The Question
Coding

Merge Overlapping Intervals

Given an array of intervals where intervals[i] = [start_i, end_i], representing the time ranges of medical procedures for a patient, merge all overlapping intervals. Return an array of the non-overlapping intervals that cover all the intervals in the input. Two intervals [1, 3] and [3, 4] are considered overlapping because they touch at the boundary. Constraints: - 1 <= intervals.length <= 10^4 - intervals[i].length == 2 - 0 <= start_i <= end_i <= 10^4
Python
Sorting
Greedy
Questions & Insights

Clarifying Questions

Interval Definition: How are the boundaries of the intervals defined? Are they inclusive (e.g., [1, 5] and [5, 10] overlap at 5)?
Assumption: Intervals are inclusive [start, end]. If the end of one equals the start of another, they should be merged.
Input Constraints: What is the maximum number of intervals we might encounter, and what is the range of the start/end values?
Assumption: Up to 10^5 intervals. Start/end values are non-negative integers.
Order of Input: Is the input list of intervals pre-sorted by start time?
Assumption: No, the input is unsorted.
Edge Cases: How should we handle empty inputs or intervals where start == end?
Assumption: An empty input returns an empty list. A point interval like [5, 5] is treated as a valid interval.

Thinking Process

Sorting: To efficiently find overlaps, we must first sort the intervals based on their start times. This ensures that any potential overlap can only occur with the most recently processed interval in our merged result.
Linear Scan: After sorting, we iterate through the list once. We maintain a list of merged intervals. For each current interval:
If merged is empty or the current interval's start is greater than the last merged interval's end, there is no overlap. We append the current interval to merged.
Otherwise, there is an overlap. we update the last merged interval's end time to be the maximum of its current end and the current interval's end.
Complexity Awareness: Sorting will dominate the time complexity at O(N \log N), while the merge step is a simple linear O(N) pass.
In-place vs. New List: Using a new list for merged results is generally safer and more readable in Python, though it requires O(N) space.
Implementation Breakdown

Problem Set

Functional Requirements:
Input: A list of integer pairs [[start_1, end_1], ..., [start_n, end_n]].
Output: A list of merged, non-overlapping intervals sorted by start time.
Constraints:
0 \le \text{intervals.length} \le 10^4
0 \le \text{start}_i \le \text{end}_i \le 10^4

Approach

Algorithm: Sorting + Greedy Linear Scan.
Data Structure: Array/List.
Complexity:
Time: O(N \log N) due to sorting.
Space: O(N) to store the result (or O(\log N) if ignoring output space, depending on the sorting implementation).

Implementation

Wrap Up

Advanced Topics

Readability vs. Performance: In Python, sorting the list in-place (intervals.sort()) saves memory compared to sorted(intervals), which creates a copy. In a production health-tech system processing millions of records, memory efficiency is paramount.
Streaming/Iterative version: If intervals were coming from a stream (e.g., real-time health sensor data), we would maintain the merged state and only output/finalize an interval once we see a new interval with a start time strictly greater than our current "running" end time.
Concurrency: If the dataset is massive (e.g., distributed across multiple servers), we can use a "Divide and Conquer" approach: split intervals, merge them locally on different nodes, and then perform a final merge of the results (similar to the merge step in Merge Sort).