What is the optimal time complexity of solving Insert Interval?

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 Insert Interval?

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 Insert Interval?

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 Insert Interval?

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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Insert Interval

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

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Problem Statement

Easy

You are given an array of non-overlapping intervals intervals where intervals[i] = [starti, endi] represent the start and the end of the ith interval and intervals is sorted in ascending order by starti. You are also given an interval newInterval = [start, end] that represents the start and end of another interval. Insert newInterval into intervals such that intervals is still sorted in ascending order by starti and intervals still does not have any overlapping intervals (merge overlapping intervals if necessary).

Return intervals after the insertion.

Write a function insert(intervals: List[List[int]], newInterval: List[int]) -> List[List[int]].

Constraints

•0 <= len(intervals) <= 10^4
•intervals[i].length == 2
•0 <= starti <= endi <= 10^5
•intervals is sorted by starti in ascending order
•newInterval.length == 2
•0 <= start <= end <= 10^5

Examples

Example 1

Input

intervals = [[1,3],[6,9]], newInterval = [2,5]

Output

[[1,5],[6,9]]

Explanation

The new interval [2,5] overlaps with [1,3], so they are merged into [1,5].

Example 2

Input

intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]], newInterval = [4,8]

Output

[[1,2],[3,10],[12,16]]

Explanation

Because [4,8] overlaps with [3,5],[6,7],[8,10], they merge to [3,10].

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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