalls in generating the array, such as unnecessary calculations.

warning

常见陷阱

外企场景

error
Failing to account for distinct values: Ensure the arrangement does not have repeated numbers.
error
Overcomplicating the solution: Aim for a simple yet efficient construction of the array without unnecessary operations.
error
Incorrect handling of edge cases: Pay attention to how different values of k impact the arrangement and its validity.

swap_horiz

进阶变体

外企场景

arrow_right_alt
A variation of this problem could involve ensuring the arrangement meets specific conditions related to the positions of the integers.
arrow_right_alt
A challenge could involve generating multiple valid arrangements that satisfy different values of k.
arrow_right_alt
You might be tasked with modifying this problem to handle large values of n and k, pushing for further optimization.

help

常见问题

外企场景

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