哈希表是一种数据结构，它可以提供快速的插入操作和查找操作。
哈希表的缺点：基于数组，数组创建后难于扩展。不能有序遍历
哈希化
把关键字转换成数组下标（哈希函数）
冲突（碰撞）
开放地址法
线性探测
// hash.java
// demonstrates hash table with linear probing
// to run this program: C:>java HashTableApp
import java.io.*;
////////////////////////////////////////////////////////////////
class DataItem
{ // (could have more data)
private int iData; // data item (key)
//--------------------------------------------------------------
public DataItem(int ii) // constructor
{ iData = ii; }
//--------------------------------------------------------------
public int getKey()
{ return iData; }
//--------------------------------------------------------------
} // end class DataItem
////////////////////////////////////////////////////////////////
class HashTable
{
private DataItem[] hashArray; // array holds hash table
private int arraySize;
private DataItem nonItem; // for deleted items
// -------------------------------------------------------------
public HashTable(int size) // constructor
{
arraySize = size;
hashArray = new DataItem[arraySize];
nonItem = new DataItem(-1); // deleted item key is -1
}
// -------------------------------------------------------------
public void displayTable()
{
System.out.print("Table: ");
for(int j=0; j<arraySize; j++)
{
if(hashArray[j] != null)
System.out.print(hashArray[j].getKey() + " ");
else
System.out.print("** ");
}
System.out.println("");
}
// -------------------------------------------------------------
public int hashFunc(int key)
{
return key % arraySize; // hash function
}
// -------------------------------------------------------------
public void insert(DataItem item) // insert a DataItem
// (assumes table not full)
{
int key = item.getKey(); // extract key
int hashVal = hashFunc(key); // hash the key
// until empty cell or -1,
while(hashArray[hashVal] != null &&
hashArray[hashVal].getKey() != -1)
{
++hashVal; // go to next cell
hashVal %= arraySize; // wraparound if necessary
}
hashArray[hashVal] = item; // insert item
} // end insert()
// -------------------------------------------------------------
public DataItem delete(int key) // delete a DataItem
{
int hashVal = hashFunc(key); // hash the key
while(hashArray[hashVal] != null) // until empty cell,
{ // found the key?
if(hashArray[hashVal].getKey() == key)
{
DataItem temp = hashArray[hashVal]; // save item
hashArray[hashVal] = nonItem; // delete item
return temp; // return item
}
++hashVal; // go to next cell
hashVal %= arraySize; // wraparound if necessary
}
return null; // can't find item
} // end delete()
// -------------------------------------------------------------
public DataItem find(int key) // find item with key
{
int hashVal = hashFunc(key); // hash the key
while(hashArray[hashVal] != null) // until empty cell,
{ // found the key?
if(hashArray[hashVal].getKey() == key)
return hashArray[hashVal]; // yes, return item
++hashVal; // go to next cell
hashVal %= arraySize; // wraparound if necessary
}
return null; // can't find item
}
// -------------------------------------------------------------
} // end class HashTable
////////////////////////////////////////////////////////////////
class HashTableApp
{
public static void main(String[] args) throws IOException
{
DataItem aDataItem;
int aKey, size, n, keysPerCell;
// get sizes
System.out.print("Enter size of hash table: ");
size = getInt();
System.out.print("Enter initial number of items: ");
n = getInt();
keysPerCell = 10;
// make table
HashTable theHashTable = new HashTable(size);
for(int j=0; j<n; j++) // insert data
{
aKey = (int)(java.lang.Math.random() *
keysPerCell * size);
aDataItem = new DataItem(aKey);
theHashTable.insert(aDataItem);
}
while(true) // interact with user
{
System.out.print("Enter first letter of ");
System.out.print("show, insert, delete, or find: ");
char choice = getChar();
switch(choice)
{
case 's':
theHashTable.displayTable();
break;
case 'i':
System.out.print("Enter key value to insert: ");
aKey = getInt();
aDataItem = new DataItem(aKey);
theHashTable.insert(aDataItem);
break;
case 'd':
System.out.print("Enter key value to delete: ");
aKey = getInt();
theHashTable.delete(aKey);
break;
case 'f':
System.out.print("Enter key value to find: ");
aKey = getInt();
aDataItem = theHashTable.find(aKey);
if(aDataItem != null)
{
System.out.println("Found " + aKey);
}
else
System.out.println("Could not find " + aKey);
break;
default:
System.out.print("Invalid entry\n");
} // end switch
} // end while
} // end main()
//--------------------------------------------------------------
public static String getString() throws IOException
{
InputStreamReader isr = new InputStreamReader(System.in);
BufferedReader br = new BufferedReader(isr);
String s = br.readLine();
return s;
}
//--------------------------------------------------------------
public static char getChar() throws IOException
{
String s = getString();
return s.charAt(0);
}
//-------------------------------------------------------------
public static int getInt() throws IOException
{
String s = getString();
return Integer.parseInt(s);
}
//--------------------------------------------------------------
} // end class HashTableApp
////////////////////////////////////////////////////////////////
扩展数组
二次探测
双重散列/二次哈希
// hashDouble.java
// demonstrates hash table with double hashing
// to run this program: C:>java HashDoubleApp
import java.io.*;
////////////////////////////////////////////////////////////////
class DataItem
{ // (could have more items)
private int iData; // data item (key)
//--------------------------------------------------------------
public DataItem(int ii) // constructor
{ iData = ii; }
//--------------------------------------------------------------
public int getKey()
{ return iData; }
//--------------------------------------------------------------
} // end class DataItem
////////////////////////////////////////////////////////////////
class HashTable
{
private DataItem[] hashArray; // array is the hash table
private int arraySize;
private DataItem nonItem; // for deleted items
// -------------------------------------------------------------
HashTable(int size) // constructor
{
arraySize = size;
hashArray = new DataItem[arraySize];
nonItem = new DataItem(-1);
}
// -------------------------------------------------------------
public void displayTable()
{
System.out.print("Table: ");
for(int j=0; j<arraySize; j++)
{
if(hashArray[j] != null)
System.out.print(hashArray[j].getKey()+ " ");
else
System.out.print("** ");
}
System.out.println("");
}
// -------------------------------------------------------------
public int hashFunc1(int key)
{
return key % arraySize;
}
// -------------------------------------------------------------
public int hashFunc2(int key)
{
// non-zero, less than array size, different from hF1
// array size must be relatively prime to 5, 4, 3, and 2
return 5 - key % 5;
}
// -------------------------------------------------------------
// insert a DataItem
public void insert(int key, DataItem item)
// (assumes table not full)
{
int hashVal = hashFunc1(key); // hash the key
int stepSize = hashFunc2(key); // get step size
// until empty cell or -1
while(hashArray[hashVal] != null &&
hashArray[hashVal].getKey() != -1)
{
hashVal += stepSize; // add the step
hashVal %= arraySize; // for wraparound
}
hashArray[hashVal] = item; // insert item
} // end insert()
// -------------------------------------------------------------
public DataItem delete(int key) // delete a DataItem
{
int hashVal = hashFunc1(key); // hash the key
int stepSize = hashFunc2(key); // get step size
while(hashArray[hashVal] != null) // until empty cell,
{ // is correct hashVal?
if(hashArray[hashVal].getKey() == key)
{
DataItem temp = hashArray[hashVal]; // save item
hashArray[hashVal] = nonItem; // delete item
return temp; // return item
}
hashVal += stepSize; // add the step
hashVal %= arraySize; // for wraparound
}
return null; // can't find item
} // end delete()
// -------------------------------------------------------------
public DataItem find(int key) // find item with key
// (assumes table not full)
{
int hashVal = hashFunc1(key); // hash the key
int stepSize = hashFunc2(key); // get step size
while(hashArray[hashVal] != null) // until empty cell,
{ // is correct hashVal?
if(hashArray[hashVal].getKey() == key)
return hashArray[hashVal]; // yes, return item
hashVal += stepSize; // add the step
hashVal %= arraySize; // for wraparound
}
return null; // can't find item
}
// -------------------------------------------------------------
} // end class HashTable
////////////////////////////////////////////////////////////////
class HashDoubleApp
{
public static void main(String[] args) throws IOException
{
int aKey;
DataItem aDataItem;
int size, n;
// get sizes
System.out.print("Enter size of hash table: ");
size = getInt();
System.out.print("Enter initial number of items: ");
n = getInt();
// make table
HashTable theHashTable = new HashTable(size);
for(int j=0; j<n; j++) // insert data
{
aKey = (int)(java.lang.Math.random() * 2 * size);
aDataItem = new DataItem(aKey);
theHashTable.insert(aKey, aDataItem);
}
while(true) // interact with user
{
System.out.print("Enter first letter of ");
System.out.print("show, insert, delete, or find: ");
char choice = getChar();
switch(choice)
{
case 's':
theHashTable.displayTable();
break;
case 'i':
System.out.print("Enter key value to insert: ");
aKey = getInt();
aDataItem = new DataItem(aKey);
theHashTable.insert(aKey, aDataItem);
break;
case 'd':
System.out.print("Enter key value to delete: ");
aKey = getInt();
theHashTable.delete(aKey);
break;
case 'f':
System.out.print("Enter key value to find: ");
aKey = getInt();
aDataItem = theHashTable.find(aKey);
if(aDataItem != null)
System.out.println("Found " + aKey);
else
System.out.println("Could not find " + aKey);
break;
default:
System.out.print("Invalid entry\n");
} // end switch
} // end while
} // end main()
//--------------------------------------------------------------
public static String getString() throws IOException
{
InputStreamReader isr = new InputStreamReader(System.in);
BufferedReader br = new BufferedReader(isr);
String s = br.readLine();
return s;
}
//--------------------------------------------------------------
public static char getChar() throws IOException
{
String s = getString();
return s.charAt(0);
}
//-------------------------------------------------------------
public static int getInt() throws IOException
{
String s = getString();
return Integer.parseInt(s);
}
//--------------------------------------------------------------
} // end class HashDoubleApp
////////////////////////////////////////////////////////////////
链地址法
数组 + 链表，桶结构
装载因子
// hashChain.java
// demonstrates hash table with separate chaining
// to run this program: C:>java HashChainApp
import java.io.*;
////////////////////////////////////////////////////////////////
class Link
{ // (could be other items)
private int iData; // data item
public Link next; // next link in list
// -------------------------------------------------------------
public Link(int it) // constructor
{ iData= it; }
// -------------------------------------------------------------
public int getKey()
{ return iData; }
// -------------------------------------------------------------
public void displayLink() // display this link
{ System.out.print(iData + " "); }
} // end class Link
////////////////////////////////////////////////////////////////
class SortedList
{
private Link first; // ref to first list item
// -------------------------------------------------------------
public void SortedList() // constructor
{ first = null; }
// -------------------------------------------------------------
public void insert(Link theLink) // insert link, in order
{
int key = theLink.getKey();
Link previous = null; // start at first
Link current = first;
// until end of list,
while( current != null && key > current.getKey() )
{ // or current > key,
previous = current;
current = current.next; // go to next item
}
if(previous==null) // if beginning of list,
first = theLink; // first --> new link
else // not at beginning,
previous.next = theLink; // prev --> new link
theLink.next = current; // new link --> current
} // end insert()
// -------------------------------------------------------------
public void delete(int key) // delete link
{ // (assumes non-empty list)
Link previous = null; // start at first
Link current = first;
// until end of list,
while( current != null && key != current.getKey() )
{ // or key == current,
previous = current;
current = current.next; // go to next link
}
// disconnect link
if(previous==null) // if beginning of list
first = first.next; // delete first link
else // not at beginning
previous.next = current.next; // delete current link
} // end delete()
// -------------------------------------------------------------
public Link find(int key) // find link
{
Link current = first; // start at first
// until end of list,
while(current != null && current.getKey() <= key)
{ // or key too small,
if(current.getKey() == key) // is this the link?
return current; // found it, return link
current = current.next; // go to next item
}
return null; // didn't find it
} // end find()
// -------------------------------------------------------------
public void displayList()
{
System.out.print("List (first-->last): ");
Link current = first; // start at beginning of list
while(current != null) // until end of list,
{
current.displayLink(); // print data
current = current.next; // move to next link
}
System.out.println("");
}
} // end class SortedList
////////////////////////////////////////////////////////////////
class HashTable
{
private SortedList[] hashArray; // array of lists
private int arraySize;
// -------------------------------------------------------------
public HashTable(int size) // constructor
{
arraySize = size;
hashArray = new SortedList[arraySize]; // create array
for(int j=0; j<arraySize; j++) // fill array
hashArray[j] = new SortedList(); // with lists
}
// -------------------------------------------------------------
public void displayTable()
{
for(int j=0; j<arraySize; j++) // for each cell,
{
System.out.print(j + ". "); // display cell number
hashArray[j].displayList(); // display list
}
}
// -------------------------------------------------------------
public int hashFunc(int key) // hash function
{
return key % arraySize;
}
// -------------------------------------------------------------
public void insert(Link theLink) // insert a link
{
int key = theLink.getKey();
int hashVal = hashFunc(key); // hash the key
hashArray[hashVal].insert(theLink); // insert at hashVal
} // end insert()
// -------------------------------------------------------------
public void delete(int key) // delete a link
{
int hashVal = hashFunc(key); // hash the key
hashArray[hashVal].delete(key); // delete link
} // end delete()
// -------------------------------------------------------------
public Link find(int key) // find link
{
int hashVal = hashFunc(key); // hash the key
Link theLink = hashArray[hashVal].find(key); // get link
return theLink; // return link
}
// -------------------------------------------------------------
} // end class HashTable
////////////////////////////////////////////////////////////////
class HashChainApp
{
public static void main(String[] args) throws IOException
{
int aKey;
Link aDataItem;
int size, n, keysPerCell = 100;
// get sizes
System.out.print("Enter size of hash table: ");
size = getInt();
System.out.print("Enter initial number of items: ");
n = getInt();
// make table
HashTable theHashTable = new HashTable(size);
for(int j=0; j<n; j++) // insert data
{
aKey = (int)(java.lang.Math.random() *
keysPerCell * size);
aDataItem = new Link(aKey);
theHashTable.insert(aDataItem);
}
while(true) // interact with user
{
System.out.print("Enter first letter of ");
System.out.print("show, insert, delete, or find: ");
char choice = getChar();
switch(choice)
{
case 's':
theHashTable.displayTable();
break;
case 'i':
System.out.print("Enter key value to insert: ");
aKey = getInt();
aDataItem = new Link(aKey);
theHashTable.insert(aDataItem);
break;
case 'd':
System.out.print("Enter key value to delete: ");
aKey = getInt();
theHashTable.delete(aKey);
break;
case 'f':
System.out.print("Enter key value to find: ");
aKey = getInt();
aDataItem = theHashTable.find(aKey);
if(aDataItem != null)
System.out.println("Found " + aKey);
else
System.out.println("Could not find " + aKey);
break;
default:
System.out.print("Invalid entry\n");
} // end switch
} // end while
} // end main()
//--------------------------------------------------------------
public static String getString() throws IOException
{
InputStreamReader isr = new InputStreamReader(System.in);
BufferedReader br = new BufferedReader(isr);
String s = br.readLine();
return s;
}
//-------------------------------------------------------------
public static char getChar() throws IOException
{
String s = getString();
return s.charAt(0);
}
//-------------------------------------------------------------
public static int getInt() throws IOException
{
String s = getString();
return Integer.parseInt(s);
}
//--------------------------------------------------------------
} // end class HashChainApp
////////////////////////////////////////////////////////////////
哈希函数
快速的计算
随机的关键字
使用质数作为取模的基数
