problem715

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715. Range Module (Hard)

A Range Module is a module that tracks ranges of numbers. Your task is to design and implement the following interfaces in an efficient manner.

addRange(int left, int right) Adds the half-open interval [left, right), tracking every real number in that interval. Adding an interval that partially overlaps with currently tracked numbers should add any numbers in the interval [left, right) that are not already tracked.

queryRange(int left, int right) Returns true if and only if every real number in the interval [left, right) is currently being tracked.

removeRange(int left, int right) Stops tracking every real number currently being tracked in the interval [left, right).

Example 1:

addRange(10, 20): null
removeRange(14, 16): null
queryRange(10, 14): true (Every number in [10, 14) is being tracked)
queryRange(13, 15): false (Numbers like 14, 14.03, 14.17 in [13, 15) are not being tracked)
queryRange(16, 17): true (The number 16 in [16, 17) is still being tracked, despite the remove operation)

Note:

A half open interval [left, right) denotes all real numbers left <= x < right.

0 < left < right < 10^9 in all calls to addRange, queryRange, removeRange.

The total number of calls to addRange in a single test case is at most 1000.

The total number of calls to queryRange in a single test case is at most 5000.

The total number of calls to removeRange in a single test case is at most 1000.

Related Topics

[Segment Tree] [Ordered Map]

Similar Questions

1. Merge Intervals (Medium)
2. Insert Interval (Medium)
3. Data Stream as Disjoint Intervals (Hard)

Hints

Hint 1

Maintain a sorted set of disjoint intervals. addRange and removeRange can be performed with time complexity linear to the size of this set; queryRange can be performed with time complexity logarithmic to the size of this set.