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Data structure

MINISTRY OF EDUCATION & HIGHER EDUCATION COLLEGE OF SCIENCE AND TECHNOLOGY KHANYOUNIS- PALESTINE. Using C#. Information Technology , 3’rd Semester. Data structure. Lecture 17: An Overview of Hashing. Presented By: Mahmoud Rafeek Alfarra. Outline. What is Hashing? What is Hash tables?

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Data structure

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

  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. • Hash tables, sometimes also called dictionaries. • HTs are data structures that store values along with identification keys for easy access. Presented & Prepared by: Mahmoud R. Alfarra

  4. What is Hash tables? 4 • 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. Presented & Prepared by: Mahmoud R. Alfarra

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

  6. What is Hash tables? 6 • Each data item is stored in the array based on some piece of the data, called the key. • 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. Presented & Prepared by: Mahmoud R. Alfarra

  7. What is a hash function? 7 • 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. Presented & Prepared by: Mahmoud R. Alfarra

  8. What is a hash function? 8 • 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 Presented & Prepared by: Mahmoud R. Alfarra

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

  10. Hash method works something like this 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 hash(key) AAAAAAAA 8482 1273 zzzzzzzz hash(key) Domain: "!" .. "zzzzzzzz" Range: 0 ... 9996

  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 • Could use String keys each ASCII character equals some unique integer • "able" = 97 + 98 + 108 + 101 == 404 Presented & Prepared by: Mahmoud R. Alfarra

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

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

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

  16. Find object with key "baab "IKLT" 0 "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 ... 80 "abba" 81 "baab" 82 83 84 "abcd" 85 "abce" 86 ... "KLMP" 308

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

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