Count Integers in Intervals
<p>Given an <strong>empty</strong> set of intervals, implement a data structure that can:</p>

<ul>
	<li><strong>Add</strong> an interval to the set of intervals.</li>
	<li><strong>Count</strong> the number of integers that are present in <strong>at least one</strong> interval.</li>
</ul>

<p>Implement the <code>CountIntervals</code> class:</p>

<ul>
	<li><code>CountIntervals()</code> Initializes the object with an empty set of intervals.</li>
	<li><code>void add(int left, int right)</code> Adds the interval <code>[left, right]</code> to the set of intervals.</li>
	<li><code>int count()</code> Returns the number of integers that are present in <strong>at least one</strong> interval.</li>
</ul>

<p><strong>Note</strong> that an interval <code>[left, right]</code> denotes all the integers <code>x</code> where <code>left &lt;= x &lt;= right</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input</strong>
[&quot;CountIntervals&quot;, &quot;add&quot;, &quot;add&quot;, &quot;count&quot;, &quot;add&quot;, &quot;count&quot;]
[[], [2, 3], [7, 10], [], [5, 8], []]
<strong>Output</strong>
[null, null, null, 6, null, 8]

<strong>Explanation</strong>
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].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= left &lt;= right &lt;= 10<sup>9</sup></code></li>
	<li>At most <code>10<sup>5</sup></code> calls <strong>in total</strong> will be made to <code>add</code> and <code>count</code>.</li>
	<li>At least <strong>one</strong> call will be made to <code>count</code>.</li>
</ul>
Design; Segment Tree; Ordered Set
class Node {
    Node left;
    Node right;
    int l;
    int r;
    int mid;
    int v;
    int add;

    public Node(int l, int r) {
        this.l = l;
        this.r = r;
        this.mid = (l + r) >> 1;
    }
}

class SegmentTree {
    private Node root = new Node(1, (int) 1e9 + 1);

    public SegmentTree() {
    }

    public void modify(int l, int r, int v) {
        modify(l, r, v, root);
    }

    public void modify(int l, int r, int v, Node node) {
        if (l > r) {
            return;
        }
        if (node.l >= l && node.r <= r) {
            node.v = node.r - node.l + 1;
            node.add = v;
            return;
        }
        pushdown(node);
        if (l <= node.mid) {
            modify(l, r, v, node.left);
        }
        if (r > node.mid) {
            modify(l, r, v, node.right);
        }
        pushup(node);
    }

    public int query(int l, int r) {
        return query(l, r, root);
    }

    public int query(int l, int r, Node node) {
        if (l > r) {
            return 0;
        }
        if (node.l >= l && node.r <= r) {
            return node.v;
        }
        pushdown(node);
        int v = 0;
        if (l <= node.mid) {
            v += query(l, r, node.left);
        }
        if (r > node.mid) {
            v += query(l, r, node.right);
        }
        return v;
    }

    public void pushup(Node node) {
        node.v = node.left.v + node.right.v;
    }

    public void pushdown(Node node) {
        if (node.left == null) {
            node.left = new Node(node.l, node.mid);
        }
        if (node.right == null) {
            node.right = new Node(node.mid + 1, node.r);
        }
        if (node.add != 0) {
            Node left = node.left, right = node.right;
            left.add = node.add;
            right.add = node.add;
            left.v = left.r - left.l + 1;
            right.v = right.r - right.l + 1;
            node.add = 0;
        }
    }
}

class CountIntervals {
    private SegmentTree tree = new SegmentTree();

    public CountIntervals() {
    }

    public void add(int left, int right) {
        tree.modify(left, right, 1);
    }

    public int count() {
        return tree.query(1, (int) 1e9);
    }
}

/**
 * Your CountIntervals object will be instantiated and called as such:
 * CountIntervals obj = new CountIntervals();
 * obj.add(left,right);
 * int param_2 = obj.count();
 */