红黑树

参考资料：

• http://algs4.cs.princeton.edu/33balanced/RedBlackBST.java.html
• 算法导论第13章
• http://blog.csdn.net/skylinesky/article/details/6610950

代码：（我添上了toString，以及改写了main中的测试代码）

package trees;

/*************************************************************************
 *  Compilation:  javac RedBlackBST.java
 *  Execution:    java RedBlackBST < input.txt
 *  Dependencies: StdIn.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.
 *
 *  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.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Queue;
import java.util.Random;

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 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;
        }
        
        @Override
        public String toString() {
            return "["+key+","+val+","+(color==RED?"R":"B")+"]";
        }
    }

   /*************************************************************************
    *  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;
    }

   /*************************************************************************
    *  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;
    }

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

        return h;
    }

   /*************************************************************************
    *  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 (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.
    *************************************************************************/

    // 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
    public Iterable<Key> keys(Key lo, Key hi) {
        Queue<Key> queue = new LinkedList<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.offer(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);
    } 
    
    /**
     * in-order traverse
     * */
    @Override
    public String toString() {
        StringBuilder builder = new StringBuilder("[");
        inOrderTraverse(root, builder);
        builder.append("]");
        return builder.toString();
    }
    // helper for toString
    private void inOrderTraverse(Node node, StringBuilder builder) {
        if (node != null) {
            inOrderTraverse(node.left, builder);
            builder.append(node+",");
            inOrderTraverse(node.right, builder);
        }
    }


   /*****************************************************************************
    *  Test client
    *****************************************************************************/
    public static void main(String[] args) { 
        RedBlackBST<String, Integer> rbTree = new RedBlackBST<String, Integer>();
        List<String> keys = new LinkedList<>();
        List<Integer> vals = new LinkedList<>();
        int upperBound = 50;
        Random random = new Random();
        for (int i = 0; i < 6; ++i) {
            int val = random.nextInt(upperBound);
            keys.add(Integer.toString(val));
            vals.add(val);
        }
        
        System.out.println("----put----");
        
        for (int i = 0; i < keys.size(); i++) {
            rbTree.put(keys.get(i), vals.get(i));
            System.out.println(rbTree);
        }
        
        System.out.println("----get----");
        
        Collections.shuffle(keys);
        for (int i = 0; i < keys.size(); i++) {
            System.out.println(
                    rbTree.get(keys.get(i)));
        }
        
        System.out.println("----delete----");
        
        Collections.shuffle(keys);
        for (int i = 0; i < keys.size(); i++) {
            System.out.println(rbTree);
            rbTree.delete(keys.get(i));
        }
        
    }
}