CSC352 Red-Black Trees in Java

--D. Thiebaut (talk) 20:02, 25 September 2013 (EDT)

---

/*************************************************************************
 *  Compilation:  javac RedBlackTree.java
 *  Execution:    java RedBlackTree < input.txt
 *  Dependencies: System.In.java System.out.java  
 *  Data files:   http://algs4.cs.princeton.edu/33balanced/tinyST.txt  
 *    
 *  A symbol table implemented using a left-leaning red-black BST.
 *  This is the 2-3 version.
 *
 *  % more tinyST.txt
 *  S E A R C H E X A M P L E
 *  
 *  % java RedBlackTree < tinyST.txt
 *  A 8
 *  C 4
 *  E 12
 *  H 5
 *  L 11
 *  M 9
 *  P 10
 *  R 3
 *  S 0
 *  X 7
 *
 *  http://algs4.cs.princeton.edu/33balanced/RedBlackBST.java.html
 *************************************************************************/

import java.util.ArrayList;
import java.util.NoSuchElementException;

public class RedBlackTree<Key extends Comparable<Key>, Value> {

	private static final boolean RED = true;
	protected static final boolean BLACK = false;

	protected Node root; // root of the BST

	// BST helper node data type
	class Node {
		private Key key; // key
		private Value val; // associated data
		private Node left, right; // links to left and right subtrees
		boolean color; // color of parent link
		private int N; // subtree count

		public Node(Key key, Value val, boolean color, int N) {
			this.key = key;
			this.val = val;
			this.color = color;
			this.N = N;
			left = right = null;
		}
	}

	/*************************************************************************
	 * Node helper methods
	 *************************************************************************/
	// is node x red; false if x is null ?
	private boolean isRed(Node x) {
		if (x == null)
			return false;
		return (x.color == RED);
	}

	// number of node in subtree rooted at x; 0 if x is null
	private int size(Node x) {
		if (x == null)
			return 0;
		return x.N;
	}

	/*************************************************************************
	 * Size methods
	 *************************************************************************/

	// return number of key-value pairs in this symbol table
	public int size() {
		return size(root);
	}

	// is this symbol table empty?
	public boolean isEmpty() {
		return root == null;
	}

	public RedBlackTree<Integer, Segment> deepCopy() {
		RedBlackTree<Integer, Segment> copy = new RedBlackTree<Integer, Segment>();
		for (Key key : keys())
			copy.put((Integer) key, ((Segment) get(key)).deepCopy());
		return copy;
	}

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

	public int noItems(Node x) {
		if (x == null)
			return 0;
		int sum = 0;
		sum += noItems(x.left);
		sum += noItems(x.right);
		return sum + 1;
	}

	/*************************************************************************
	 * Standard BST search
	 *************************************************************************/

	// value associated with the given key; null if no such key
	public Value get(Key key) {
		return get(root, key);
	}

	// value associated with the given key in subtree rooted at x; null if no
	// such key
	private Value get(Node x, Key key) {
		while (x != null) {
			int cmp = key.compareTo(x.key);
			if (cmp < 0)
				x = x.left;
			else if (cmp > 0)
				x = x.right;
			else
				return x.val;
		}
		return null;
	}

	/*************************************************************************
	 * DT's Helper Methods
	 *************************************************************************/

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

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

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

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

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

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

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

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

	// the Segments between lo and hi, as an Iterable
	public Iterable<Value> valuesBetweenKeys(Key lo, Key hi) {
		Queue<Value> queue = new Queue<Value>();
		valuesBetweenKeys(root, queue, lo, hi);
		return queue;
	}

	// add the keys between lo and hi in the subtree rooted at x
	// to the queue
	private void valuesBetweenKeys(Node x, Queue<Value> queue, Key lo, Key hi) {
		if (x == null)
			return;
		int cmplo = lo.compareTo(x.key);
		int cmphi = hi.compareTo(x.key);
		if (cmplo < 0)
			valuesBetweenKeys(x.left, queue, lo, hi);
		if (cmplo <= 0 && cmphi >= 0)
			queue.enqueue(x.val);
		if (cmphi > 0)
			valuesBetweenKeys(x.right, queue, lo, hi);
	}

	/*************************************************************************
	 * Standard search
	 *************************************************************************/

	// is there a key-value pair with the given key?
	public boolean contains(Key key) {
		return (get(key) != null);
	}

	// is there a key-value pair with the given key in the subtree rooted at x?
	private boolean contains(Node x, Key key) {
		return (get(x, key) != null);
	}

	/*************************************************************************
	 * Red-black insertion
	 *************************************************************************/

	// insert the key-value pair; overwrite the old value with the new value
	// if the key is already present
	public void put(Key key, Value val) {
		root = put(root, key, val);
		root.color = BLACK;
		assert check();
	}

	// insert the key-value pair in the subtree rooted at h
	protected Node put(Node h, Key key, Value val) {
		if (h == null)
			return new Node(key, val, RED, 1);

		int cmp = key.compareTo(h.key);
		if (cmp < 0)
			h.left = put(h.left, key, val);
		else if (cmp > 0)
			h.right = put(h.right, key, val);
		else
			h.val = val;

		// fix-up any right-leaning links
		if (isRed(h.right) && !isRed(h.left))
			h = rotateLeft(h);
		if (isRed(h.left) && isRed(h.left.left))
			h = rotateRight(h);
		if (isRed(h.left) && isRed(h.right))
			flipColors(h);
		h.N = size(h.left) + size(h.right) + 1;

		return h;
	}

	// insert the key-value pair; overwrite the old value with the new value
	// if the key is already present

	/*************************************************************************
	 * Red-black deletion
	 *************************************************************************/

	// delete the key-value pair with the minimum key
	public void deleteMin() {
		if (isEmpty())
			throw new NoSuchElementException("BST underflow");

		// if both children of root are black, set root to red
		if (!isRed(root.left) && !isRed(root.right))
			root.color = RED;

		root = deleteMin(root);
		if (!isEmpty())
			root.color = BLACK;
		assert check();
	}

	// delete the key-value pair with the minimum key rooted at h
	private Node deleteMin(Node h) {
		if (h.left == null)
			return null;

		if (!isRed(h.left) && !isRed(h.left.left))
			h = moveRedLeft(h);

		h.left = deleteMin(h.left);
		return balance(h);
	}

	// delete the key-value pair with the maximum key
	public void deleteMax() {
		if (isEmpty())
			throw new NoSuchElementException("BST underflow");

		// if both children of root are black, set root to red
		if (!isRed(root.left) && !isRed(root.right))
			root.color = RED;

		root = deleteMax(root);
		if (!isEmpty())
			root.color = BLACK;
		assert check();
	}

	// delete the key-value pair with the maximum key rooted at h
	private Node deleteMax(Node h) {
		if (isRed(h.left))
			h = rotateRight(h);

		if (h.right == null)
			return null;

		if (!isRed(h.right) && !isRed(h.right.left))
			h = moveRedRight(h);

		h.right = deleteMax(h.right);

		return balance(h);
	}

	// delete the key-value pair with the given key
	public void delete(Key key) {
		if (!contains(key)) {
			System.err.println("symbol table does not contain " + key);
			return;
		}

		// if both children of root are black, set root to red
		if (!isRed(root.left) && !isRed(root.right))
			root.color = RED;

		root = delete(root, key);
		if (!isEmpty())
			root.color = BLACK;
		assert check();
	}

	// delete the key-value pair with the given key rooted at h
	private Node delete(Node h, Key key) {
		assert contains(h, key);

		if (key.compareTo(h.key) < 0) {
			if (!isRed(h.left) && !isRed(h.left.left))
				h = moveRedLeft(h);
			h.left = delete(h.left, key);
		} else {
			if (isRed(h.left))
				h = rotateRight(h);
			if (key.compareTo(h.key) == 0 && (h.right == null))
				return null;
			if (!isRed(h.right) && !isRed(h.right.left))
				h = moveRedRight(h);
			if (key.compareTo(h.key) == 0) {
				Node x = min(h.right);
				h.key = x.key;
				h.val = x.val;
				// h.val = get(h.right, min(h.right).key);
				// h.key = min(h.right).key;
				h.right = deleteMin(h.right);
			} else
				h.right = delete(h.right, key);
		}
		return balance(h);
	}

	/*************************************************************************
	 * red-black tree helper functions
	 *************************************************************************/

	// make a left-leaning link lean to the right
	private Node rotateRight(Node h) {
		assert (h != null) && isRed(h.left);
		Node x = h.left;
		h.left = x.right;
		x.right = h;
		x.color = x.right.color;
		x.right.color = RED;
		x.N = h.N;
		h.N = size(h.left) + size(h.right) + 1;
		return x;
	}

	// make a right-leaning link lean to the left
	private Node rotateLeft(Node h) {
		assert (h != null) && isRed(h.right);
		Node x = h.right;
		h.right = x.left;
		x.left = h;
		x.color = x.left.color;
		x.left.color = RED;
		x.N = h.N;
		h.N = size(h.left) + size(h.right) + 1;
		return x;
	}

	// flip the colors of a node and its two children
	private void flipColors(Node h) {
		// h must have opposite color of its two children
		assert (h != null) && (h.left != null) && (h.right != null);
		assert (!isRed(h) && isRed(h.left) && isRed(h.right))
				|| (isRed(h) && !isRed(h.left) && !isRed(h.right));
		h.color = !h.color;
		h.left.color = !h.left.color;
		h.right.color = !h.right.color;
	}

	// Assuming that h is red and both h.left and h.left.left
	// are black, make h.left or one of its children red.
	private Node moveRedLeft(Node h) {
		assert (h != null);
		assert isRed(h) && !isRed(h.left) && !isRed(h.left.left);

		flipColors(h);
		if (isRed(h.right.left)) {
			h.right = rotateRight(h.right);
			h = rotateLeft(h);
		}
		return h;
	}

	// Assuming that h is red and both h.right and h.right.left
	// are black, make h.right or one of its children red.
	private Node moveRedRight(Node h) {
		assert (h != null);
		assert isRed(h) && !isRed(h.right) && !isRed(h.right.left);
		flipColors(h);
		if (isRed(h.left.left)) {
			h = rotateRight(h);
		}
		return h;
	}

	// restore red-black tree invariant
	private Node balance(Node h) {
		assert (h != null);

		if (isRed(h.right))
			h = rotateLeft(h);
		if (isRed(h.left) && isRed(h.left.left))
			h = rotateRight(h);
		if (isRed(h.left) && isRed(h.right))
			flipColors(h);

		h.N = size(h.left) + size(h.right) + 1;
		return h;
	}

	/*************************************************************************
	 * Utility functions
	 *************************************************************************/

	// height of tree; 0 if empty
	public int height() {
		return height(root);
	}

	private int height(Node x) {
		if (x == null)
			return 0;
		return 1 + Math.max(height(x.left), height(x.right));
	}

	/*************************************************************************
	 * Ordered symbol table methods.
	 *************************************************************************/

	// the smallest key; null if no such key
	public Key min() {
		if (isEmpty())
			return null;
		return min(root).key;
	}

	// the smallest key in subtree rooted at x; null if no such key
	private Node min(Node x) {
		assert x != null;
		if (x.left == null)
			return x;
		else
			return min(x.left);
	}

	// the largest key; null if no such key
	public Key max() {
		if (isEmpty())
			return null;
		return max(root).key;
	}

	// the largest key in the subtree rooted at x; null if no such key
	private Node max(Node x) {
		assert x != null;
		if (x.right == null)
			return x;
		else
			return max(x.right);
	}

	// the largest key less than or equal to the given key
	public Key floor(Key key) {
		Node x = floor(root, key);
		if (x == null)
			return null;
		else
			return x.key;
	}

	// the largest key in the subtree rooted at x less than or equal to the
	// given 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;
	}

	// the smallest key greater than or equal to the given key
	public Key ceiling(Key key) {
		Node x = ceiling(root, key);
		if (x == null)
			return null;
		else
			return x.key;
	}

	// the smallest key in the subtree rooted at x greater than or equal to the
	// given 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)
			return ceiling(x.right, key);
		Node t = ceiling(x.left, key);
		if (t != null)
			return t;
		else
			return x;
	}

	// the key of rank k
	public Key select(int k) {
		if (k < 0 || k >= size())
			return null;
		Node x = select(root, k);
		return x.key;
	}

	// the key of rank k in the subtree rooted at x
	private Node select(Node x, int k) {
		assert x != null;
		assert k >= 0 && k < size(x);
		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;
	}

	// number of keys less than key
	public int rank(Key key) {
		return rank(key, root);
	}

	// number of keys less than key in the subtree rooted at x
	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);
	}

	/***********************************************************************
	 * Range count and range search.
	 ***********************************************************************/

	// all of the keys, as an Iterable
	public Iterable<Key> keys() {
		return keys(min(), max());
	}

	// the keys between lo and hi, as an Iterable. lo and hi are included in the
	// returned
	// iterable if they are part of the keys.
	public Iterable<Key> keys(Key lo, Key hi) {
		Queue<Key> queue = new Queue<Key>();
		// if (isEmpty() || lo.compareTo(hi) > 0) return queue;
		keys(root, queue, lo, hi);
		return queue;
	}

	// add the keys between lo and hi in the subtree rooted at x
	// to the queue
	private void keys(Node x, Queue<Key> queue, Key lo, Key hi) {
		if (x == null)
			return;
		int cmplo = lo.compareTo(x.key);
		int cmphi = hi.compareTo(x.key);
		if (cmplo < 0)
			keys(x.left, queue, lo, hi);
		if (cmplo <= 0 && cmphi >= 0)
			queue.enqueue(x.key);
		if (cmphi > 0)
			keys(x.right, queue, lo, hi);
	}

	// number keys between lo and hi
	public int size(Key lo, Key hi) {
		if (lo.compareTo(hi) > 0)
			return 0;
		if (contains(hi))
			return rank(hi) - rank(lo) + 1;
		else
			return rank(hi) - rank(lo);
	}

	/*************************************************************************
	 * Check integrity of red-black BST data structure
	 *************************************************************************/
	private boolean check() {
		if (!isBST())
			System.out.println("Not in symmetric order");
		if (!isSizeConsistent())
			System.out.println("Subtree counts not consistent");
		if (!isRankConsistent())
			System.out.println("Ranks not consistent");
		if (!is23())
			System.out.println("Not a 2-3 tree");
		if (!isBalanced())
			System.out.println("Not balanced");
		return isBST() && isSizeConsistent() && isRankConsistent() && is23()
				&& isBalanced();
	}

	// does this binary tree satisfy symmetric order?
	// Note: this test also ensures that data structure is a binary tree since
	// order is strict
	private boolean isBST() {
		return isBST(root, null, null);
	}

	// is the tree rooted at x a BST with all keys strictly between min and max
	// (if min or max is null, treat as empty constraint)
	// Credit: Bob Dondero's elegant solution
	private boolean isBST(Node x, Key min, Key max) {
		if (x == null)
			return true;
		if (min != null && x.key.compareTo(min) <= 0)
			return false;
		if (max != null && x.key.compareTo(max) >= 0)
			return false;
		return isBST(x.left, min, x.key) && isBST(x.right, x.key, max);
	}

	// are the size fields correct?
	private boolean isSizeConsistent() {
		return isSizeConsistent(root);
	}

	private boolean isSizeConsistent(Node x) {
		if (x == null)
			return true;
		if (x.N != size(x.left) + size(x.right) + 1)
			return false;
		return isSizeConsistent(x.left) && isSizeConsistent(x.right);
	}

	// check that ranks are consistent
	private boolean isRankConsistent() {
		for (int i = 0; i < size(); i++)
			if (i != rank(select(i)))
				return false;
		for (Key key : keys())
			if (key.compareTo(select(rank(key))) != 0)
				return false;
		return true;
	}

	// Does the tree have no red right links, and at most one (left)
	// red links in a row on any path?
	private boolean is23() {
		return is23(root);
	}

	private boolean is23(Node x) {
		if (x == null)
			return true;
		if (isRed(x.right))
			return false;
		if (x != root && isRed(x) && isRed(x.left))
			return false;
		return is23(x.left) && is23(x.right);
	}

	// do all paths from root to leaf have same number of black edges?
	private boolean isBalanced() {
		int black = 0; // number of black links on path from root to min
		Node x = root;
		while (x != null) {
			if (!isRed(x))
				black++;
			x = x.left;
		}
		return isBalanced(root, black);
	}

	// does every path from the root to a leaf have the given number of black
	// links?
	private boolean isBalanced(Node x, int black) {
		if (x == null)
			return black == 0;
		if (!isRed(x))
			black--;
		return isBalanced(x.left, black) && isBalanced(x.right, black);
	}

	/*****************************************************************************
	 * Test client
	 *****************************************************************************/
	public static void main(String[] args) {

		RedBlackTree<Integer, Segment> st = new RedBlackTree<Integer, Segment>();
		st.put(2, new Segment(2, 4));
		st.put(7, new Segment(7, 1));
		st.put(1, new Segment(1, 2));
		st.put(9, new Segment(9, 3));
		st.put(13, new Segment(13, 2));

		for (int x : st.keys())
			System.out.println(x + " --> " + st.get(x));

		for (int i = 0; i < 20; i++) {
			Segment x = st.getGreaterThanOrEqual(i);
			System.out.println(x + " greater than or equal to " + i);
		}

		System.out.println("\n\n");

		for (int i = 0; i < 20; i++) {
			Segment x = st.getLessThanOrEqual(i);
			System.out.println(x + " less than or equal to " + i);
		}

		System.out.println("\n\n");

		for (int i = 0; i < 20; i++) {
			Segment x = st.getGreaterThan(i);
			System.out.println(x + " greater than  " + i);
		}

		System.out.println("\n\n");

		for (int i = 0; i < 20; i++) {
			Segment x = st.getLessThan(i);
			System.out.println(x + " less than  " + i);
		}

		for (int x : st.keys(3, 12)) {
			System.out.println("st.keys(3,12) --> " + x);
		}

	}

}