1. Hash Tables: A basic O(1)verview
Niteesh Prasad
CS-265

2. Hash Tables in C Data structure used for mapping/ searching.
Increased efficiency to $O(1)$- Constant Look up time.
Disadvantage: Wastage of memory
Used in database indexing and associate arrays. Commonly used applications like web-browsers use hash tables.
Creates a table with operations such as Insert and Retrieve(look up).

3. Basic Idea
Store records of data in the hash table, which is either an array (when main memory is used), or a file (if disk space is used).
Each record has a key field and an associated data field. The record is stored in a location that is based on its key.
The function that produces this location for each given key is called a hash function

4. More Background
Each element of the array is a list that chains together items that share a hash value.
Basic element type would look like this:
typedef structNameval Nameval;
struct Nameval {
char *name;
int value;
Nameval *next; /* in chain */ };
Hash function is important in deciding the efficiency of the search.

5. It’s not a “perfect” world out there
Finding the perfect hash function is difficult (a function that maps each input to a different has value)
Consequences: Conflicts b/w keys (Hash Collision)
Collision resolution :(1) Resolution by overflow (Creating a separate table)
(2) Double Hashing (Two independent hash functions)
(3) Rehashing (Rebuilding the entire table )
The Multiplication method is the most-widely used to find the indices.
(1) Multiply the key by a constant A, 0 < A < 1
(2) Extract the fractional part of the product
(3) Multiply this value by m

6. Hash Function Hash function
/* hash: compute hash value for array of NPREF strings */
unsigned int hash(char *s[NPREF]) {
unsigned int h;
unsigned char *p;
int i;
h = 0;
for (i = 0; i < NPREF; i++) // traversal through the array
for (p = (unsigned char *) s[i]; *p != '\0'; p++)
h = MULTIPLIER * h + *p;
return h % NHASH; }

7. Insert and Look up
/* lookup: find name in symtab, with optional create */
Nameval* lookup(char *name, int create, int value) {
int h;
Nameval *sym;
h = hash(name);
for (sym = symtab[h]; sym != NULL; sym = sym->next)
if (strcmp(name, sym->name) == 0)
return sym; // To avoid duplication
if (create) {
sym = (Nameval *) emalloc(sizeof(Nameval));
sym->name=name; /* assumed allocated elsewhere */
sym->value=value;
sym->next=symtab[h];
symtab[h]=sym; }
return sym;

8. Sources
Brian Kernighan and Rob Pike, The Practice of Programming, Addison Wesley, 1999