原则：

• 一致性：如果a==b,则hash(a) == hash(b)
• 高效性：计算高效简便
• 均匀性：哈希值均匀分布
• 哈希函数：键转化成索引(空间换时间)

设计

冲突处理

代码示例

import java.util.TreeMap;
//哈希表
public class HashTable <K, V>{

    private static final int upperTol = 10;
    private static final int lowerTol = 2;

    private final int[] capacity = {53, 97, 193, 389, 769, 1543, 3079, 6151, 12289, 24593,
            49157, 98317, 196613, 393142, 786433, 1572869, 3145739, 6291469, 12582917, 25165843,
            50331653, 100663319, 201326611, 402653189, 805306457, 1610612741}; //1610612741 几乎int 型可承载的极限

    private int capacityIndex = 0;

    private TreeMap<K, V>[] hashtable;
    private int M;
    private int size;

    public HashTable(int M) {
        this.M = M;
        size = 0;
        hashtable = new TreeMap[M];
        for (int i = 0; i < M; i++) {
            hashtable[i]= new TreeMap<>();
        }
    }

    private int hash(K key) {
        //0x7fffffff 表示去除符号(可能为负数)
        return (key.hashCode() & 0x7fffffff) % M;
    }

    public int getSize() {
        return size;
    }

    public void add(K key, V value) {
        TreeMap<K, V> map = hashtable[hash(key)];
        if(map.containsKey(key))
            //修改
            map.put(key, value);
        else {
            map.put(key, value);
            size++;

            if( size >= upperTol * M && capacityIndex + 1 < capacity.length)
                capacityIndex ++;
                resize(capacity[capacityIndex]);
        }
    }

    public V remove(K key) {

        TreeMap<K, V> map = hashtable[hash(key)];
        V ret =  null;

        if (map.containsKey(key)) {
            ret = map.remove(key);
            size --;

            if( size < lowerTol * M && capacityIndex -1 > 0)
                capacityIndex --;
                resize(capacity[capacityIndex]);
        }
        return ret;
    }

    //动态扩容
    private void resize(int newM) {
        TreeMap<K, V>[] newHashTable = new TreeMap[newM];
        for (int i = 0; i < newM; I++)
            newHashTable[i] = new TreeMap<>();
        int oldM = M;
        this.M = newM;
        for (int i = 0; i < oldM; i++) {
            TreeMap<K, V> map = hashtable[I];
            for(K key: map.keySet())
                newHashTable[hash(key)].put(key, map.get(key));
        }
        this.hashtable = newHashTable;
    }


    public void set(K key, V value){
        TreeMap<K, V> map = hashtable[hash(key)];
        if (!map.containsKey(key))
            throw new IllegalArgumentException(key + "doesn't exist!");
        map.put(key, value);
    }

    public boolean contains(K key){
       return hashtable[hash(key)].containsKey(key);
    }

    public V get(K key) {
        return hashtable[hash(key)].get(key);
    }

}

时间复杂度

动态扩容

复杂度分析