What is the time complexity of Construct the Lexicographically Largest Valid Sequence?

The optimal solution for Construct the Lexicographically Largest Valid Sequence runs in O(n) time and uses O(n) space. The time complexity is O(n) because we iterate through the numbers from n down to 2 and place them in the sequence, which takes linear time.

What is the brute force solution for Construct the Lexicographically Largest Valid Sequence?

The brute force approach for Construct the Lexicographically Largest Valid Sequence is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible sequences of numbers from 1 to n and checking which ones satisfy the given conditions. This is straightforward but inefficient, especially as n increases. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Construct the Lexicographically Largest Valid Sequence?

Construct the Lexicographically Largest Valid Sequence uses the following concepts: Array, Backtracking. The recommended patterns to study are: Backtracking, Greedy Algorithms.

What are the interview tips for Construct the Lexicographically Largest Valid Sequence?

Clearly explain your thought process while solving the problem. Consider edge cases, such as the smallest values of n. Practice constructing sequences manually to understand the constraints better.

What are common mistakes when solving Construct the Lexicographically Largest Valid Sequence?

Not checking the distance condition correctly. Failing to consider the lexicographical order when generating sequences.

#1718

Construct the Lexicographically Largest Valid Sequence

Medium

ArrayBacktrackingBacktrackingGreedy Algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(n)

The optimal approach constructs the sequence directly by placing the numbers in a specific order that guarantees the largest lexicographical order while satisfying the distance constraints. This avoids the need for permutations and checks.

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Algorithm

3 steps

1Step 1: Initialize an empty list of size 2n with -1 to represent the sequence.
2Step 2: Start placing numbers from n down to 2, ensuring that each number i is placed such that the distance between its two occurrences is exactly i.
3Step 3: Place 1 in the middle of the sequence.

solution.py8 lines

1def largest_sequence_optimal(n):
2    seq = [-1] * (2 * n)
3    for i in range(n, 1, -1):
4        first = seq.index(-1)
5        seq[first] = i
6        seq[first + i] = i
7    seq[seq.index(-1)] = 1
8    return seq

ℹ

Complexity note: The time complexity is O(n) because we iterate through the numbers from n down to 2 and place them in the sequence, which takes linear time.

1The placement of numbers must consider both the distance and the lexicographical order.
2Using a greedy approach helps in constructing the sequence directly.

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