# 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)

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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 ``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 search key in hash table``    ``void` `search(``int` `key)``    ``{``        ``int` `index1 = hash1(key);``        ``int` `index2 = hash2(key);``        ``int` `i = 0;``        ``while` `(hashTable[(index1 + i * index2) % TABLE_SIZE] != key) {``            ``if` `(hashTable[(index1 + i * index2) % TABLE_SIZE] == -1) {``                ``cout << key << ``" does not exist"` `<< endl;``                ``return``;``            ``}``            ``i++;``        ``}``        ``cout << key << ``" found"` `<< endl;``    ``}`` ` `    ``// 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);`` ` `    ``// inserting keys into hash table``    ``DoubleHash h;``    ``for` `(``int` `i = 0; i < n; i++) {``        ``h.insertHash(a[i]);``    ``}``    ``// searching some keys``    ``h.search(36); ``// This key is present in hash table``    ``h.search(100); ``// This key does not exist in hash table``    ``// display the hash Table``    ``h.displayHash();``    ``return` `0;``}`
Output:
```36 found
100 does not exist
0
1 --> 27
2
3
4
5 --> 10
6 --> 19
7
8
9
10 --> 36
11
12 --> 64
```

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