Solution 1 binary search + simulate

• t-complexity: $O(n^2 * logn)$

• s-complexity: $O(n)$

Maintain a disjoint 2-d array. When add a new number, simulate according to description.

Use an unordered_set to remember a number has been added to stream. Duplicate nubmer won't change the outcome.

When add number val, there're four cases:

1. val-1 and val+1 is already in stream, then the intervals than ends with val-1 and starts with val+1 can be merged in to one.

2. val-1 is in stream but not val+1, just add val to interval that ends with val-1.

3. val+1 is in stream but not val-1, this case is symmetry to case 2.

4. Both val-1 and val+1 are not in stream, val will form a new interval.