雜湊查詢演算法

（一）用雜湊函式將被查詢的鍵轉化為陣列的索引 （二）處理碰撞衝突：拉鍊法和線性探測法 散列表是演算法在時間和空間上作出權衡的經典例子

雜湊函式

特點

（一）易於計算 （二）均勻分佈

基於拉鍊法的散列表

（一） 將大小為M的陣列中的每個元素指向一條連結串列，連結串列中每個節點都儲存了雜湊值為該元素索引的鍵值對 （二） 選擇足夠大的M，使得所有連結串列都儘可能的的高效查詢 （三） 查詢分兩步：（1）根據雜湊值找到對應的連結串列（2）沿著列表順序查詢相應的鍵

實現

package com.lwl.algorithm.hash;

import com.lwl.algorithm.linkedlist.Queue;
import com.lwl.algorithm.stack.StdIn;
import com.lwl.algorithm.stack.StdOut;
import com.lwl.algorithm.tree.SequentialSearchST;

/**
 * @author liuweilong
 * @ClassName: SeparateChainingHashST
 * @Description: 基於拉鍊法的散列表
 * @Version 1.0
 **/
public class SeparateChainingHashST<Key, Value> {
    private static final int INIT_CAPACITY = 4;

    private int n;                                // number of key-value pairs
    private int m;                                // hash table size
    private SequentialSearchST<Key, Value>[] st;  // array of linked-list symbol tables


    /**
     * Initializes an empty symbol table.
     */
    public SeparateChainingHashST() {
        this(INIT_CAPACITY);
    }

    /**
     * Initializes an empty symbol table with {@code m} chains.
     * @param m the initial number of chains
     */
    public SeparateChainingHashST(int m) {
        this.m = m;
        st = (SequentialSearchST<Key, Value>[]) new SequentialSearchST[m];
        for (int i = 0; i < m; i++)
            st[i] = new SequentialSearchST<Key, Value>();
    }

    // resize the hash table to have the given number of chains,
    // rehashing all of the keys
    private void resize(int chains) {
        SeparateChainingHashST<Key, Value> temp = new SeparateChainingHashST<Key, Value>(chains);
        for (int i = 0; i < m; i++) {
            for (Key key : st[i].keys()) {
                temp.put(key, st[i].get(key));
            }
        }
        this.m  = temp.m;
        this.n  = temp.n;
        this.st = temp.st;
    }

    // hash value between 0 and m-1
    private int hash(Key key) {
        return (key.hashCode() & 0x7fffffff) % m;
    }

    /**
     * Returns the number of key-value pairs in this symbol table.
     *
     * @return the number of key-value pairs in this symbol table
     */
    public int size() {
        return n;
    }

    /**
     * Returns true if this symbol table is empty.
     *
     * @return {@code true} if this symbol table is empty;
     *         {@code false} otherwise
     */
    public boolean isEmpty() {
        return size() == 0;
    }

    /**
     * Returns true if this symbol table contains the specified key.
     *
     * @param  key the key
     * @return {@code true} if this symbol table contains {@code key};
     *         {@code false} otherwise
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public boolean contains(Key key) {
        if (key == null) throw new IllegalArgumentException("argument to contains() is null");
        return get(key) != null;
    }

    /**
     * Returns the value associated with the specified key in this symbol table.
     *
     * @param  key the key
     * @return the value associated with {@code key} in the symbol table;
     *         {@code null} if no such value
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public Value get(Key key) {
        if (key == null) throw new IllegalArgumentException("argument to get() is null");
        int i = hash(key);
        return st[i].get(key);
    }

    /**
     * Inserts the specified key-value pair into the symbol table, overwriting the old
     * value with the new value if the symbol table already contains the specified key.
     * Deletes the specified key (and its associated value) from this symbol table
     * if the specified value is {@code null}.
     *
     * @param  key the key
     * @param  val the value
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public void put(Key key, Value val) {
        if (key == null) throw new IllegalArgumentException("first argument to put() is null");
        if (val == null) {
            delete(key);
            return;
        }

        // double table size if average length of list >= 10
        if (n >= 10*m) resize(2*m);

        int i = hash(key);
        if (!st[i].contains(key)) n++;
        st[i].put(key, val);
    }

    /**
     * Removes the specified key and its associated value from this symbol table
     * (if the key is in this symbol table).
     *
     * @param  key the key
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public void delete(Key key) {
        if (key == null) throw new IllegalArgumentException("argument to delete() is null");

        int i = hash(key);
        if (st[i].contains(key)) n--;
        st[i].delete(key);

        // halve table size if average length of list <= 2
        if (m > INIT_CAPACITY && n <= 2*m) resize(m/2);
    }

    // return keys in symbol table as an Iterable
    public Iterable<Key> keys() {
        Queue<Key> queue = new Queue<Key>();
        for (int i = 0; i < m; i++) {
            for (Key key : st[i].keys())
                queue.enqueue(key);
        }
        return queue;
    }


    /**
     * Unit tests the {@code SeparateChainingHashST} data type.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {
        SeparateChainingHashST<String, Integer> st = new SeparateChainingHashST<String, Integer>();
        for (int i = 0; !StdIn.isEmpty(); i++) {
            String key = StdIn.readString();
            st.put(key, i);
        }

        // print keys
        for (String s : st.keys())
            StdOut.println(s + " " + st.get(s));

    }

}

 

基於線性探測法的散列表

（一）用大小為M的陣列儲存N個鍵值對，M>N，依靠陣列中空缺位解決碰撞衝突，基於這種策略的所有方法統稱為開發地址散列表 （二）開放地址法中最簡單的方法為線性探測法：當碰撞傳送時（一個鍵的雜湊值已經被另一個不同的鍵佔用），直接檢查散列表中的下一個位置（將索引值加1） （三）線性探測會產生三種結果：（1）命中（2）未命中，鍵未空（3）繼續查詢

package com.lwl.algorithm.hash;

import com.lwl.algorithm.stack.StdIn;
import com.lwl.algorithm.stack.StdOut;

/**
 * @author liuweilong
 * @ClassName: LinearProbingHashST 基於線性探測的符號表
 * @Description: TODO
 * @Version 1.0
 **/
public class LinearProbingHashST<Key, Value> {
    private static final int INIT_CAPACITY = 4;

    private int n;           // number of key-value pairs in the symbol table 鍵值對數量
    private int m;           // size of linear probing table 表大小
    private Key[] keys;      // the keys
    private Value[] vals;    // the values


    /**
     * Initializes an empty symbol table.
     */
    public LinearProbingHashST() {
        this(INIT_CAPACITY);
    }

    /**
     * Initializes an empty symbol table with the specified initial capacity.
     *
     * @param capacity the initial capacity
     */
    public LinearProbingHashST(int capacity) {
        m = capacity;
        n = 0;
        keys = (Key[])   new Object[m];
        vals = (Value[]) new Object[m];
    }

    /**
     * Returns the number of key-value pairs in this symbol table.
     *
     * @return the number of key-value pairs in this symbol table
     */
    public int size() {
        return n;
    }

    /**
     * Returns true if this symbol table is empty.
     *
     * @return {@code true} if this symbol table is empty;
     *         {@code false} otherwise
     */
    public boolean isEmpty() {
        return size() == 0;
    }

    /**
     * Returns true if this symbol table contains the specified key.
     *
     * @param  key the key
     * @return {@code true} if this symbol table contains {@code key};
     *         {@code false} otherwise
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public boolean contains(Key key) {
        if (key == null) throw new IllegalArgumentException("argument to contains() is null");
        return get(key) != null;
    }

    // hash function for keys - returns value between 0 and M-1
    private int hash(Key key) {
        return (key.hashCode() & 0x7fffffff) % m;
    }

    // resizes the hash table to the given capacity by re-hashing all of the keys
    private void resize(int capacity) {
        LinearProbingHashST<Key, Value> temp = new LinearProbingHashST<Key, Value>(capacity);
        for (int i = 0; i < m; i++) {
            if (keys[i] != null) {
                temp.put(keys[i], vals[i]);
            }
        }
        keys = temp.keys;
        vals = temp.vals;
        m    = temp.m;
    }

    /**
     * Inserts the specified key-value pair into the symbol table, overwriting the old
     * value with the new value if the symbol table already contains the specified key.
     * Deletes the specified key (and its associated value) from this symbol table
     * if the specified value is {@code null}.
     *
     * @param  key the key
     * @param  val the value
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public void put(Key key, Value val) {
        if (key == null) throw new IllegalArgumentException("first argument to put() is null");

        if (val == null) {
            delete(key);
            return;
        }

        // double table size if 50% full
        if (n >= m/2) resize(2*m);

        int i;
        for (i = hash(key); keys[i] != null; i = (i + 1) % m) {
            if (keys[i].equals(key)) {
                vals[i] = val;
                return;
            }
        }
        keys[i] = key;
        vals[i] = val;
        n++;
    }

    /**
     * Returns the value associated with the specified key.
     * @param key the key
     * @return the value associated with {@code key};
     *         {@code null} if no such value
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public Value get(Key key) {
        if (key == null) throw new IllegalArgumentException("argument to get() is null");
        for (int i = hash(key); keys[i] != null; i = (i + 1) % m)
            if (keys[i].equals(key))
                return vals[i];
        return null;
    }

    /**
     * Removes the specified key and its associated value from this symbol table
     * (if the key is in this symbol table).
     *
     * @param  key the key
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public void delete(Key key) {
        if (key == null) throw new IllegalArgumentException("argument to delete() is null");
        if (!contains(key)) return;

        // find position i of key
        int i = hash(key);
        while (!key.equals(keys[i])) {
            i = (i + 1) % m;
        }

        // delete key and associated value
        keys[i] = null;
        vals[i] = null;

        // rehash all keys in same cluster
        i = (i + 1) % m;
        while (keys[i] != null) {
            // delete keys[i] an vals[i] and reinsert
            Key   keyToRehash = keys[i];
            Value valToRehash = vals[i];
            keys[i] = null;
            vals[i] = null;
            n--;
            put(keyToRehash, valToRehash);
            i = (i + 1) % m;
        }

        n--;

        // halves size of array if it's 12.5% full or less
        if (n > 0 && n <= m/8) resize(m/2);

        assert check();
    }

    /**
     * Returns all keys in this symbol table as an {@code Iterable}.
     * To iterate over all of the keys in the symbol table named {@code st},
     * use the foreach notation: {@code for (Key key : st.keys())}.
     *
     * @return all keys in this symbol table
     */
    public Iterable<Key> keys() {
        Queue<Key> queue = new Queue<Key>();
        for (int i = 0; i < m; i++)
            if (keys[i] != null) queue.enqueue(keys[i]);
        return queue;
    }

    // integrity check - don't check after each put() because
    // integrity not maintained during a delete()
    private boolean check() {

        // check that hash table is at most 50% full
        if (m < 2*n) {
            System.err.println("Hash table size m = " + m + "; array size n = " + n);
            return false;
        }

        // check that each key in table can be found by get()
        for (int i = 0; i < m; i++) {
            if (keys[i] == null) continue;
            else if (get(keys[i]) != vals[i]) {
                System.err.println("get[" + keys[i] + "] = " + get(keys[i]) + "; vals[i] = " + vals[i]);
                return false;
            }
        }
        return true;
    }


    /**
     * Unit tests the {@code LinearProbingHashST} data type.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {
        LinearProbingHashST<String, Integer> st = new LinearProbingHashST<String, Integer>();
        for (int i = 0; !StdIn.isEmpty(); i++) {
            String key = StdIn.readString();
            st.put(key, i);
        }

        // print keys
        for (String s : st.keys())
            StdOut.println(s + " " + st.get(s));
    }
}