How do you solve Beautiful Array on LeetCode?

Beautiful Array (LeetCode #932) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Using divide-and-conquer can simplify complex problems.

What is the brute force solution for Beautiful Array?

The brute force approach for Beautiful Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible permutations of the numbers from 1 to n and checking each permutation to see if it meets the beautiful array criteria. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Beautiful Array?

Beautiful Array uses the following concepts: Array, Math, Divide and Conquer. The recommended patterns to study are: Divide and Conquer, Recursion.

What are the interview tips for Beautiful Array?

Always consider edge cases, like n = 1. Think about how you can break the problem down into smaller parts. Practice explaining your thought process clearly while coding.

What are common mistakes when solving Beautiful Array?

Relying solely on brute-force without considering optimizations. Not recognizing the recursive structure of the problem.

#932

Beautiful Array

Medium

ArrayMathDivide and ConquerDivide and ConquerRecursion

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses a divide-and-conquer strategy to construct the beautiful array directly. By separating odd and even numbers, we ensure that the condition for a beautiful array is satisfied without needing to check every permutation.

⚙️

Algorithm

3 steps

1Step 1: If n is 1, return [1].
2Step 2: Recursively build the beautiful array for n/2 and n/2 + n%2 (odd/even).
3Step 3: Combine the results by placing odds first followed by evens.

solution.py7 lines

1# Full working Python code
2def beautifulArray(n):
3    if n == 1:
4        return [1]
5    odds = beautifulArray((n + 1) // 2)
6    evens = beautifulArray(n // 2)
7    return odds + [x + len(odds) for x in evens]

ℹ

Complexity note: The time complexity is O(n) because we build the array recursively, and each level of recursion processes a linear number of elements. The space complexity is also O(n) due to the recursion stack and the resulting array.

1Using divide-and-conquer can simplify complex problems.
2Understanding the properties of permutations helps in constructing solutions.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.