A Range Module is a module that tracks ranges of numbers. Design a data structure to track the ranges represented as half-open intervals and query about them.

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

Implement the RangeModule class:

• RangeModule() Initializes the object of the data structure.
• void 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.

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

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

Example 1:

Input
["RangeModule", "addRange", "removeRange", "queryRange", "queryRange", "queryRange"]
[[], [10, 20], [14, 16], [10, 14], [13, 15], [16, 17]]
Output
[null, null, null, true, false, true]

Explanation
RangeModule rangeModule = new RangeModule();
rangeModule.addRange(10, 20);
rangeModule.removeRange(14, 16);
rangeModule.queryRange(10, 14); // return True,(Every number in [10, 14) is being tracked)
rangeModule.queryRange(13, 15); // return False,(Numbers like 14, 14.03, 14.17 in [13, 15) are not being tracked)
rangeModule.queryRange(16, 17); // return True, (The number 16 in [16, 17) is still being tracked, despite the remove operation)

 1 class RangeModule {
 2     TreeMap<Integer, Integer> map;
 3 
 4     public RangeModule() {
 5         map = new TreeMap<>();
 6     }
 7 
 8     public void addRange(int left, int right) {
 9         Map.Entry<Integer, Integer> start = map.floorEntry(left);
10         Map.Entry<Integer, Integer> end = map.floorEntry(right);
11         if (start != null && start.getValue() >= left) {
12             left = start.getKey();
13         }
14         if (end != null && end.getValue() > right) {
15             right = end.getValue();
16         }
17         map.put(left, right);
18         map.subMap(left, false, right, true).clear();
19     }
20 
21     public boolean queryRange(int left, int right) {
22         Map.Entry<Integer, Integer> entry = map.floorEntry(left);
23         return entry != null && entry.getValue() >= right;
24     }
25 
26     public void removeRange(int left, int right) {
27         Map.Entry<Integer, Integer> start = map.floorEntry(left);
28         Map.Entry<Integer, Integer> end = map.floorEntry(right);
29         if (start != null && start.getValue() > left) {
30             map.put(start.getKey(), left);
31         }
32         if (end != null && end.getValue() > right) {
33             map.put(right, end.getValue());
34         }
35         map.subMap(left, true, right, false).clear();
36     }
37 }