Hash Tables(chaining)

Hash Table，叫做哈希表，也叫做散列表。
概念:通过某种对应关系h，使得每一个元素和储存位置一一对应。这种对应关系称为哈希函数。它最大的优点就是插入、搜索和删除得很快（O（1））。
碰撞（Collision)：不同的关键字对应同一个哈希地址
本文主要介绍的是解决碰撞的方法之一：chaining

原理：
In chainning,wo palce all the elements that hash to the same plot into the same list.
如果不同的key通过hash function得到的相同结果，那么就将他们放在同一个list中。如下图：

操作:
1.查找：
先找到key的索引：index=hashFunction(key)
然后遍历这个链表：

  // get the hash index of key
  int index = hashFunction(key);

  // find the key in (inex)th list
  list <int> :: iterator i;
  for (i = table[index].begin();
           i != table[index].end(); i++) {
    if (*i == key)
      break;
  }

2.插入:

void Hash::insertItem(int key)
{
    int index = hashFunction(key);
    table[index].push_back(key);
}

3.删除：
首先先查找这个元素，如果找到的话，则删除

void Hash::deleteItem(int key)
{
  // get the hash index of key
  int index = hashFunction(key);

  // find the key in (inex)th list
  list <int> :: iterator i;
  for (i = table[index].begin();
           i != table[index].end(); i++) {
    if (*i == key)
      break;
  }

  // if key is found in hash table, remove it
  if (i != table[index].end())
    table[index].erase(i);
}

完整代码：

// CPP program to implement hashing with chaining
#include<iostream>
#include <list>
using namespace std;

class Hash
{
    int BUCKET;    // No. of buckets

    // Pointer to an array containing buckets
    list<int> *table;
public:
    Hash(int V);  // Constructor

    // inserts a key into hash table
    void insertItem(int x);

    // deletes a key from hash table
    void deleteItem(int key);

    // hash function to map values to key
    int hashFunction(int x) {
        return (x % BUCKET);
    }

    void displayHash();
};

Hash::Hash(int b)
{
    this->BUCKET = b;
    table = new list<int>[BUCKET];
}

void Hash::insertItem(int key)
{
    int index = hashFunction(key);
    table[index].push_back(key);
}

void Hash::deleteItem(int key)
{
  // get the hash index of key
  int index = hashFunction(key);

  // find the key in (inex)th list
  list <int> :: iterator i;
  for (i = table[index].begin();
           i != table[index].end(); i++) {
    if (*i == key)
      break;
  }

  // if key is found in hash table, remove it
  if (i != table[index].end())
    table[index].erase(i);
}

// function to display hash table
void Hash::displayHash() {
  for (int i = 0; i < BUCKET; i++) {
    cout << i;
    for (auto x : table[i])
      cout << " --> " << x;
    cout << endl;
  }
}

// Driver program
int main()
{
  // array that contains keys to be mapped
  int a[] = {15, 11, 27, 8, 12};
  int n = sizeof(a)/sizeof(a[0]);

  // insert the keys into the hash table
  Hash h(7);   // 7 is count of buckets in
               // hash table
  for (int i = 0; i < n; i++)
    h.insertItem(a[i]);

  // delete 12 from hash table
  h.deleteItem(12);

  // display the Hash table
  h.displayHash();

  return 0;
}