Below is the syntax highlighted version of BST.java
from §3.2 Binary Search Trees.
/****************************************************************************** * Compilation: javac BST.java * Execution: java BST * Dependencies: StdIn.java StdOut.java Queue.java * Data files: https://algs4.cs.princeton.edu/32bst/tinyST.txt * * A symbol table implemented with a binary search tree. * * % more tinyST.txt * S E A R C H E X A M P L E * * % java BST < 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>, <em>select</em>, <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 an (unbalanced) <em>binary search tree</em>. * The <em>put</em>, <em>contains</em>, <em>remove</em>, <em>minimum</em>, * <em>maximum</em>, <em>ceiling</em>, <em>floor</em>, <em>select</em>, and * <em>rank</em> operations each take Θ(<em>n</em>) time in the worst * case, where <em>n</em> is the number of key-value pairs. * The <em>size</em> and <em>is-empty</em> operations take Θ(1) time. * The keys method takes Θ(<em>n</em>) time in the worst case. * Construction takes Θ(1) time. * <p> * For alternative implementations of the symbol table API, see {@link ST}, * {@link BinarySearchST}, {@link SequentialSearchST}, {@link RedBlackBST}, * {@link SeparateChainingHashST}, and {@link LinearProbingHashST}, * For additional documentation, see * <a href="https://algs4.cs.princeton.edu/32bst">Section 3.2</a> of * <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne. * * @author Robert Sedgewick * @author Kevin Wayne */ 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 size; // number of nodes in subtree public Node(Key key, Value val, int size) { this.key = key; this.val = val; this.size = size; } } /** * Initializes an empty symbol table. */ public BST() { } /** * Returns true if this symbol table is empty. * @return {@code true} if this symbol table is empty; {@code false} otherwise */ public boolean isEmpty() { return size() == 0; } /** * 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); } // return number of key-value pairs in BST rooted at x private int size(Node x) { if (x == null) return 0; else return x.size; } /** * 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) { if (key == null) throw new IllegalArgumentException("argument to contains() is null"); return get(key) != null; } /** * 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) { return get(root, key); } private Value get(Node x, Key key) { if (key == null) throw new IllegalArgumentException("calls get() with a null 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; } /** * 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("calls put() with a null key"); if (val == null) { delete(key); return; } root = put(root, key, val); assert check(); } 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.val = val; x.size = 1 + size(x.left) + size(x.right); return x; } /** * 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("Symbol table underflow"); root = deleteMin(root); assert check(); } private Node deleteMin(Node x) { if (x.left == null) return x.right; x.left = deleteMin(x.left); x.size = size(x.left) + size(x.right) + 1; return x; } /** * 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("Symbol table underflow"); root = deleteMax(root); assert check(); } private Node deleteMax(Node x) { if (x.right == null) return x.left; x.right = deleteMax(x.right); x.size = size(x.left) + size(x.right) + 1; return x; } /** * 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("calls delete() with a null key"); root = delete(root, key); assert check(); } 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.size = size(x.left) + size(x.right) + 1; return x; } /** * 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; } private Node min(Node x) { 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; } private Node max(Node x) { 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; } 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 floor2(Key key) { Key x = floor2(root, key, null); if (x == null) throw new NoSuchElementException("argument to floor() is too small"); else return x; } private Key floor2(Node x, Key key, Key best) { if (x == null) return best; int cmp = key.compareTo(x.key); if (cmp < 0) return floor2(x.left, key, best); else if (cmp > 0) return floor2(x.right, key, x.key); else return x.key; } /** * 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; } 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); } /** * 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 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); } /** * 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>(); keys(root, queue, lo, hi); return 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); } /** * 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)); } /** * Returns the keys in the BST in level order (for debugging). * * @return the keys in the BST in level order traversal */ public Iterable<Key> levelOrder() { Queue<Key> keys = new Queue<Key>(); Queue<Node> queue = new Queue<Node>(); queue.enqueue(root); while (!queue.isEmpty()) { Node x = queue.dequeue(); if (x == null) continue; keys.enqueue(x.key); queue.enqueue(x.left); queue.enqueue(x.right); } return keys; } /************************************************************************* * Check integrity of BST 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"); return isBST() && isSizeConsistent() && isRankConsistent(); } // 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; } /** * Unit tests the {@code BST} data type. * * @param args the command-line arguments */ public static void main(String[] args) { BST<String, Integer> st = new BST<String, Integer>(); for (int i = 0; !StdIn.isEmpty(); i++) { String key = StdIn.readString(); st.put(key, i); } for (String s : st.levelOrder()) StdOut.println(s + " " + st.get(s)); StdOut.println(); for (String s : st.keys()) StdOut.println(s + " " + st.get(s)); } }