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)); } } }