Given a collection of intervals, merge all overlapping intervals.

**Example 1**:

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

Output: [[1,6],[8,10],[15,18]]

Explanation: Since intervals [1,3] and [2,6] overlaps, merge them into [1,6].

**Example 2**:

Input: [[1,4],[4,5]]

Output: [[1,5]]

Explanation: Intervals [1,4] and [4,5] are considered overlapping.

**NOTE**: input types have been changed on April 15, 2019. Please reset to default code definition to get new method signature.

## Solution

```
from typing import List
class Solution:
def merge(self, intervals: List[List[int]]) -> List[List[int]]:
if not intervals: return []
intervals.sort(key = lambda n: n[0])
result = [intervals[0]]
for i in range(1, len(intervals)):
if result[-1][1] >= intervals[i][0]:
result[-1][1] = max(result[-1][1], intervals[i][1])
else:
result.append(intervals[i])
return result
```

## Test Cases

```
test = Solution()
assert test.merge([[1,3],[2,6],[8,10],[15,18]]) == [[1,6],[8,10],[15,18]]
assert test.merge([[1,4],[4,5]]) == [[1,5]]
assert test.merge([]) == []
print('All Passed!')
```

## Big O Analysis

**Space Complexity**: O(1)

**Time Complexity**: O(N log N)