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散列查找算法
（一）用散列函数将被查找的键转化为数组的索引
（二）处理碰撞冲突：拉链法和线性探测法
散列表是算法在时间和空间上作出权衡的经典例子
散列函数
特点
（一）易于计算
（二）均匀分布
基于拉链法的散列表
（一）
将大小为M的数组中的每个元素指向一条链表，链表中每个节点都存储了散列值为该元素索引的键值对
（二）
选择足够大的M，使得所有链表都尽可能的的高效查找
（三）
查找分两步：（1）根据散列值找到对应的链表（2）沿着列表顺序查找相应的键
实现
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: 基于拉链法的散列表
* @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));
}
}
基于线性探测法的散列表
（一）用大小为M的数组保存N个键值对，M>N，依靠数组中空缺位解决碰撞冲突，基于这种策略的所有方法统称为开发地址散列表
（二）开放地址法中最简单的方法为线性探测法：当碰撞发送时（一个键的散列值已经被另一个不同的键占用），直接检查散列表中的下一个位置（将索引值加1）
（三）线性探测会产生三种结果：（1）命中（2）未命中，键未空（3）继续查找
package com.lwl.algorithm.hash;
import com.lwl.algorithm.stack.StdIn;
import com.lwl.algorithm.stack.StdOut;
/**
* @author liuweilong
* @ClassName: LinearProbingHashST 基于线性探测的符号表
* @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 键值对数量
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));
}
}