1. Hash Tables and Constant Access Time CS-2303, C-Term 20101 Hash Tables and Constant Access Time CS-2303 System Programming Concepts (Slides include materials from The C Programming Language, 2 nd edition, by Kernighan and Ritchie and from C: How to Program, 5 th and 6 th editions, by Deitel and Deitel)

2. Hash Tables and Constant Access Time CS-2303, C-Term 20102 New Challenge What if we require a data structure that has to be accessed by value in constant time? I.e., O(log n) is not good enough! Need to be able to add or delete items Total number of items unknown But an approximate maximum might be known

3. Hash Tables and Constant Access Time CS-2303, C-Term 20103 Examples Anti-virus scanner Symbol table of compiler Virtual memory tables in operating system Bank or credit card account for a person

4. Hash Tables and Constant Access Time CS-2303, C-Term 20104 Example – Validate a Credit Card 16-digit credit card numbers 10 16 possible card numbers Sparsely populated space E.g., 10 8 MasterCard holders, similar for Visa Not random enough for a binary tree Too many single branches really deep searches Need to respond to customer in 1-2 seconds 1000s or tens of 1000s of customers per second! Same is true for ATM card numbers Bank account numbers Etc.

5. Hash Tables and Constant Access Time CS-2303, C-Term 20105 Example Anti-Virus Scanner Look at each sequence of bytes in a file See if it matches against library of virus patterns How many possible patterns? If so, flag it as a possible problem Tens of Thousands!

6. Hash Tables and Constant Access Time CS-2303, C-Term 20106 Anti-Virus Scanner (continued) Time to scan a file? O(length) O(# of patterns) Can we do better? Store patterns in a tree O(length) O(log (# of patterns)) Can we do even better? Yes a Hash Table. Todays topic.

7. Hash Tables and Constant Access Time CS-2303, C-Term 20107 Requirement In these applications (and many like them), need constant time access I.e., O(1) Need to access by value!

8. Hash Tables and Constant Access Time CS-2303, C-Term 20108 Observation Arrays provide constant time access … … but you have to know which element you want! We only know the contents of the item we want! Also Not easy to grow or shrink Not open-ended Can we do better?

9. Hash Tables and Constant Access Time CS-2303, C-Term 20109 Definition – Hash Table A data structure comprising an array for constant time access A set of linked lists one list for each array element A hashing function to convert search key to array index a randomizing function to assure uniform distribution of values across array indices Also known as a hash function

10. Hash Tables and Constant Access Time CS-2303, C-Term 201010 Definition – Search Key A value stored as (part of) the payload of the item you are looking for E.g., your credit card number Your account number at Amazon A pattern characteristic of a virus Need to find the item containing that value (i.e., that key)

11. Hash Tables and Constant Access Time CS-2303, C-Term 201011 Definition – Hash Function A function that randomizes the search key it to produce an index into the array Always returns the same value for the same key So that non-random keys dont concentrate around a subset of the indices in the array See §6.6 in Kernighan & Ritchie

12. Hash Tables and Constant Access Time CS-2303, C-Term 201012 data next Hash Table Structure item... data next data next data next data next data next data next data next data next data next data next data next data next The array The lists

13. Hash Tables and Constant Access Time CS-2303, C-Term 201013 data next Hash Table Structure (continued) item... data next data next data next data next data next data next data next data next data next data next data next data next The array Note that some of the lists are empty Average length of list should be in single digits

14. Hash Tables and Constant Access Time CS-2303, C-Term 201014 Guidelines for Hash Tables Lists from each item should be short I.e., with short search time (approximately constant) Size of array should be based on expected # of entries Err on large side if possible Hashing function Should spread out the values relatively uniformly Multiplication and division by prime numbers usually works well

15. Hash Tables and Constant Access Time CS-2303, C-Term 201015 Example Hashing Function P. 144 of K & R #define HASHSIZE 101 unsigned int hash(char *s) { unsigned int hashval; for (hashval = 0; *s != '\0'; s++) hashval = *s + 31 * hashval; return hashval % HASHSIZE } Note prime numbers to mix it up

16. Hash Tables and Constant Access Time CS-2303, C-Term 201016 Using a Hash Table struct item *lookup(char *s) { struct item *np; for (np = hashtab[hash(s)]; np != NULL; np = np -> next) if (strcmp(s, np->data) == 0) return np; /*found*/ return NULL;/* not found */ }

17. Hash Tables and Constant Access Time CS-2303, C-Term 201017 Using a Hash Table struct item *lookup(char *s) { struct item *np; for (np = hashtab[hash(s)]; np != NULL; np = np -> next) if (strcmp(s, np->data) == 0) return np; /*found*/ return NULL;/* not found */ } Hash table is indexed by hash value of s

18. Hash Tables and Constant Access Time CS-2303, C-Term 201018 Using a Hash Table struct item *lookup(char *s) { struct item *np; for (np = hashtab[hash(s)]; np != NULL; np = np -> next) if (strcmp(s, np->data) == 0) return np; /*found*/ return NULL;/* not found */ } Traverse the linked list to find item s

19. Hash Tables and Constant Access Time CS-2303, C-Term 201019 Using a Hash Table (continued) struct item *addItem(char *s, …) { struct item *np; unsigned int hv; if ((np = lookup(s)) == NULL) { np = malloc(item); /* fill in s and data */ np -> next = hashtab[hv = hash(s)]; hashtab[hv] = np; }; return np; }

20. Hash Tables and Constant Access Time CS-2303, C-Term 201020 Using a Hash Table (continued) struct item *addItem(char *s, …) { struct item *np; unsigned int hv; if ((np = lookup(s)) == NULL) { np = malloc(item); /* fill in s and data */ np -> next = hashtab[hv = hash(s)]; hashtab[hv] = np; }; return np; } Inserts new item at head of the list indexed by hash value

21. Hash Tables and Constant Access Time CS-2303, C-Term 201021 Challenge What kinds of situations in your field might you need a hash table?

22. Hash Tables and Constant Access Time CS-2303, C-Term 201022 Example Source Code Control System System stores every version of every file since creation Storage for one file comprises two parts: Hash table of lines of the file List of lines for each version of that file Easy to reconstruct any version of the file Easy to do an intelligent diff of two files I.e., each line that has ever been part of that file!

23. Hash Tables and Constant Access Time CS-2303, C-Term 201023 Hash Table Summary Widely used for constant time access Easy to build and maintain There is an art and science regarding the choice of hashing functions Consult textbooks, web, etc.

24. Hash Tables and Constant Access Time CS-2303, C-Term 201024 Questions?