Hashing

1. Hashing

2. Hashing • Hashing is the transformation of a string of characters into a usually shorter fixed-length value or key that represents the original string. Hashing is used to index and retrieve items in a database because it is faster to find the item using the shorter hashed key than to find it using the original value. It is also used in many encryption algorithms.

3. Hash Table • Is a data structure that associates keys with values A small phone book as a hash table.

4. Hash Table (1) • The primary operation it supports efficiently is a lookup: given a key (a person's name), find the corresponding value (that person's telephone number). It works by transforming the key using a hash function into a hash, a number that is used as an index in an array to locate the desired location where the values should be.

5. Hash Function • The hashing algorithm • is any well-defined procedure or mathematical function which converts a large, possibly variable-sized amount of data into a small datum, usually a single integer that may serve as an index into an array. The values returned by a hash function are called hash values, hash codes, hash sums, or simply hashes.

6. Hash Function

7. 1.Direct Hashing The key is the address without any algorith- mic manipulation. The data structure must therefore contain an element for every possible key. While the situations where you can use direct hashing are limited, when it can be used it is very powerful because it guarantees that there are no synonyms.

8. Address 5 005 Hash Function 100 100 2 002 Key

9. 2.Subtration Method Sometimes we have keys that are consecutive but do not start from one. Example: A company may have only 100 employees, but the employee numbers start from 1000 and go to 1100. In this case, we use a very simple hashing function that subtracts 1000 from the key to determine the address.

10. 3.Digit Extraction Selected digits are extracted from the key and used as the address. Example: Using six-digit employee number to hash to a three-digit address (000-999), we could select the first, third, and fourth digits. 379452 = 394 121267 = 112 378845 = 388 160252 = 102

11. 4.Mod division [001] Divides the key by the array size and uses the remainder + 1 [002] [003] [004] [005] 3 121267 Hash Function 307 [006] 045128 1 379452 [007] . . . . . [306] [307]

12. 5.Midsquare Hashing The key is squared and the address selected from the middle of the squared number. Example: 9452 * 9452 = 89340304 : address is 3403 As a variation, we can select a portion of the key, and then use them rather than the whole key. 379452 : 379 * 379 = 143641 : address is 364 378845 : 378 * 378 = 142884 : address is 288

13. 6.Folding Methods There are two folding methods that are used: Fold Shift, the key value is divided into parts whose size matches the size of the required address. Then, the left and right parts are shifted and added with the middle part. Fold Boundary, the left and right numbers are folded on a fixed boundary between them and the center number. This results in a two outside values being reverse

14. 123 321 456 456 789 987 368 764 1 1 Key Digits reversed 123456789 123 123 789 789 Digits reversed Discarded

15. Load Factor Is the number of elements in the list divided by the number of physical elements allocated for the list expressed for a percentage. a = k / n x 100 Clustering The tendency of data to build up unevenly across a hashed list. It is usually created by collisions.

16. Collision

17. Collision Is the event that occurs when a hashing algorithm produce an address for an insertion key and that address is already occupied. Home Address The address produced by hashing algorithm. Prime Area The memory that contains all of the home addresses. Probe Calculation of address and test for success.

18. B & A Collides C & B Collides C A B [9] [17] [1] [5] 1. hash(A) 2. hash(B) 3. hash(C)

19. Collision Resolution • The process of finding alternate location • Collision strategy techniques: • Separate chaining • Open addressing • Coalesced hashing • Perfect hashing • Dynamic perfect hashing • Probabilistic hashing • Robin hood hashing • Cache-conscious collision resolution

20. Separate Chaining • Sometimes called simply chaining or direct chaining, in its simplest form each slot in the array is a linked list, or the head cell of a linked list, where the list contains the elements that hashed to the same location. Insertion requires finding the correct slot, then appending to either end of the list in that slot

21. Open Addressing • Open addressing hash tables store the records directly within the array. This approach is also called closed hashing. A hash collision is resolved by probing, or searching through alternate locations in the array (following a probe sequence) until either the target record is found, or an unused array slot is found, which indicates that there is no such key in the table.

22. Well Known Probe Sequences

23. [001] 070918 Redjie [002] [003] 166702 Reymund [004] [005] 070918 Hash Function [006] 166702 [007] . . . . . Linear Probing Collision is resolved by adding one(1) to the current address [306] [307]

24. Quadratic Probing The increment is the collision probe number squared. Probe Collision Probe2 and New Num Location Increment Address 1 1 12 = 1 1 2 2 22 = 4 3 3 6 32 = 9 5 4 15 42 = 16 7 5 31 52 = 25 9 6 56 62 = 36 11

25. Key Offset Is a double hashing method that produces different collision path for different keys. Formula: offset = (key / listsize) adress = ((offset + old address) modulo listsize) + 1 For example if the key is 166702 and the listsize is 307, using the modulo division… offset = (166702 / 307) = 543 address = ((543 + 002) modulo 307) + 1 = 239

26. [001] [002] [003] [004] [005] [006] [007] . . . . . [306] [307]

27. Hash collision resolved by linear probing (interval=1).