Below is the syntax highlighted version of RedBlackBST.java
from §3.3 Balanced Search Trees.
/****************************************************************************** * Compilation: javac RedBlackBST.java * Execution: java RedBlackBST < input.txt * Dependencies: StdIn.java StdOut.java * Data files: https://algs4.cs.princeton.edu/33balanced/tinyST.txt * * A symbol table implemented using a left-leaning red-black BST. * This is the 2-3 version. * * Note: commented out assertions because DrJava now enables assertions * by default. * * % more tinyST.txt * S E A R C H E X A M P L E * * % java RedBlackBST < tinyST.txt * A 8 * C 4 * E 12 * H 5 * L 11 * M 9 * P 10 * R 3 * S 0 * X 7 * ******************************************************************************/ import java.util.NoSuchElementException; /** * The {@code BST} class represents an ordered symbol table of generic * key-value pairs. * It supports the usual <em>put</em>, <em>get</em>, <em>contains</em>, * <em>delete</em>, <em>size</em>, and <em>is-empty</em> methods. * It also provides ordered methods for finding the <em>minimum</em>, * <em>maximum</em>, <em>floor</em>, and <em>ceiling</em>. * It also provides a <em>keys</em> method for iterating over all of the keys. * A symbol table implements the <em>associative array</em> abstraction: * when associating a value with a key that is already in the symbol table, * the convention is to replace the old value with the new value. * Unlike {@link java.util.Map}, this class uses the convention that * values cannot be {@code null}—setting the * value associated with a key to {@code null} is equivalent to deleting the key * from the symbol table. * <p> * It requires that * the key type implements the {@code Comparable} interface and calls the * {@code compareTo()} and method to compare two keys. It does not call either * {@code equals()} or {@code hashCode()}. * <p> * This implementation uses a <em>left-leaning red-black BST</em>. * The <em>put</em>, <em>get</em>, <em>contains</em>, <em>remove</em>, * <em>minimum</em>, <em>maximum</em>, <em>ceiling</em>, <em>floor</em>, * <em>rank</em>, and <em>select</em> operations each take * Θ(log <em>n</em>) time in the worst case, where <em>n</em> is the * number of key-value pairs in the symbol table. * The <em>size</em>, and <em>is-empty</em> operations take Θ(1) time. * The <em>keys</em> methods take * <em>O</em>(log <em>n</em> + <em>m</em>) time, where <em>m</em> is * the number of keys returned by the iterator. * Construction takes Θ(1) time. * <p> * For alternative implementations of the symbol table API, see {@link ST}, * {@link BinarySearchST}, {@link SequentialSearchST}, {@link BST}, * {@link SeparateChainingHashST}, {@link LinearProbingHashST}, and * {@link AVLTreeST}. * For additional documentation, see * <a href="https://algs4.cs.princeton.edu/33balanced">Section 3.3</a> of * <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne. * * @author Robert Sedgewick * @author Kevin Wayne */ public class RedBlackBST<Key extends Comparable<Key>, Value> { private static final boolean RED = true; private static final boolean BLACK = false; private Node root; // root of the BST // BST helper node data type private class Node { private Key key; // key private Value val; // associated data private Node left, right; // links to left and right subtrees private boolean color; // color of parent link private int size; // subtree count public Node(Key key, Value val, boolean color, int size) { this.key = key; this.val = val; this.color = color; this.size = size; } } /** * Initializes an empty symbol table. */ public RedBlackBST() { } /*************************************************************************** * 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.size; } /** * Returns the number of key-value pairs in this symbol table. * @return the number of key-value pairs in this symbol table */ public int size() { return size(root); } /** * Is this symbol table empty? * @return {@code true} if this symbol table is empty and {@code false} otherwise */ public boolean isEmpty() { return root == null; } /*************************************************************************** * Standard BST search. ***************************************************************************/ /** * Returns the value associated with the given key. * @param key the key * @return the value associated with the given key if the key is in the symbol table * and {@code null} if the key is not in the symbol table * @throws IllegalArgumentException if {@code key} is {@code null} */ public Value get(Key key) { if (key == null) throw new IllegalArgumentException("argument to get() is null"); 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; } /** * Does this symbol table contain the given key? * @param key the key * @return {@code true} if this symbol table contains {@code key} and * {@code false} otherwise * @throws IllegalArgumentException if {@code key} is {@code null} */ public boolean contains(Key key) { return get(key) != null; } /*************************************************************************** * Red-black tree insertion. ***************************************************************************/ /** * Inserts the specified key-value pair into the symbol table, overwriting the old * value with the new value if the symbol table already contains the specified key. * Deletes the specified key (and its associated value) from this symbol table * if the specified value is {@code null}. * * @param key the key * @param val the value * @throws IllegalArgumentException if {@code key} is {@code null} */ public void put(Key key, Value val) { if (key == null) throw new IllegalArgumentException("first argument to put() is null"); if (val == null) { delete(key); return; } root = put(root, key, val); root.color = BLACK; // assert check(); } // insert the key-value pair in the subtree rooted at h private 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.size = size(h.left) + size(h.right) + 1; return h; } /*************************************************************************** * Red-black tree deletion. ***************************************************************************/ /** * Removes the smallest key and associated value from the symbol table. * @throws NoSuchElementException if the symbol table is empty */ 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); } /** * Removes the largest key and associated value from the symbol table. * @throws NoSuchElementException if the symbol table is empty */ 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); } /** * Removes the specified key and its associated value from this symbol table * (if the key is in this symbol table). * * @param key the key * @throws IllegalArgumentException if {@code key} is {@code null} */ public void delete(Key key) { if (key == null) throw new IllegalArgumentException("argument to delete() is null"); if (!contains(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 get(h, key) != null; 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); // assert (h != null) && isRed(h.left) && !isRed(h.right); // for insertion only Node x = h.left; h.left = x.right; x.right = h; x.color = h.color; h.color = RED; x.size = h.size; h.size = 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); // assert (h != null) && isRed(h.right) && !isRed(h.left); // for insertion only Node x = h.right; h.right = x.left; x.left = h; x.color = h.color; h.color = RED; x.size = h.size; h.size = 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); flipColors(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); flipColors(h); } return h; } // restore red-black tree invariant private Node balance(Node h) { // assert (h != null); 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.size = size(h.left) + size(h.right) + 1; return h; } /*************************************************************************** * Utility functions. ***************************************************************************/ /** * Returns the height of the BST (for debugging). * @return the height of the BST (a 1-node tree has height 0) */ 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)); } /*************************************************************************** * Ordered symbol table methods. ***************************************************************************/ /** * Returns the smallest key in the symbol table. * @return the smallest key in the symbol table * @throws NoSuchElementException if the symbol table is empty */ public Key min() { if (isEmpty()) throw new NoSuchElementException("calls min() with empty symbol table"); 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); } /** * Returns the largest key in the symbol table. * @return the largest key in the symbol table * @throws NoSuchElementException if the symbol table is empty */ public Key max() { if (isEmpty()) throw new NoSuchElementException("calls max() with empty symbol table"); 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); } /** * Returns the largest key in the symbol table less than or equal to {@code key}. * @param key the key * @return the largest key in the symbol table less than or equal to {@code key} * @throws NoSuchElementException if there is no such key * @throws IllegalArgumentException if {@code key} is {@code null} */ public Key floor(Key key) { if (key == null) throw new IllegalArgumentException("argument to floor() is null"); if (isEmpty()) throw new NoSuchElementException("calls floor() with empty symbol table"); Node x = floor(root, key); if (x == null) throw new NoSuchElementException("argument to floor() is too small"); 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; } /** * Returns the smallest key in the symbol table greater than or equal to {@code key}. * @param key the key * @return the smallest key in the symbol table greater than or equal to {@code key} * @throws NoSuchElementException if there is no such key * @throws IllegalArgumentException if {@code key} is {@code null} */ public Key ceiling(Key key) { if (key == null) throw new IllegalArgumentException("argument to ceiling() is null"); if (isEmpty()) throw new NoSuchElementException("calls ceiling() with empty symbol table"); Node x = ceiling(root, key); if (x == null) throw new NoSuchElementException("argument to ceiling() is too large"); 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; } /** * Return the key in the symbol table of a given {@code rank}. * This key has the property that there are {@code rank} keys in * the symbol table that are smaller. In other words, this key is the * ({@code rank}+1)st smallest key in the symbol table. * * @param rank the order statistic * @return the key in the symbol table of given {@code rank} * @throws IllegalArgumentException unless {@code rank} is between 0 and * <em>n</em>–1 */ public Key select(int rank) { if (rank < 0 || rank >= size()) { throw new IllegalArgumentException("argument to select() is invalid: " + rank); } return select(root, rank); } // Return key in BST rooted at x of given rank. // Precondition: rank is in legal range. private Key select(Node x, int rank) { if (x == null) return null; int leftSize = size(x.left); if (leftSize > rank) return select(x.left, rank); else if (leftSize < rank) return select(x.right, rank - leftSize - 1); else return x.key; } /** * Return the number of keys in the symbol table strictly less than {@code key}. * @param key the key * @return the number of keys in the symbol table strictly less than {@code key} * @throws IllegalArgumentException if {@code key} is {@code null} */ public int rank(Key key) { if (key == null) throw new IllegalArgumentException("argument to rank() is null"); 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. ***************************************************************************/ /** * Returns all keys in the symbol table in ascending order as an {@code Iterable}. * To iterate over all of the keys in the symbol table named {@code st}, * use the foreach notation: {@code for (Key key : st.keys())}. * @return all keys in the symbol table in ascending order */ public Iterable<Key> keys() { if (isEmpty()) return new Queue<Key>(); return keys(min(), max()); } /** * Returns all keys in the symbol table in the given range in ascending order, * as an {@code Iterable}. * * @param lo minimum endpoint * @param hi maximum endpoint * @return all keys in the symbol table between {@code lo} * (inclusive) and {@code hi} (inclusive) in ascending order * @throws IllegalArgumentException if either {@code lo} or {@code hi} * is {@code null} */ public Iterable<Key> keys(Key lo, Key hi) { if (lo == null) throw new IllegalArgumentException("first argument to keys() is null"); if (hi == null) throw new IllegalArgumentException("second argument to keys() is null"); 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); } /** * Returns the number of keys in the symbol table in the given range. * * @param lo minimum endpoint * @param hi maximum endpoint * @return the number of keys in the symbol table between {@code lo} * (inclusive) and {@code hi} (inclusive) * @throws IllegalArgumentException if either {@code lo} or {@code hi} * is {@code null} */ public int size(Key lo, Key hi) { if (lo == null) throw new IllegalArgumentException("first argument to size() is null"); if (hi == null) throw new IllegalArgumentException("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); } /*************************************************************************** * Check integrity of red-black tree data structure. ***************************************************************************/ private boolean check() { if (!isBST()) StdOut.println("Not in symmetric order"); if (!isSizeConsistent()) StdOut.println("Subtree counts not consistent"); if (!isRankConsistent()) StdOut.println("Ranks not consistent"); if (!is23()) StdOut.println("Not a 2-3 tree"); if (!isBalanced()) StdOut.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: elegant solution due to Bob Dondero 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.size != 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); } /** * Unit tests the {@code RedBlackBST} data type. * * @param args the command-line arguments */ public static void main(String[] args) { RedBlackBST<String, Integer> st = new RedBlackBST<String, Integer>(); for (int i = 0; !StdIn.isEmpty(); i++) { String key = StdIn.readString(); st.put(key, i); } StdOut.println(); for (String s : st.keys()) StdOut.println(s + " " + st.get(s)); StdOut.println(); } }