Count Integers in Intervals

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Description

Given an empty set of intervals, implement a data structure that can:

- Add an interval to the set of intervals.

- Count the number of integers that are present in at least one interval.

Implement the CountIntervals class:

- CountIntervals() Initializes the object with an empty set of intervals.

- void add(int left, int right) Adds the interval [left, right] to the set of intervals.

- int count() Returns the number of integers that are present in at least one interval.

Note that an interval [left, right] denotes all the integers x where left <= x <= right.

Example 1:

Input

["CountIntervals", "add", "add", "count", "add", "count"]

[[], [2, 3], [7, 10], [], [5, 8], []]

Output

[null, null, null, 6, null, 8]

Example 2:

Explanation

CountIntervals countIntervals = new CountIntervals(); // initialize the object with an empty set of intervals.

countIntervals.add(2, 3); // add [2, 3] to the set of intervals.

countIntervals.add(7, 10); // add [7, 10] to the set of intervals.

countIntervals.count(); // return 6

// the integers 2 and 3 are present in the interval [2, 3].

// the integers 7, 8, 9, and 10 are present in the interval [7, 10].

countIntervals.add(5, 8); // add [5, 8] to the set of intervals.

countIntervals.count(); // return 8

// the integers 2 and 3 are present in the interval [2, 3].

// the integers 5 and 6 are present in the interval [5, 8].

// the integers 7 and 8 are present in the intervals [5, 8] and [7, 10].

// the integers 9 and 10 are present in the interval [7, 10].

Solution