# 56 Merge Intervals

Given a collection of intervals, merge all overlapping intervals.

For example,\
Given`[1,3],[2,6],[8,10],[15,18]`,\
return`[1,6],[8,10],[15,18]`.

**The Idea:** We can sort the intervals by start time, the intervals would fall under one of three cases which are illustrated below. In the first case, there are no updates. In the second case, the interval end updates, and in the third case, we add the previous interval and update the current interval.

![](/files/-LoJIpfpVdXnY0gwn3Kq)

**Complexity:** O(nlogn + n) time and O(1) space

```python
class Interval:
    def __init__(self, s=0, e=0):
        self.start = s
        self.end = e


class Solution:
    def merge(self, intervals):
        """
        :type intervals: List[Interval]
        :rtype: List[Interval]
        """

        if not intervals:
            return []

        intervals.sort(key=lambda i: i.start)
        merged_intervals = []

        cur_start = intervals[0].start
        cur_end = intervals[0].end
        for i, interval in enumerate(intervals[1:], 1):
            if cur_start <= interval.start <= cur_end and \
                                    cur_start <= interval.end <= cur_end:
                continue
            if cur_start <= interval.start <= cur_end:
                cur_end = interval.end
            else:
                merged_intervals.append(Interval(cur_start, cur_end))
                cur_start = interval.start
                cur_end = interval.end
        merged_intervals.append(Interval(cur_start, cur_end))

        return merged_intervals


def print_intervals(intervals):
    for i in intervals:
        print('(', i.start, i. end, ')', end='')
    print('\n')

obj = Solution()
print_intervals(obj.merge([Interval(1, 4), Interval(2, 3)]))  # ( 1 4 )
print_intervals(obj.merge([]))  # ( )
print_intervals(obj.merge([Interval(5, 10)]))  # ( 5 10 )
print_intervals(obj.merge([Interval(1, 3), Interval(2, 10), Interval(8, 15)]))  # ( 1 15 )
print_intervals(obj.merge([Interval(1, 3), Interval(2, 6), Interval(8, 10), Interval(15, 18)]))  # ( 1 6 )( 8 10 )( 15 18 )
print_intervals(obj.merge([Interval(1, 3), Interval(4, 6), Interval(7, 10)]))  # ( 1 3 )( 4 6 )( 7 10 )
```


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