Hashing is an improvement over Direct Access Table. The idea is to use a hash function that converts a given phone number or any other key to a smaller number and uses the small number as the index in a table called a hash table.

Hash Function: A function that converts a given big number to a small practical integer value. The mapped integer value is used as an index in the hash table. In simple terms, a hash function maps a big number or string to a small integer that can be used as an index in the hash table.

Quadratic Probing: Quadratic probing is an open-addressing scheme where we look for i2‘th slot in i’th iteration if the given hash vale x collides in the hash table.

Let hash(x) be the slot index computed using the hash function.

• If the slot hash(x) % S is full, then we try (hash(x) + 1*1) % S.
• If (hash(x) + 1*1) % S is also full, then we try (hash(x) + 2*2) % S.
• If (hash(x) + 2*2) % S is also full, then we try (hash(x) + 3*3) % S.
• This process is repeated for all the values of i until an empty slot is found.

For example: Let us consider a simple hash function as “key mod 7” and sequence of keys as 50, 700, 76, 85, 92, 73, 101. Below is the implementation of the above approach:

## Java

 `// Java implementation of the Quadratic Probing ` ` `  `class` `GFG { ` ` `  `    ``// Function to print an array ` `    ``static` `void` `printArray(``int` `arr[]) ` `    ``{ ` ` `  `        ``// Iterating and printing the array ` `        ``for` `(``int` `i = ``0``; i < arr.length; i++) { ` `            ``System.out.print(arr[i] + ``" "``); ` `        ``} ` `    ``} ` ` `  `    ``// Function to implement the ` `    ``// quadratic probing ` `    ``static` `void` `hashing(``int` `table[], ``int` `tsize, ` `                        ``int` `arr[], ``int` `N) ` `    ``{ ` ` `  `        ``// Iterating through the array ` `        ``for` `(``int` `i = ``0``; i < N; i++) { ` ` `  `            ``// Computing the hash value ` `            ``int` `hv = arr[i] % tsize; ` ` `  `            ``// Insert in the table if there ` `            ``// is no collision ` `            ``if` `(table[hv] == -``1``) ` `                ``table[hv] = arr[i]; ` `            ``else` `{ ` ` `  `                ``// If there is a collision ` `                ``// iterating through all ` `                ``// possible quadratic values ` `                ``for` `(``int` `j = ``0``; j < tsize; j++) { ` ` `  `                    ``// Computing the new hash value ` `                    ``int` `t = (hv + j * j) % tsize; ` `                    ``if` `(table[t] == -``1``) { ` ` `  `                        ``// Break the loop after ` `                        ``// inserting the value ` `                        ``// in the table ` `                        ``table[t] = arr[i]; ` `                        ``break``; ` `                    ``} ` `                ``} ` `            ``} ` `        ``} ` ` `  `        ``printArray(table); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `arr[] = { ``50``, ``700``, ``76``, ``85``, ` `                      ``92``, ``73``, ``101` `}; ` `        ``int` `N = ``7``; ` ` `  `        ``// Size of the hash table ` `        ``int` `L = ``7``; ` `        ``int` `hash_table[] = ``new` `int``[L]; ` ` `  `        ``// Initializing the hash table ` `        ``for` `(``int` `i = ``0``; i < L; i++) { ` `            ``hash_table[i] = -``1``; ` `        ``} ` ` `  `        ``// Quadratic probing ` `        ``hashing(hash_table, L, arr, N); ` `    ``} ` `} `

## C#

 `// C# implementation of the Quadratic Probing ` `using` `System; ` ` `  `class` `GFG{ ` ` `  `// Function to print an array ` `static` `void` `printArray(``int` `[]arr) ` `{ ` ` `  `    ``// Iterating and printing the array ` `    ``for``(``int` `i = 0; i < arr.Length; i++) ` `    ``{ ` `       ``Console.Write(arr[i] + ``" "``); ` `    ``} ` `} ` ` `  `// Function to implement the ` `// quadratic probing ` `static` `void` `hashing(``int` `[]table, ``int` `tsize, ` `                    ``int` `[]arr, ``int` `N) ` `{ ` ` `  `    ``// Iterating through the array ` `    ``for``(``int` `i = 0; i < N; i++)  ` `    ``{ ` `        `  `       ``// Computing the hash value ` `       ``int` `hv = arr[i] % tsize; ` `        `  `       ``// Insert in the table if there ` `       ``// is no collision ` `       ``if` `(table[hv] == -1) ` `           ``table[hv] = arr[i]; ` `       ``else` `       ``{ ` `            `  `           ``// If there is a collision ` `           ``// iterating through all ` `           ``// possible quadratic values ` `           ``for``(``int` `j = 0; j < tsize; j++) ` `           ``{ ` `                `  `              ``// Computing the new hash value ` `              ``int` `t = (hv + j * j) % tsize; ` `              ``if` `(table[t] == -1)  ` `              ``{ ` `                   `  `                  ``// Break the loop after ` `                  ``// inserting the value ` `                  ``// in the table ` `                  ``table[t] = arr[i]; ` `                  ``break``; ` `              ``} ` `           ``} ` `       ``} ` `    ``} ` `    ``printArray(table); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String []args) ` `{ ` `    ``int` `[]arr = { 50, 700, 76, 85, ` `                  ``92, 73, 101 }; ` `    ``int` `N = 7; ` ` `  `    ``// Size of the hash table ` `    ``int` `L = 7; ` `    ``int` `[]hash_table = ``new` `int``[L]; ` ` `  `    ``// Initializing the hash table ` `    ``for``(``int` `i = 0; i < L; i++) ` `    ``{ ` `       ``hash_table[i] = -1; ` `    ``} ` `     `  `    ``// Quadratic probing ` `    ``hashing(hash_table, L, arr, N); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```700 50 85 73 101 92 76
```

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