# 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 ` `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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