Analyze Overlap in Closed Intervals

Question

The question asks the candidate to analyze and identify the overlap between a set of closed intervals.

Codemia · Accepted Answer

To analyze overlap in closed intervals, we can follow these steps: 1. Sort the intervals based on their starting points. 2. Iterate through the sorted intervals and check for overlaps. If the start of the current interval is less than or equal to the end of the previous interval, we have an overlap.

Here is a Python implementation of the proposed approach:

```python
def analyze_overlap(intervals):
    if not intervals:
        return []
    
    # Step 1: Sort intervals by the starting point
    intervals.sort(key=lambda x: x[0])
    
    # Step 2: Initialize a list to hold merged intervals
    merged = []
    
    # Step 3: Iterate through sorted intervals
    for current in intervals:
        # If merged is empty or there is no overlap, append the current interval
        if not merged or merged[-1][1] < current[0]:
            merged.append(current)
        else:
            # There is an overlap, merge the current interval with the last one
            merged[-1][1] = max(merged[-1][1], current[1])
    
    return merged
```

The time complexity of this solution is O(n log n) due to the sorting step, where n is the number of intervals. The iteration through the intervals is O(n), making the overall complexity dominated by the sorting step. The space complexity is O(n) for storing the merged intervals in the worst case.

When implementing this solution, it is important to consider edge cases such as: 1. Empty input list of intervals. 2. Intervals that are completely overlapping. 3. Intervals that touch at the endpoints but do not overlap. Testing these scenarios ensures robustness.

To validate the solution, we can run the following test cases: 1. Input: [[1, 3], [2, 4], [5, 7]]; Expected Output: [[1, 4], [5, 7]]. 2. Input: [[1, 2], [3, 4]]; Expected Output: [[1, 2], [3, 4]]. 3. Input: []; Expected Output: [].

Analyze Overlap in Closed Intervals

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