[CC150][4.5] Implement a function to check if a binary tree is a binary search tree.

isBST.java

// traverse the tree in order
public class isBST<Key extends Comparable<Key>> {
	private Node<Key> prev;
	public boolean check(Node<Key> node) {
		prev = null;
		return isBst(node);
	}
	
	private boolean isBst(Node<Key> x) {
		if (x == null) return true;

		if (!isBst(x.left))
			return false;
		if (prev != null && prev.key.compareTo(x.key) > 0)
			return false;
		prev = x;
		System.out.println(prev.key);
		return (isBst(x.right));
	}
	
	public static void main(String[] args) {
		isBST<Integer> test = new isBST<Integer>();
		Node<Integer> root = new Node<Integer>(0);
		root.left = new Node<Integer>(2);
		root.left.left = new Node<Integer>(1);
		root.left.right = new Node<Integer>(3);
		root.right = new Node<Integer>(6);
		root.right.left = new Node<Integer>(5);
		root.right.right = new Node<Integer>(8);
		if (test.check(root)) 
			System.out.println("Yes");
		else System.out.println("No");
	}
}

Node.java

public class Node<Key> {
	public Key key;
	public Node<Key> left, right;
	
	public Node(Key key) {
		this.key = key;
	}
}