Double Hashing

Double hashing is a collision resolving technique in Open Addressed Hash tables. Double hashing uses the idea of applying a second hash function to key when a collision occurs.

Double hashing can be done using :
(hash1(key) + i * hash2(key)) % TABLE_SIZE
Here hash1() and hash2() are hash functions and TABLE_SIZE
is size of hash table.
(We repeat by increasing i when collision occurs)

First hash function is typically hash1(key) = key % TABLE_SIZE

A popular second hash function is : hash2(key) = PRIME – (key % PRIME) where PRIME is a prime smaller than the TABLE_SIZE.

A good second Hash function is:

  • It must never evaluate to zero
  • Must make sure that all cells can be probed

// CPP program to implement double hashing
#include <bits/stdc++.h>
using namespace std;
  
// Hash table size
#define TABLE_SIZE 13
  
// Used in second hash function.
#define PRIME 7
  
class DoubleHash
{
    // Pointer to an array containing buckets
    int *hashTable;
    int curr_size;
  
public:
  
    // function to check if hash table is full
    bool isFull()
    {
  
        // if hash size reaches maximum size
        return (curr_size == TABLE_SIZE);
    }
  
    // function to calculate first hash
    int hash1(int key)
    {
        return (key % TABLE_SIZE);
    }
  
    // function to calculate second hash
    int hash2(int key)
    {
        return (PRIME - (key % PRIME));
    }
  
    DoubleHash()
    {
        hashTable = new int[TABLE_SIZE];
        curr_size = 0;
        for (int i=0; i<TABLE_SIZE; i++)
            hashTable[i] = -1;
    }
  
    // function to insert key into hash table
    void insertHash(int key)
    {
        // if hash table is full
        if (isFull())
            return;
  
        // get index from first hash
        int index = hash1(key);
  
        // if collision occurs
        if (hashTable[index] != -1)
        {
            // get index2 from second hash
            int index2 = hash2(key);
            int i = 1;
            while (1)
            {
                // get newIndex
                int newIndex = (index + i * index2) %
                                        TABLE_SIZE;
  
                // if no collision occurs, store
                // the key
                if (hashTable[newIndex] == -1)
                {
                    hashTable[newIndex] = key;
                    break;
                }
                i++;
            }
        }
  
        // if no collision occurs
        else
            hashTable[index] = key;
        curr_size++;
    }
  
    // function to display the hash table
    void displayHash()
    {
        for (int i = 0; i < TABLE_SIZE; i++)
        {
            if (hashTable[i] != -1)
                cout << i << " --> "
                     << hashTable[i] << endl;
            else
                cout << i << endl;
        }
    }
};
  
// Driver's code
int main()
{
    int a[] = {19, 27, 36, 10, 64};
    int n = sizeof(a)/sizeof(a[0]);
  
    // inserting keys into hash table
    DoubleHash h;
    for (int i = 0; i < n; i++)
        h.insertHash(a[i]);
  
    // display the hash Table
    h.displayHash();
    return 0;
}

Output:

0
1 --> 27
2
3
4
5 --> 10
6 --> 19
7
8
9
10 --> 36
11
12 --> 64


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