What is the optimal time complexity of solving Insertion Sort?

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

What is the auxiliary space complexity for Insertion Sort?

The space complexity is O(1) 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 Insertion Sort?

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 Insertion Sort?

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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DSA SectionEasy

Insertion Sort

Learn how to solve the 'Insertion Sort' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function insertion_sort(arr) that sorts a list of integers arr in ascending order using the Insertion Sort algorithm and returns the sorted list.

Constraints

•0 <= len(arr) <= 500
•-10^4 <= arr[i] <= 10^4

Examples

Example 1

Input

arr = [4, 3, 2, 10, 12, 1, 5, 6]

Output

[1, 2, 3, 4, 5, 6, 10, 12]

Explanation

Elements are sequentially inserted into their correct positions in the sorted portion of the array.

Example 2

Input

arr = [3, 1, 2]

Output

[1, 2, 3]

Explanation

1 is inserted before 3 -> [1, 3, 2], then 2 is inserted between 1 and 3 -> [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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