Range Module

Statement

Design a Range Module data structure that effectively tracks ranges of numbers using half-open intervals and allows querying these ranges. A half-open interval $[left, right)$ includes all real numbers $n$ where $left\leq n <right$.

Implement the RangeModule class with the following specifications:

• Constructor(): Initializes a new instance of the data structure.

• Add Range(): Adds the half-open interval $[left,~right)$ to the ranges being tracked. If the interval overlaps with existing ranges, it should add only the numbers within $[left,~right)$ that are not already being tracked.

• Query Range(): Returns true if every real number within the interval $[left,~right)$ is currently being tracked, and false otherwise.

• Remove Range(): Removes tracking for every real number within the half-open interval $[left,~right)$.

Constraints:

• $1 \leq$ left $<$ right $\leq 10^4$

• At most, $10^3$ calls will be made to Add Range(), Query Range(), and Remove Range().

Examples