What is the optimal time complexity of solving Lexicographically smallest array?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Lexicographically smallest array?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Lexicographically smallest array?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Lexicographically smallest array?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Competitive ProgrammingMedium

Lexicographically smallest array

Learn how to solve the 'Lexicographically smallest array' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

Write a function lexicographically_smallest(arr, k) that returns the lexicographically smallest array that can be obtained by swapping adjacent elements at most k times. Elements in arr are unique.

Constraints

•1 <= len(arr) <= 1000
•0 <= k <= 10^5
•-10^9 <= arr[i] <= 10^9

Examples

Example 1

Input

lexicographically_smallest([7, 6, 9, 2, 1], 3)

Output

[2, 7, 6, 9, 1]

Explanation

To get the smallest possible element 2 to the front, we swap 9 and 2, then 6 and 2, then 7 and 2. This takes exactly 3 swaps, resulting in [2, 7, 6, 9, 1].

Example 2

Input

lexicographically_smallest([2, 1, 3], 1)

Output

[1, 2, 3]

Explanation

Swap 2 and 1 (1 swap) to get [1, 2, 3].

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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