The document provides an overview of hash tables, including how they store key-value pairs using hashing to map keys to indexes. It discusses hashing functions and how they should be stable, uniform, efficient and possibly secure. It describes how hash tables handle collisions through open addressing or chaining and how items can be added, removed, searched for and enumerated from a hash table.

1. Hash Table
Code Review 1/20/11
S

2. Outline
S Hash Table Overview
S Hashing Overview
S Add Items
S Remove Items
S Search For Items
S Enumerate Items

3. Hash Table Overview
S Associative Array
S Storage of Key / Value Pairs
S Like an array, but the index can be any comparable type
S Each Key is Unique, though Keys can point to the same
value
S The Key Type is mapped to an Index

4. Hashed???
S Hashing derives a fixed size result from an input
S every hash returns same size and type
S Stable
S The same input generates the same output ALWAYS
S Uniform
S The hash value use should be uniformly distributed through available
space (though impossible to have perfect uniformity)
S Efficient
S The cost of generating a hash must be balanced with application needs
S Secure
S The cost of finding data that produces a given hash is prohibitive

5. Hashing A String
S Naïve implementation
S Summing the ASCII value for each character
F O O 102 111 111 324
S Pros
S Stable
S Efficient
S Cons
S Not Uniform
S AdditiveHash(“foo”) = AdditiveHash(“oof ”)
S Not Secure

6. Hashing A String
S Somewhat better
S “Folds” bytes of every four characters into an integer (32bit)
Lore m ip sum dolo r
170199844 1885937773 54404403 1869377380 114
-707031079 -162986676 1706390704 1706390818
S Pros
S Stable, Efficient and better uniformity
S Cons
S Not secure (can be treated essentially as additive)

7. Hashing Functions
S There are lots of good hashing algorithms, you don’t have to write
your own.
S Pick the right hash for the job at hand (all these are available in the
.net framework)
Name Stable Uniform Efficient Secure
Additive ✔ ✔
Folding ✔ ✔ ✔
CRC32 ✔ ✔ ✔
MD5 ✔ ✔
SHA-2 ✔ ✔ ✔

8. Hash Table Overview
S Adding Jane
S int index = GetIndex(Jane.Name);
S _array[index] = Jane;
S What does GetIndex() do? It hashes the string

9. Simple Hash Examples

10. Handling Collisions
S Two distinct items have the same hash value
S Items are assigned to the same index in the hash table
S Two common strategies
S Open Addressing
S Moving to next index in the table
S Chaining
S Storing items into a linked list
S Frequency of Collisions
S # of slots in the array
S # of filled slots in the array

11. Finding Items
S Items are found by key
S Person p = HashTable.Find(“Jane”)
S Open Addressing
S Get the index of the key
S If the value != null
S If keys match, return value
S If keys don’t match, check next index
S Chaining
S Get index of the key
S Find index in the list

12. Removing Items
S Items are removed by key
S HashTable.Remove(“Jane”)
S Open Addressing
S Get index of the key
S If value != null
S If keys match, remove
S If keys don’t match, check next index
S Chaining
S Get index of the key
S Remove item from the linked list

13. Enumerating Keys & Values
S Open Addressing
S Foreach(item in array)
{if(item!=null) return item;}
S Chaining
S Foreach(list in array)
{if(list !=null)
{foreach(item in list){return item;}}
}