Data Stream as Disjoint Intervals

Given a data stream input of non-negative integers a1, a2, …, an, …, summarize the numbers seen so far as a list of disjoint intervals.

For example, suppose the integers from the data stream are 1, 3, 7, 2, 6, …, then the summary will be:

  1. [1, 1]
  2. [1, 1], [3, 3]
  3. [1, 1], [3, 3], [7, 7]
  4. [1, 3], [7, 7]
  5. [1, 3], [6, 7]

Follow up:

What if there are lots of merges and the number of disjoint intervals are small compared to the data stream’s size?