insert-interval

Interval"

Since we only have to insert one interval here, and our intervals are already sorted, we can do this in O(n) time by thinking about it as having three sections:

1. All intervals that come before the new interval (we'll call this left)
2. All intervals that come after the interval (we'll call this right).
3. All intervals that overlap with the new interval

• If the interval's end time is before the new interval's start time, we know that this interval comes before.
• If the interval's start time is after the new interval's end time, we know that this interval comes after.
• Otherwise, we have to do some kind of merge. Since we want to subsume all intervals, we will take the minimum starting time and the maximum ending time.

def main(intervals, newInterval):
  left = []
  right = []
  mid = [newInterval[0], newInterval[1]]

  for interval in intervals:
      if interval[1] < start:
          left.append(interval)
      elif interval[0] > end:
          right.append(interval)
      else:
          mid[0] = min(mid[0], interval[0])
          mid[1] = max(mid[1], interval[1])

  return left + [mid] + right