57. Insert Interval

Description:

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.

 

'''
[re use module]
    def merge(self, intervals: List[List[int]]) -> List[List[int]]:
        answer=[]
        
        intervals.sort(key=lambda x:x[0]);  # O(nlogn)
        
        tmp=intervals[0]
        
        for ele in intervals:
            
            if ele[0] > tmp[1]:
                interval=[tmp[0],tmp[1]]
                answer.append(interval)
                tmp[0]=ele[0]
                tmp[1]=ele[1]
                
            else:
                if ele[1]>tmp[1]:
                    tmp[1]=ele[1]
                else:
                    continue
        
        answer.append(tmp)
        return answer
        
'''

'''
[1] re-use solution 1)

idea::
insert newInterval at appropriate position, and merge it using module which is 56. Merge Intervals(but, not sorting, already sorted)

- T/C: O(n)
- S/C: O(n+1)
'''

'''
[2] re-use solution 2)

idea::
(using module which is 56. Merge Intervals)
insert newInterval to intervals
sort intervals and merge overlapping intervals

code::
    def insert(self, intervals, newInterval):
        intervals.append(newInterval)
        return self.merge(intervals)
    
    
    def merge(self, intervals: List[List[int]]) -> List[List[int]]:
        answer=[]
        
        intervals.sort(key=lambda x:x[0]);  # O(nlogn)
        
        tmp=intervals[0]
        
        for ele in intervals:
            
            if ele[0] > tmp[1]:
                interval=[tmp[0],tmp[1]]
                answer.append(interval)
                tmp[0]=ele[0]
                tmp[1]=ele[1]
                
            else:
                if ele[1]>tmp[1]:
                    tmp[1]=ele[1]
                else:
                    continue
        
        answer.append(tmp)
        return answer

- T/C: O((n+1)log(n+1)) 
- S/C: O(n+1)   # when append new Interval, there is no overlapping interval
'''

class Solution:
     def insert(self, intervals: List[List[int]], newInterval: List[int]) -> List[List[int]]:
        intervals.append(newInterval)
        return self.merge(intervals)
    
    
     def merge(self, intervals: List[List[int]]) -> List[List[int]]:
        answer=[]
        
        intervals.sort(key=lambda x:x[0]);  # O(nlogn)
        
        tmp=intervals[0]
        
        for ele in intervals:
            
            if ele[0] > tmp[1]:
                interval=[tmp[0],tmp[1]]
                answer.append(interval)
                tmp[0]=ele[0]
                tmp[1]=ele[1]
                
            else:
                if ele[1]>tmp[1]:
                    tmp[1]=ele[1]
                else:
                    continue
        
        answer.append(tmp)
        return answer