What is the optimal time complexity of solving Non Overlapping Intervals?

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 Non Overlapping Intervals?

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 Non Overlapping Intervals?

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 Non Overlapping Intervals?

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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Non Overlapping Intervals

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

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Problem Statement

Easy

Given an array of intervals intervals where intervals[i] = [starti, endi], return the minimum number of intervals you need to remove to make the rest of the intervals non-overlapping.

Write a function eraseOverlapIntervals(intervals: List[List[int]]) -> int.

Constraints

•1 <= len(intervals) <= 10^5
•intervals[i].length == 2
•-5 * 10^4 <= starti < endi <= 5 * 10^4

Examples

Example 1

Input

intervals = [[1,2],[2,3],[3,4],[1,3]]

Output

Explanation

[1,3] can be removed and the rest are non-overlapping.

Example 2

Input

intervals = [[1,2],[1,2],[1,2]]

Output

Explanation

Remove two [1,2] to make the rest non-overlapping.

Example 3

Input

intervals = [[1,2],[2,3]]

Output

Explanation

Already non-overlapping.

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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