Given a set of non-overlapping intervals and a new interval, insert the interval at correct position. If the insertion results in overlapping intervals, then merge the overlapping intervals. Assume that the set of non-overlapping intervals is sorted on the basis of start time, to find correct position of insertion.
Prerequisite : Merge the intervals
Input : Set : [1, 3], [6, 9] New Interval : [2, 5] Output : [1, 5], [6, 9] The correct position to insert new interval [2, 5] is between the two given intervals. The resulting set would have been [1, 3], [2, 5], [6, 9], but the intervals [1, 3], [2, 5] are overlapping. So, they are merged together in one interval [1, 5]. Input : Set : [1, 2], [3, 5], [6, 7], [8, 10], [12, 16] New Interval : [4, 9] Output : [1, 2], [3, 10], [12, 16] First the interval is inserted between intervals [3, 5] and [6, 7]. Then overlapping intervals are merged together in one interval.
Let the new interval to be inserted is : [a, b]
Case 1 : b < (starting time of first interval in set)
In this case simply insert new interval at the beginning of the set.
Case 2 : (ending value of last interval in set) < a
In this case simply insert new interval at the end of the set.
Case 3 : a ≤ (starting value of first interval) and b ≥ (ending value of last interval)
In this case the new interval overlaps with all the intervals, i.e., it contains all the intervals. So the final answer is the new interval itself.
Case 4 : The new interval does not overlap with any interval in the set and falls between any two intervals in the set
In this case simply insert the interval in the correct position in the set. A sample test case for this is :
Input : Set : [1, 2], [6, 9] New interval : [3, 5] Output : [1, 2], [3, 5], [6, 9]
Case 5 : The new interval overlaps with the interval(s) of the set.
In this case simply merge the new interval with overlapping intervals. To have a better understanding of how to merge overlapping intervals, refer this post : Merge Overlapping Intervals
Example 2 of sample test cases above cover this case.
1, 2 3, 10 12, 16
Time Complexity : O(n)
Auxiliary Space : O(n)
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