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

<p>A <strong>half-open interval</strong> <code>[left, right)</code> denotes all the real numbers <code>x</code> where <code>left &lt;= x &lt; right</code>.</p>

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

<ul>
	<li><code>RangeModule()</code> Initializes the object of the data structure.</li>
	<li><code>void addRange(int left, int right)</code> Adds the <strong>half-open interval</strong> <code>[left, right)</code>, tracking every real number in that interval. Adding an interval that partially overlaps with currently tracked numbers should add any numbers in the interval <code>[left, right)</code> that are not already tracked.</li>
	<li><code>boolean queryRange(int left, int right)</code> Returns <code>true</code> if every real number in the interval <code>[left, right)</code> is currently being tracked, and <code>false</code> otherwise.</li>
	<li><code>void removeRange(int left, int right)</code> Stops tracking every real number currently being tracked in the <strong>half-open interval</strong> <code>[left, right)</code>.</li>
</ul>

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

<pre>
<strong>Input</strong>
[&quot;RangeModule&quot;, &quot;addRange&quot;, &quot;removeRange&quot;, &quot;queryRange&quot;, &quot;queryRange&quot;, &quot;queryRange&quot;]
[[], [10, 20], [14, 16], [10, 14], [13, 15], [16, 17]]
<strong>Output</strong>
[null, null, null, true, false, true]

<strong>Explanation</strong>
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)
</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>4</sup></code> calls will be made to <code>addRange</code>, <code>queryRange</code>, and <code>removeRange</code>.</li>
</ul>
Design; Segment Tree; Ordered Set
class Node {
    Node left;
    Node right;
    int add;
    boolean v;
}

class SegmentTree {
    private Node root = new Node();

    public SegmentTree() {
    }

    public void modify(int left, int right, int v) {
        modify(left, right, v, 1, (int) 1e9, root);
    }

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

    public boolean query(int left, int right) {
        return query(left, right, 1, (int) 1e9, root);
    }

    public boolean query(int left, int right, int l, int r, Node node) {
        if (l >= left && r <= right) {
            return node.v;
        }
        pushdown(node);
        int mid = (l + r) >> 1;
        boolean v = true;
        if (left <= mid) {
            v = v && query(left, right, l, mid, node.left);
        }
        if (right > mid) {
            v = v && query(left, right, mid + 1, r, node.right);
        }
        return v;
    }

    public void pushup(Node node) {
        node.v = node.left != null && node.left.v && node.right != null && node.right.v;
    }

    public void pushdown(Node node) {
        if (node.left == null) {
            node.left = new Node();
        }
        if (node.right == null) {
            node.right = new Node();
        }
        if (node.add != 0) {
            node.left.add = node.add;
            node.right.add = node.add;
            node.left.v = node.add == 1;
            node.right.v = node.add == 1;
            node.add = 0;
        }
    }
}

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

    public RangeModule() {
    }

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

    public boolean queryRange(int left, int right) {
        return tree.query(left, right - 1);
    }

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

/**
 * Your RangeModule object will be instantiated and called as such:
 * RangeModule obj = new RangeModule();
 * obj.addRange(left,right);
 * boolean param_2 = obj.queryRange(left,right);
 * obj.removeRange(left,right);
 */