java平衡二叉树代码

Java中的平衡二叉树实现通常是基于红黑树算法，这是一种自平衡二叉查找树。在红黑树中，每个节点都被标记为红色或黑色，并满足以下特性：
1. 根节点是黑色的。
2. 所有叶子节点都是黑色的（叶子节点为NIL节点）。
3. 如果一个节点是红色的，则它的两个子节点都是黑色的。
4. 从任意节点到其每个叶子节点的所有路径都包含相同数目的黑色节点。

这些特性确保了红黑树是平衡的，因为任意路径上的黑色节点数目相同。插入和删除操作可以通过对颜色和结构进行适当的旋转来维护树的平衡性。

下面是一个简单的Java平衡二叉树实现示例：

import java.util.*;

public class RedBlackTree<K extends Comparable<K>, V> {

    private static final boolean RED   = true;
    private static final boolean BLACK = false;

    private Node root;

    private class Node {
        K key;
        V val;
        Node left, right;
        int size;
        boolean color;

        public Node(K key, V val, boolean color, int size) {
            this.key = key;
            this.val = val;
            this.color = color;
            this.size = size;
        }
    }

    private boolean isRed(Node x) {
        if (x == null) return false;
        return x.color == RED;
    }

    private int size(Node x) {
        if (x == null) return 0;
        return x.size;
    }    

    public int size() {
        return size(root);
    }

    public boolean isEmpty() {
        return root == null;
    }

    public V get(K key) {
        if (key == null) throw new IllegalArgumentException("argument to get() is null");
        return get(root, key);
    }

    private V get(Node x, K 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;
    }

    public boolean contains(K key) {
        return get(key) != null;
    }

    public void put(K key, V 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;
    }

    private Node put(Node h, K key, V 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;
    }

    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;
    }

    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);
    }

    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;
    }

    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);
    }

    public void delete(K 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;
    }

    private Node delete(Node h, K 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.right = deleteMin(h.right);
            }
            else h.right = delete(h.right, key);
        }
        return balance(h);
    }

    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.size = h.size;
        h.size = size(h.left) + size(h.right) + 1;
        return x;
    }

    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.size = h.size;
        h.size = size(h.left) + size(h.right) + 1;
        return x;
    }

    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;
    }

    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;
    }

    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;
     }

     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.size = size(h.left) + size(h.right) + 1;
         return h;
     }

     public K 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); 
     } 

     public K 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); 
     } 

     public Iterable<K> keys() {
         if (isEmpty()) return new LinkedList<K>();
         return keys(min(), max());
     }

     public Iterable<K> keys(K lo, K 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<K> queue = new LinkedList<K>();
         keys(root, queue, lo, hi);
         return queue;
     } 

     private void keys(Node x, Queue<K> queue, K lo, K 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); 
     }
}