What is the optimal time complexity of solving Insertions?

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 Insertions?

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 Insertions?

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 Insertions?

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

Insertions

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

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Problem Statement

Easy

Write a function insert_node(arr, val, pos) that represents a linked list as a Python list arr. Insert an integer val at the 0-based index pos (where pos ranges from 0 to the current length of the list) and return the updated list.

Constraints

•0 <= len(arr) <= 1000
•0 <= pos <= len(arr)
•-10^4 <= val <= 10^4

Examples

Example 1

Input

arr = [1, 2, 3], val = 5, pos = 1

Output

[1, 5, 2, 3]

Explanation

We insert the value 5 at index 1, shifting 2 and 3 to the right.

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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