Track Coverage of Half-Open Real Intervals

### Problem Implement RangeModule, initially tracking no numbers. addRange(left,right) includes every real x with left<=x<right. removeRange stops tracking that interval. queryRange returns whether every real number in the requested interval is tracked. Overlapping additions form a union. ```cpp class RangeModule { public: RangeModule(); void addRange(int left, int right); bool queryRange(int left, int right); void removeRange(int left, int right); }; ``` ### Examples **Example 1:** ```text RangeModule(); addRange(2,9); removeRange(4,6); queryRange(2,4); queryRange(3,7); queryRange(6,9) Query returns: [true,false,true] Explanation: Coverage is [2,4) together with [6,9). ``` **Example 2:** ```text RangeModule(); addRange(1,3); addRange(3,5); queryRange(1,5) Query returns: [true] Explanation: Touching half-open ranges leave no uncovered real point. ``` ### Constraints - Endpoints satisfy 1 <= left < right <= 1000000000. - Total calls across addRange, queryRange and removeRange are at most 10000. ### Contract considerations Keep the original constructor and three persistent methods. ```hint Read the boundary condition Can disjoint covered intervals answer a range query with one predecessor lookup? ``` ### Boundary reminders Keep the original constructor and three persistent methods.