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Hashing with Quadratic Probing

Hashing is a technique used for storing , searching and removing elements in almost constant time. Hashing is done with help of a hash function that generates index for a given input, then this index can be used to search the elements, store an element, or remove that element from that index.

A hash function is a function that is used to map the data elements to their position in the data structure used. For example if we use an array to store the integer elements then the hash function will generate position for each element so that searching, storing and removing operation on the array can be done in constant time that is independent of the number of elements in the array. For better look at the example below.


Hashing using mod function

now we face a problem if for 2 numbers same position is generated example consider elements 1 and 14

1 % 13 = 1

14 % 13 = 1

so when we get 1 we store it at the first position, but when we get 14 we see that the position 1 is already taken, this is a case of collision.

Inorder to resolve collision we employ various collision resolving methods here we use quadratic probing to resolve collision.

In Quadratic Probing we find the new Position using the formula

new_Position = old_Position + (i^2)
where i is a natural number

so for the above example we get position 1 for 14 but 1 is already taken hence we calculate new position,

new_Position = 1 + (1^2) = 2


now we check if position is taken or not, if position 2 is empty then we store 14 at second position, else we calculate new position by taking i as 2

new_Position = 1 + (2^2) = 5

We keep repeating this till we find a new position

To know more about hash functions and how to select hash function click Here.
To know more about quadratic probing click Here


C++ Program

Sample input and output to check the program



You might also be interested in

Hashing with Linear Probing
Double Hashing
Find Trailing number of zeros in factorial of a number.
Check if a number is a Fibonacci number or not
Insertion Sort
Bubble sort Algorithm

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