# LeetCode 56: Merge Intervals — Step-by-Step Visual Trace

**Medium** — Array | Sorting | Intervals | Greedy

## The Problem

Given an array of intervals where intervals[i] = [starti, endi], merge all overlapping intervals and return an array of the non-overlapping intervals that cover all the intervals in the input.

## Approach

Sort intervals by start time, then iterate through them maintaining a result list. For each interval, if it overlaps with the last merged interval (current start ≤ last end), merge them by updating the end time to the maximum of both ends, otherwise add it as a new interval.

**Time:** O(n log n) · **Space:** O(1)

## Code

```python
class Solution:
    def merge(self, intervals: List[List[int]]) -> List[List[int]]:
        if not intervals:
            return []

        intervals.sort(key=lambda x: x[0])
        result = [intervals[0]]

        for interval in intervals[1:]:
            if interval[0] <= result[-1][1]:
                result[-1][1] = max(result[-1][1], interval[1])
            else:
                result.append(interval)

        return result
```

## Watch It Run

> **[Open interactive visualization](https://tracelit.dev/app?trace=0056_merge-intervals)**

> **Try it yourself:** Open [TraceLit](https://tracelit.dev/app?trace=0056_merge-intervals) and step through every line.

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