实现映射

映射也就是Map,这里是指一对一的映射。也成为字典

  • 映射迎来存储键值数据对(Key,Value)
  • 根据Key寻找对应的Value
  • 用链表或者二分搜索树实现比较简单

BST的结构:

class Node {
  K key;
  V value;
  Node left;
  Node right;
}

链表的结构:

class Node {
  K key;
  V value;
  Node next;
}

即本来存储一个数据的节点现在存储两个(Key,Value).

定义Map接口:

public interface Map<K,V> {
    void add(K key,V value);
    V remove(K key);            //删除key对应的键值对,并返回值
    boolean contains(K key);  //是否存已在key
    V get(K key);               //获得key对应的value值
    void set(K key,V newValue); //更新值
    int getSize();
    boolean isEmpty();
}

基于链表实现Map

public class LinkedListMap<K,V> implements Map<K,V> {
    //定义节点
    private class Node {
        public K key;
        public V value;
        public Node next;
        public Node(K key,V value,Node node){
            this.key = key;
            this.value = value;
            this.next = null;
        }
        public Node(K key){
            this(key,null,null);
        }
        public Node(){
            this(null,null,null);
        }

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

    private Node dummyHead;
    private int size;
    public LinkedListMap(){
        dummyHead = new Node();
        size = 0;
    }

    @Override
    public void add(K key, V value) {
        Node node = getNode(key);
        if(node == null){
            dummyHead.next = new Node(key,value,dummyHead.next);
            size ++;
        }
        else //如果已经存在,则进行值的覆盖
            node.value = value;
    }

    @Override
    public V remove(K key) {
        Node prev = dummyHead;
        while(prev.next != null){
            if(prev.next.key.equals(key))
                break;
            prev = prev.next;
        }
        Node delNode;
        if(prev.next != null){
            delNode = prev.next;
            prev.next = delNode.next;
            delNode.next = null;
            return delNode.value;
        }
        return null;
    }

    @Override
    public boolean contains(K key) {
        return getNode(key) != null;
    }

    @Override
    public V get(K key) {
        Node result = getNode(key);
        return result == null ? null : result.value;
    }

    @Override
    public void set(K key, V newValue) {
        Node result = getNode(key);
        if(result != null)
            result.value = newValue;
        else
            throw new IllegalArgumentException(key + "doesn't exists");
    }

    @Override
    public int getSize() {
        return size;
    }

    @Override
    public boolean isEmpty() {
        return size == 0;
    }

    private Node getNode(K k){
        Node cur = dummyHead.next;
        while(cur != null){
            if(cur.key.equals(k))
                return cur;
            cur = cur.next;
        }
        return null;
    }
    
}

基于二分搜索树实现Map

public class BSTMap<K extends Comparable<K>,V> implements Map<K,V> {
    private class Node {
        public K key;
        public V value;
        public Node left,right;

        public Node(K key,V value){
            this.key = key;
            this.value = value;
            this.left = null;
            this.right = null;
        }
    }
    private Node root;
    private int size;
    @Override
    //向二分搜索树中添加新元素(key,value)
    public void add(K key, V value) {
        root = add(root,key,value);
    }

    @Override
    //借助辅助函数remove(Node node,K key)
    public V remove(K key) {
        Node node = getNode(root,key);
        if(node != null){
            root = remove(root,key);
            return node.value;
        }
        return null;
    }

    @Override
    public boolean contains(K key) {
        return getNode(root,key) != null ? true : false;
    }

    @Override
    public V get(K key) {
        Node node = getNode(root,key);
        return node == null ? null : node.value;
    }

    @Override
    public void set(K key, V newValue) {
        Node node = getNode(root,key);
        if(node == null)
            throw new IllegalArgumentException(key + "doesn't exist!");
        node.value = newValue;
    }

    @Override
    public int getSize() {
        return size;
    }

    @Override
    public boolean isEmpty() {
        return size == 0;
    }

    //向以node为根的二分搜索树中插入元素,采用递归算法
    //返回插入新节点后二分搜索树的根
    private Node add(Node node,K key,V value){
        if(node == null){
            size ++;
            return new Node(key,value);
        }

        if(key.compareTo(node.key) < 0){
            node.left = add(node.left,key,value);
        }
        if(key.compareTo(node.key) > 0){
            node.right = add(node.right,key,value);
        }
        else //key.compareTo(node.key)==0
            node.value = value;
        return node;
    }

    //返回以node为根节点的二分搜索树中,key所在的节点
    private Node getNode(Node node,K key){
        if(node == null){
            return null;
        }
        if(key.compareTo(node.key) == 0){
            return node;
        }
        if(key.compareTo(node.key) < 0){
            return getNode(node.left,key);
        }
        else{ //key.compareTo(node.key) > 0)
            return getNode(node.right,key);
        }
    }

    //删除掉以node为根的二分搜索树中键为key的节点
    //返回删除节点后新的二分搜索树的根
    private Node remove(Node node,K key){
        if(node == null)
            return null;
        if(key.compareTo(node.key) < 0){
            node.left = remove(node.left,key);
            return node;
        }
        else if(key.compareTo(node.key) > 0 ){
            node.right = remove(node.right,key);
            return node;
        }
        else{//key.compareTo(node.key) == 0
            //待删除左子树为空
            if(node.left == null){
                Node rightNode = node.right;
                node.right = null;
                size --;
                return rightNode;
            }
            //待删除右子树为空
            if(node.right == null){
                Node leftNode = node.left;
                node.left = null;
                size --;
                return leftNode;
            }
            //待删除左右子树均不为空
            //先找到比待删除节点大的最小节点,即待删除节点右子树的最小节点
            //用这个节点顶替待删除节点的位置
            Node successor = minmum(node.right);
            successor.right = removeMin(node.right);
            successor.left = node.left;

            node.left = node.right = null;

            return successor;
        }
    }

    //返回以node为根的二分搜索树的最小值所在的节点
    private Node minmum(Node node){
        if(node.left == null){
            return node;
        }
        return minmum(node.left);
    }

    //删除掉以node为根的二分搜索树中的最小节点
    //返回删除节点后的最新的二分搜索树的根
    private Node removeMin(Node node){
        if(node.left == null){
            Node rightNode = node.right;
            node.right = null;
            size --;
            return rightNode;
        }
        node.left = removeMin(node.left);
        return node;
    }
}

其实明显可以感受到BSTMap的存储速度要快于LinkedListMap

基于链表的Map和基于二分搜索树的Map的时间复杂度对比

操作 LinkedListMap BSTMap(平均) BSTMap最差)
增add O(n) O(logn) O(n)
删remove O(n) O(logn) O(n)
改set O(n) O(logn) O(n)
查get O(n) O(logn) O(n)
查contains O(n) O(logn) O(n)