目录

二叉查找树实现

今天是农历腊月二十四,也是过年前上班的最后一天,乘着工作不忙的功夫,把算法4公开课的第四周做个结束,本文总结第四周中第二节符号表(Symbol Tables)中的二叉查找树(Binary Search Tree)数据结构。

二叉查找树的性质

from : wiki

二叉查找树(英语:Binary Search Tree),也称二叉搜索树、有序二叉树(英语:ordered binary tree),排序二叉树(英语:sorted binary tree),是指一棵空树或者具有下列性质的二叉树:

若任意节点的左子树不空,则左子树上所有节点的值均小于它的根节点的值;

若任意节点的右子树不空,则右子树上所有节点的值均大于它的根节点的值;

任意节点的左、右子树也分别为二叉查找树;

没有键值相等的节点。

代码实现

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import edu.princeton.cs.algs4.Queue;

/**
 * 二叉查找树的实现
 *
 * @author elong
 * @version V1.0
 * @date 2018/1/23
 */
public class BST<Key extends Comparable<Key>, Value> {

private Node root;

private class Node {
    private final Key key;
    private Value value;
    private Node left, right;
    private int count;

    public Node(Key key, Value value) {
        this.key = key;
        this.value = value;
        this.count = 1;
    }

    @Override
    public String toString() {
        return key + " : " + value;
    }
}

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

private Node put(Node x, Key key, Value value) {
    if (x == null) {
        return new Node(key, value);
    }
    int cmp = key.compareTo(x.key);
    if (cmp < 0) {
        x.left = put(x.left, key, value);
    }
    if (cmp > 0) {
        x.right = put(x.right, key, value);
    }
    if (cmp == 0) {
        x.value = value;
    }
    x.count = 1 + size(x.left) + size(x.right);
    return x;
}

public Value get(Key key) {
    Node x = root;
    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.value;
        }
    }
    return null;
}

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

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

public Key minKey() {
    Node node = minKey(root);
    if (node == null) return null;
    return node.key;
}

private Node minKey(Node node) {
    if (node.left == null) {
        return node;
    }
    return minKey(node.left);
}

public Key maxKey() {
    Node node = maxKey(root);
    if (node == null) return null;
    return node.key;
}

private Node maxKey(Node node) {
    if (node.right == null) {
        return node;
    }
    return maxKey(node.right);
}

/**
 * 小于等于给定Key的最大值
 */
public Key floor(Key key) {
    Node node = floor(root, key);
    if (node == null) return null;
    return node.key;
}

private Node floor(Node node, Key key) {
    if (node == null) return null;
    int cmp = key.compareTo(node.key);
    if (cmp == 0) {
        return node;
    }
    if (cmp < 0) {
        return floor(node.left, key);
    }
    Node x = floor(node.right, key);
    if (x != null) {
        return x;
    }
    return node;
}

/**
 * 大于等于给定Key的最小值
 */
public Key ceiling(Key key) {
    Node node = ceiling(root, key);
    if (node == null) {
        return null;
    }
    return node.key;
}

private Node ceiling(Node node, Key key) {
    if (node == null) return null;
    int cmp = key.compareTo(node.key);
    if (cmp == 0) {
        return node;
    }
    if (cmp > 0) {
        return ceiling(node.right, key);
    }
    Node x = ceiling(node.left, key);
    if (x != null) {
        return x;
    }
    return node;
}

/**
 * 小于Key的Node的数量
 */
public int rank(Key key) {
    return rank(root, key);
}

private int rank(Node node, Key key) {
    if (node == null) {
        return 0;
    }
    int cmp = key.compareTo(node.key);
    if (cmp == 0) {
        return size(node.left);
    }
    if (cmp > 0) {
        return 1 + size(node.left) + rank(node.right, key);
    }
    return rank(node.left, key);
}

public Iterable<Key> keys() {
    Queue<Key> q = new Queue<>();
    inorder(root, q);
    return q;
}

private void inorder(Node node, Queue<Key> q) {
    if (node == null) {
        return;
    }
    inorder(node.left, q);
    q.enqueue(node.key);
    inorder(node.right, q);
}

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

private Node delete(Node node, Key key) {
    if (node == null) {
        return null;
    }
    int cmp = key.compareTo(node.key);
    if (cmp < 0) {
        node.left = delete(node.left, key);
    } else if (cmp > 0) {
        node.right = delete(node.right, key);
    } else {
        if (node.right == null) return node.left;
        if (node.left == null) return node.right;

        Node t = node;
        node = minKey(t.right);
        node.right = delMin(t.right);
        node.left = t.left;
    }
    node.count = 1 + size(node.left) + size(node.right);
    return node;
}

public void delMin() {
    delMin(root);
}

private Node delMin(Node node) {
    if (node.left == null) {
        return node.right;
    }
    node.left = delMin(node.left);
    node.count = 1 + size(node.left) + size(node.right);
    return node;
}

public static void main(String[] args) {
    BST<String, String> bst = new BST<>();
    bst.put("b", "b");
    bst.put("c", "c");
    bst.put("d", "d");
    bst.put("e", "e");
    bst.put("u", "r");
    bst.put("f", "r");
    bst.put("y", "r");
    bst.put("v", "r");
    bst.put("v", "r");
    bst.put("v", "r");
    bst.put("a", "r");


    System.out.println(bst.ceiling("a"));
    System.out.println(bst.maxKey());
    System.out.println(bst.size());
    System.out.println(bst.rank("z"));

    bst.delMin();

    for (String s : bst.keys()) {
        System.out.println(s);
    }

}

}

本人思考

  1. 递归思想的运用有待提高

  2. 在写代码前,大脑中一定要有清晰的数据结构,否者容易写到一半思路断了。

The end