2406. divide intervals into minimum number of groups

You are given a 2D integer array intervals where intervals[i] = [lefti, righti] represents the inclusive interval [lefti, righti].

You have to divide the intervals into one or more groups such that each interval is in exactly one group, and no two intervals that are in the same group intersect each other.

Return the minimum number of groups you need to make.

Two intervals intersect if there is at least one common number between them. For example, the intervals [1, 5] and [5, 8] intersect.

solutions

This problem is the exact same as 253-meetings-rooms-ii.

sorting + heap

# O(nlogn + nlogk), where k is answer
def minGroups(self, intervals: List[List[int]]) -> int:
	res = 0
	# min-heap of end times
	active_meetings = []
	  
	intervals.sort(key=lambda x: x[0])
	for start, end in intervals:
		while active_meetings and active_meetings[0] < start:
			heappop(active_meetings)
		heappush(active_meetings, end)
	  
		res = max(res, len(active_meetings))
 
	return res

line-sweep

# O(nlogn)
def minGroups(self, intervals: List[List[int]]) -> int:
	START, END = 0, 1
	  
	events = []
	for start, end in intervals:
		events.append((start, START))
		events.append((end, END))
	events.sort(key=lambda x: (x[0], x[1]))
	  
	res = 0
	active_groups = 0
	for event in events:
		if event[1] == START:
			active_groups += 1
			res = max(res, active_groups)
		else:
			active_groups -= 1
	return res