57. insert interval

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.

solution

• make another array ans, and first append all the intervals that come strictly before the newInterval.
• then for the rest of the intervals including newInterval, we will merge with the interval at the end of the array ans if they overlap.

def insert(self, intervals: List[List[int]], newInterval: List[int]) -> List[List[int]]:
	ans = []
	  
	def merge_add(interval):
		x1, x2 = interval
		if not ans or x1 > ans[-1][1]: # no overlap
			ans.append([x1, x2])
		else:
			ans[-1] = [min(x1, ans[-1][0]), max(x2, ans[-1][1])]
	  
	i = 0
	# add all intervals that start before newInterval
	while i < len(intervals):
		if intervals[i][0] < newInterval[0]:
			ans.append(intervals[i])
			i += 1
		else:
			break
	  
	# add and merge if necessary new interval
	merge_add(newInterval)
	
	# add remaining intervals, merging each if necessary
	while i < len(intervals):
		merge_add(intervals[i])
		i += 1
 
	return ans