Hashing and five popular hashing functions, Data Structure & Algorithms

Q. Explain the term hashing? Explain any five well known hash functions.                        

Ans:

Hashing method provides us the direct access of record from the file dosent matter where the record is in the file. This is made possible with the help of a hashing function H which map the key with the corresponding key address. It provides us with the key- to-address transformation.

Five well known hashing functions are as follows:

The Division Method: An integer key x is divided by the table size m and the remainder is occupied as the hash value. This may be defined as

H(x)=x%m+1

Take an example, x=42 and m=13, H(42)=45%13+1=3+1=4

The Midsquare Method: In this a key is multiplied by itself and the hash value is obtained by selecting an suitable number of digits from the middle of the square. The identical positions in the square must be used for all keys. Taking an example, if the key is 12345, square of this key is given by value 152399025. If 2 digit addresses is needed then position 4th and 5th can be chosen, giving address 39.

The Folding Method: In this a key is broken into several parts. Each part has the same length similar to that of the required address apart from the last part. The parts are added together, ignoring the last carry, we get the hash address for key K.
The multiplicative method:  In this technique a real number c  such  that  0

H(x)=[m(cx%1)]+1

In this,cx%1 is the fractional part of cx and [] denotes the greatest integer less than or equal to its own contents.

The Digit Analysis: In this method the addresses is formed by selecting and shifting digits of the original key. For a given set of key, the same positions in the key and same rearrangement of the pattern must be used. By taking an example a key 7654321 is transformed to the address 1247 by selecting the digits in the position 1,2,4 and 7 then by reversing the order.

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