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Solution: Data Stream as Disjoint Intervals

Explore how to implement the Summary Ranges class to represent a stream of non-negative integers as disjoint, sorted intervals. Understand how to add new numbers, merge intervals when values connect or extend existing ranges, and efficiently retrieve the current intervals. This lesson demonstrates maintaining a compact summary using the intervals coding pattern with a focus on time and space complexity.

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Statement

You are given a stream of non-negative integers a1,a2,…,ana_1, a_2, \dots, a_n. At any point, you need to summarize all numbers seen so far as a list of disjoint intervals.

Your task is to implement the Summary Ranges class, where:

  • Constructor: Initializes the Summary Ranges object with an empty stream.

  • Add Num(int value): Adds the integer value to the stream.

  • Get Intervals(): Returns the current summary of numbers as a list of disjoint intervals [start_i, end_i], sorted by start_i.

Note: Each number belongs to exactly one interval. Intervals must merge whenever new numbers connect or extend existing ones, and duplicate insertions should not affect the summary.

Constraints:

  • ...