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)
result = [intervals]

for i in range(1, len(intervals)):
if result[-1] >= intervals[i]:
result[-1] = max(result[-1], intervals[i])
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)