1. DATA STRUCTURE Presented By: Mahmoud Rafeek Alfarra Using C# MINISTRY OF EDUCATION & HIGHER EDUCATION COLLEGE OF SCIENCE AND TECHNOLOGY KHANYOUNIS- PALESTINE Information Technology, 3’rd Semester Lecture 17: An Overview of Hashing

2. Outline  What is Hashing?  What is Hash tables?  What is a hash function?  Example: hash function using string  Emank X Mezank !!

3. What is Hashing?  Hashing is a very common technique for storing data in such a way the data can be inserted and retrieved very quickly.  Hashing uses a data structure called a hash table. dictionaries  Hash tables, sometimes also called dictionaries.  HTs are data structures that store values along with identification keys for easy access. 3 Presented & Prepared by: Mahmoud R. Alfarra

4. What is Hash tables? dictionaries  Hash tables, sometimes also called dictionaries.  HTs are data structures that store values along with identification keys for easy access.  A hash table data structure is designed around an array. 4 Presented & Prepared by: Mahmoud R. Alfarra

5. What is Hash tables? 5 Presented & Prepared by: Mahmoud R. Alfarra Keys Given a student ID find the record (entry)

6. What is Hash tables? 6 Presented & Prepared by: Mahmoud R. Alfarra key  Each data item is stored in the array based on some piece of the data, called the key. hash function  To store an element in the hash table, the key is mapped into a number in the range of 0 to the hash table size using a function called a hash function.

7. hash function What is a hash function ? 7 Presented & Prepared by: Mahmoud R. Alfarra  The ideal goal of the hash function is to store each key in its own cell in the array.  However, because there are an unlimited number of possible keys and a finite number of array cells, a more realistic goal of the hash function is to attempt to distribute the keys as evenly as possible among the cells of the array.

8. What is a hash function? 8 Presented & Prepared by: Mahmoud R. Alfarra  Choosing a hash function depends on the data type of the key you are using.  If your key is an integer, the simplest function is to return the key modulo the size of the array. f(k) = k%size f(4) = 4%10 = 4

9. What is a hash function? 9 Presented & Prepared by: Mahmoud R. Alfarra  A hash table supports fast retrieval O(1) fast deletion O(1) fast insertion O(1)

10. Hash method works something like this zzzzzzzz Domain: "!".. "zzzzzzzz"Range: 0... 9996 hash(key) AAAAAAAA 8482 hash(key) 1273 Convert a String key into an integer that will be in the range of 0 through the maximum capacity-1 Assume the array capacity is 9997

11. Hash method  What if the ASCII value of individual chars of the string key added up to a number from ("A") 65 to possibly 488 ("zzzz") 4 chars max  If the array has size = 309, mod the sum 390 % TABLE_SIZE = 81 394 % TABLE_SIZE = 85 404 % TABLE_SIZE = 95  These array indices store these keys 81 85 95 abba abcd able

12. Example: hash function using string 12 Presented & Prepared by: Mahmoud R. Alfarra  Could use String keys each ASCII character equals some unique integer  "able" = 97 + 98 + 108 + 101 == 404

13. 81 82 83 84 85 86 308 A hash table after three insertions using the too simple hash code method "abba" Keys 80... 0 insert objects with these three keys: "abba" "abcd" "abce"... "abcd" "abce"

14. Collision occurs while inserting "baab" can't insert "baab" where it hashes to same slot as "abba" Linear probe forward by 1, inserting it at the next available slot "baab" Try [81] Put in [82] 81 82 83 84 85 86 308 "abba" 80... 0 "abcd" "abce" "baab"

15. Wrap around when collision occurs at end Insert "KLMP" "IKLT" both of which have a hash value of 308 81 82 83 84 85 86 308 "abba" 80... 0 "abcd" "abce" "baab" "KLMP" "IKLT"

16. Find object with key "baab 81 82 83 84 85 86 308 "abba" 80... 0 "abcd" "abce" "baab" "KLMP" "IKLT" "baab" still hashes to 81, but since [81] does not hold it, linear probe to [82] At this point, you could return a reference to it or remove it

17. Emank X Mezank !! قال النبي صلى الله عليه وسلم: قولوا لا إله إلا الله تُفلحـوا

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