Insert Interval [LC#57]

You are given an array of non-overlapping intervals intervals where intervals[i] = [starti, endi] represent the start and the end of the ith interval and intervals is sorted in ascending order by starti. You are also given an interval newInterval = [start, end] that represents the start and end of another interval.

Insert newInterval into intervals such that intervals is still sorted in ascending order by starti and intervals still does not have any overlapping intervals (merge overlapping intervals if necessary).

Return intervals after the insertion.

Note that you don’t need to modify intervals in-place. You can make a new array and return it.

Intuition

Since the intervals are sorted by start time, when we loop through them in order, we will encounter 3 cases

1. The interval ends before the new interval
2. The interval overlaps with the new interval
3. The interval starts after the new interval

We handle each of the 3 cases separately

Code

@dataclass
class Interval:
    start: float
    end: float
    
def insert_interval(intervals: List[Interval], new: Interval) -> List[Interval]:
    ans = []
    for curr in intervals:
        if curr.end < new.start: # ends before
            ans.append(curr)
        elif curr.start > new.end: # begins after
            if new:
                ans.append(new)
                new = None
            ans.append(curr)
        else: # overlap
            new = Interval(
                min(curr.start, new.start), max(curr.end, new.end)
            )
    if new: # handle when intervals are empty
        ans.append(new)
    return ans

Time Complexity

$T(n) = O(n)$