BST.java

package Helpers;

import java.util.NoSuchElementException;

public class BST<Key extends Comparable<Key>, Value> {
	private Node root; // root of BST

	private class Node {
		private Key key; // sorted by key
		private Value val; // associated data
		private Node left, right; // left and right subtrees
		private int N; // number of nodes in subtree

		public Node(Key key, Value val, int N) {
			this.key = key;
			this.val = val;
			this.N = N;
		}
	}

	public boolean isEmpty() {
		return size() == 0;
	}

	public int size() {
		return size(root);
	}

	private int size(Node x) {
		if (x == null)
			return 0;
		else
			return x.N;
	}

	public boolean contains(Key key) {
		if (key == null)
			throw new NullPointerException("argument to contains() is null");
		return get(key) != null;
	}

	public Value get(Key key) {
		return get(root, key);
	}

	private Value get(Node x, Key key) {
		if (x == null)
			return null;
		int cmp = key.compareTo(x.key);
		if (cmp < 0)
			return get(x.left, key);
		else if (cmp > 0)
			return get(x.right, key);
		else
			return x.val;
	}

	public void put(Key key, Value val) {
		if (key == null)
			throw new NullPointerException("first argument to put() is null");
		if (val == null) {
			delete(key);
			return;
		}
		root = put(root, key, val);
	}

	private Node put(Node x, Key key, Value val) {
		if (x == null)
			return new Node(key, val, 1);
		int cmp = key.compareTo(x.key);
		if (cmp < 0)
			x.left = put(x.left, key, val);
		else if (cmp > 0)
			x.right = put(x.right, key, val);
		else
			x.left = put(x.left, key, val);
		x.N = 1 + size(x.left) + size(x.right);
		return x;
	}

	public void deleteMin() {
		if (isEmpty())
			throw new NoSuchElementException("Symbol table underflow");
		root = deleteMin(root);
	}

	private Node deleteMin(Node x) {
		if (x.left == null)
			return x.right;
		x.left = deleteMin(x.left);
		x.N = size(x.left) + size(x.right) + 1;
		return x;
	}

	public void deleteMax() {
		if (isEmpty())
			throw new NoSuchElementException("Symbol table underflow");
		root = deleteMax(root);
	}

	private Node deleteMax(Node x) {
		if (x.right == null)
			return x.left;
		x.right = deleteMax(x.right);
		x.N = size(x.left) + size(x.right) + 1;
		return x;
	}

	public void delete(Key key) {
		if (key == null)
			throw new NullPointerException("argument to delete() is null");
		root = delete(root, key);
	}

	private Node delete(Node x, Key key) {
		if (x == null)
			return null;

		int cmp = key.compareTo(x.key);
		if (cmp < 0)
			x.left = delete(x.left, key);
		else if (cmp > 0)
			x.right = delete(x.right, key);
		else {
			if (x.right == null)
				return x.left;
			if (x.left == null)
				return x.right;
			Node t = x;
			x = min(t.right);
			x.right = deleteMin(t.right);
			x.left = t.left;
		}
		x.N = size(x.left) + size(x.right) + 1;
		return x;
	}

	public Key min() {
		if (isEmpty())
			throw new NoSuchElementException("called min() with empty symbol table");
		return min(root).key;
	}

	private Node min(Node x) {
		if (x.left == null)
			return x;
		else
			return min(x.left);
	}

	public Key max() {
		if (isEmpty())
			throw new NoSuchElementException("called max() with empty symbol table");
		return max(root).key;
	}

	private Node max(Node x) {
		if (x.right == null)
			return x;
		else
			return max(x.right);
	}

	public Key floor(Key key) {
		if (key == null)
			throw new NullPointerException("argument to floor() is null");
		if (isEmpty())
			throw new NoSuchElementException("called floor() with empty symbol table");
		Node x = floor(root, key);
		if (x == null)
			return null;
		else
			return x.key;
	}

	private Node floor(Node x, Key key) {
		if (x == null)
			return null;
		int cmp = key.compareTo(x.key);
		if (cmp == 0)
			return x;
		if (cmp < 0)
			return floor(x.left, key);
		Node t = floor(x.right, key);
		if (t != null)
			return t;
		else
			return x;
	}

	public Key ceiling(Key key) {
		if (key == null)
			throw new NullPointerException("argument to ceiling() is null");
		if (isEmpty())
			throw new NoSuchElementException("called ceiling() with empty symbol table");
		Node x = ceiling(root, key);
		if (x == null)
			return null;
		else
			return x.key;
	}

	private Node ceiling(Node x, Key key) {
		if (x == null)
			return null;
		int cmp = key.compareTo(x.key);
		if (cmp == 0)
			return x;
		if (cmp < 0) {
			Node t = ceiling(x.left, key);
			if (t != null)
				return t;
			else
				return x;
		}
		return ceiling(x.right, key);
	}

	public Key select(int k) {
		if (k < 0 || k >= size())
			throw new IllegalArgumentException();
		Node x = select(root, k);
		return x.key;
	}

	// Return key of rank k.
	private Node select(Node x, int k) {
		if (x == null)
			return null;
		int t = size(x.left);
		if (t > k)
			return select(x.left, k);
		else if (t < k)
			return select(x.right, k - t - 1);
		else
			return x;
	}

	public int rank(Key key) {
		if (key == null)
			throw new NullPointerException("argument to rank() is null");
		return rank(key, root);
	}

	// Number of keys in the subtree less than key.
	private int rank(Key key, Node x) {
		if (x == null)
			return 0;
		int cmp = key.compareTo(x.key);
		if (cmp < 0)
			return rank(key, x.left);
		else if (cmp > 0)
			return 1 + size(x.left) + rank(key, x.right);
		else
			return size(x.left);
	}

	public int size(Key lo, Key hi) {
		if (lo == null)
			throw new NullPointerException("first argument to size() is null");
		if (hi == null)
			throw new NullPointerException("second argument to size() is null");

		if (lo.compareTo(hi) > 0)
			return 0;
		if (contains(hi))
			return rank(hi) - rank(lo) + 1;
		else
			return rank(hi) - rank(lo);
	}

	public int height() {
		return height(root);
	}

	private int height(Node x) {
		if (x == null)
			return -1;
		return 1 + Math.max(height(x.left), height(x.right));
	}

}