Merge Overlapping Intervals

Question

This question asks the candidate to merge overlapping intervals from a given list of intervals.

Codemia · Accepted Answer

To solve the problem of merging overlapping intervals, we will first sort the intervals based on their start times. Once sorted, we can iterate through the list and compare each interval with the last merged interval to check for overlaps. If they overlap, we merge them; if not, we add the current interval to our list of merged intervals.

Here is the step-by-step algorithm:
1. Sort the intervals by their starting values.
2. Initialize an empty list to hold the merged intervals.
3. Iterate through the sorted intervals:
   - If the list of merged intervals is empty or the current interval does not overlap with the last merged interval, append it to the merged list.
   - If there is an overlap, merge the current interval with the last merged interval by updating the end of the last merged interval.
4. Return the merged intervals.

The time complexity of this algorithm is O(n log n) due to the sorting step, where n is the number of intervals. The space complexity is O(n) in the worst case, where all intervals are merged into a single interval.

Here is a Python implementation of the algorithm:
```python
from typing import List

def merge_intervals(intervals: List[List[int]]) -> List[List[int]]:
    if not intervals:
        return []

# Sort the intervals based on the start time
    intervals.sort(key=lambda x: x[0])
    merged = []

for interval in intervals:
        # If merged is empty or there is no overlap, append the interval
        if not merged or merged[-1][1] < interval[0]:
            merged.append(interval)
        else:
            # There is an overlap, merge the intervals
            merged[-1][1] = max(merged[-1][1], interval[1])

return merged
```
This code sorts the intervals and merges them based on the logic discussed.

When implementing this solution, consider edge cases such as:
- An empty list of intervals, which should return an empty list.
- Intervals that are completely nested within each other, ensuring they are merged correctly.
- Intervals that touch at the edges, which should also be merged.

Merge Overlapping Intervals

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