How to Solve Merge Intervals in Python

Understanding the Merge Intervals Problem

You’re given intervals like:

[[1,3], [2,6], [8,10], [15,18]]

Your goal: merge overlapping intervals.

Step 1: Understand the Pattern

If:

• Current interval start ≤ previous interval end
  They overlap.

Step 2: Brute Force Approach

Compare every interval with every other interval.

Time complexity: O(n²)

This works for small datasets but fails in interviews.

Step 3: Optimal Approach

1. Sort intervals by start time.

2. Iterate once.

3. Merge if overlapping.

Time Complexity: O(n log n)

Python Implementation

def merge(intervals):
    intervals.sort(key=lambda x: x[0])
    merged = [intervals[0]]

    for current in intervals[1:]:
        last = merged[-1]

        if current[0] <= last[1]:
            last[1] = max(last[1], current[1])
        else:
            merged.append(current)

    return merged

Why Students Fail This Question

• Not sorting first

• Not understanding interval overlap logic

• Forgetting time complexity

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