红黑树-算法四 实现
算法四中给出了红黑树的构造代码：
import edu.princeton.cs.algs4.Queue; import edu.princeton.cs.algs4.StdOut; public class RedBlackLiteBST<Key extends Comparable<Key>, Value> { private static final boolean RED = true; private static final boolean BLACK = false; private Node root; // root of the BST private int n; // number of key-value pairs in 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 public Node(Key key, Value val, boolean color) { this.key = key; this.val = val; this.color = color; } } /*************************************************************************** * Standard BST search. ***************************************************************************/ // return value associated with the given key, or null if no such key exists public Value get(Key key) { return get(root, key); } public 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 in the symbol table with the given key? public boolean contains(Key key) { return get(key) != null; } /*************************************************************************** * Red-black tree insertion. ***************************************************************************/ public void put(Key key, Value val) { root = insert(root, key, val); root.color = BLACK; assert check(); } private Node insert(Node h, Key key, Value val) { if (h == null) { n++; return new Node(key, val, RED); } int cmp = key.compareTo(h.key); if (cmp < 0) h.left = insert(h.left, key, val); else if (cmp > 0) h.right = insert(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); return h; } /*************************************************************************** * Red-black tree helper functions. ***************************************************************************/ // is node x red (and non-null) ? private boolean isRed(Node x) { if (x == null) return false; return x.color == RED; } // rotate 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 = h.color; h.color = RED; return x; } // rotate 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 = h.color; h.color = RED; return x; } // precondition: two children are red, node is black // postcondition: two children are black, node is red private void flipColors(Node h) { assert !isRed(h) && isRed(h.left) && isRed(h.right); h.color = RED; h.left.color = BLACK; h.right.color = BLACK; } /*************************************************************************** * Utility functions. ***************************************************************************/ // return number of key-value pairs in symbol table public int size() { return n; } // is the symbol table empty? public boolean isEmpty() { return n == 0; } // 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)); } // return the smallest key; null if no such key public Key min() { return min(root); } private Key min(Node x) { Key key = null; while (x != null) { key = x.key; x = x.left; } return key; } // return the largest key; null if no such key public Key max() { return max(root); } private Key max(Node x) { Key key = null; while (x != null) { key = x.key; x = x.right; } return key; } /*************************************************************************** * Iterate using an inorder traversal. * Iterating through N elements takes O(N) time. ***************************************************************************/ public Iterable<Key> keys() { Queue<Key> queue = new Queue<Key>(); keys(root, queue); return queue; } private void keys(Node x, Queue<Key> queue) { if (x == null) return; keys(x.left, queue); queue.enqueue(x.key); keys(x.right, queue); } /*************************************************************************** * Check integrity of red-black tree data structure. ***************************************************************************/ private boolean check() { if (!isBST()) StdOut.println("Not in symmetric order"); if (!is23()) StdOut.println("Not a 2-3 tree"); if (!isBalanced()) StdOut.println("Not balanced"); return isBST() && 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); } // 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) { String test = "S E A R C H E X A M P L E"; String[] keys = test.split(" "); RedBlackLiteBST<String, Integer> st = new RedBlackLiteBST<String, Integer>(); for (int i = 0; i < keys.length; i++) st.put(keys[i], i); StdOut.println("size = " + st.size()); StdOut.println("min = " + st.min()); StdOut.println("max = " + st.max()); StdOut.println(); // print keys in order using allKeys() StdOut.println("Testing keys()"); StdOut.println("--------------------------------"); for (String s : st.keys()) StdOut.println(s + " " + st.get(s)); StdOut.println(); // insert N elements in order if one command-line argument supplied if (args.length == 0) return; int n = Integer.parseInt(args[0]); RedBlackLiteBST<Integer, Integer> st2 = new RedBlackLiteBST<Integer, Integer>(); for (int i = 0; i < n; i++) { st2.put(i, i); int h = st2.height(); StdOut.println("i = " + i + ", height = " + h + ", size = " + st2.size()); } StdOut.println("size = " + st2.size()); } }
