查找-二叉查找树（1）

1 二叉查找树的基本性质和 代码实现

package com.jimmysun.algorithms.chapter3_2;

import com.jimmysun.algorithms.chapter1_3.Queue;

public class BST<Key extends Comparable<Key>, Value> {
    private Node root;

    private class Node {
        private Key key;
        private Value val;
        private Node left, right;
        private int N;

        public Node(Key key, Value val, int N) {
            this.key = key;
            this.val = val;
            this.N = N;
        }
    }

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

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

    public Value get(Key key) {
        return get(root, key);
    }

    private Value get(Node x, Key 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;
        }
    }

    public void put(Key key, Value val) {
        root = put(root, key, val);
    }

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

    public Key max() {
        return max(root).key;
    }

    private Node max(Node x) {
        if (x.right == null) {
            return x;
        }
        return max(x.right);
    }

    public Key min() {
        return min(root).key;
    }

    private Node min(Node x) {
        if (x.left == null) {
            return x;
        }
        return min(x.left);
    }

    public Key floor(Key key) {
        Node x = floor(root, key);
        if (x == null) {
            return null;
        }
        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 ceiling(Key key) {
        Node x = ceiling(root, key);
        if (x == null) {
            return null;
        }
        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) {
            return floor(x.right, key);
        }
        Node t = floor(x.left, key);
        if (t != null) {
            return t;
        } else {
            return x;
        }
    }

    public Key select(int k) {
        return select(root, k).key;
    }

    private Node select(Node x, int k) {
        if (x == null) {
            return null;
        }
        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;
        }
    }

    public int rank(Key key) {
        return rank(key, root);
    }

    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);
        }
    }

    public void deleteMin() {
        root = deleteMin(root);
    }

    private Node deleteMin(Node x) {
        if (x.left == null) {
            return x.right;
        }
        x.left = deleteMin(x.left);
        x.N = size(x.left) + size(x.right) + 1;
        return x;
    }

    public void deleteMax() {
        root = deleteMax(root);
    }

    private Node deleteMax(Node x) {
        if (x.right == null) {
            return x.left;
        }
        x.right = deleteMax(x.right);
        x.N = size(x.left) + size(x.right) + 1;
        return x;
    }

    public void delete(Key key) {
        root = delete(root, key);
    }

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

    public Iterable<Key> keys() {
        return keys(min(), max());
    }

    public Iterable<Key> keys(Key lo, Key hi) {
        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);
        }
    }

    // Exercise 3.2.6
    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));
    }

    // Exercise 3.2.32
    private boolean isBST() {
        return isBST(root, null, null);
    }

    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);
    }

    /**
     * Exercise 3.2.33
     *
     * @return
     */
    public boolean isRankConsistent() {
        for (int i = 0; i < size(); i++) {
            if (i != rank(select(i))) {
                return false;
            }
        }
        for (Key key : keys()) {
            if (!key.equals(select(rank(key)))) {
                return false;
            }
        }
        return true;
    }
}