1. Hash table another data structure for implementing a map or a set

2. Quiz answer all question with true or false
A hash table stores the map elements in order of their key values
A hash table makes use of an array or a vector
Searching for an element in a hash table never requires more than 1 comparison

3. Quiz answer all question with true or false
A hash table stores the map elements in order of their key values false
A hash table makes use of an array or a vector true
Searching for an element in a hash table never requires more than 1 comparison false

4. What is a hash table?
An array (or vector) with a fixed capacity (tsize)
Add, find, retrieve and remove all start by applying a hash function to an item (or its key)
Hash function uses the key to compute a value between 0 and tsize – 1
Hash(key)  0 .. Tsize - 1
Result is Known as the home address

5. A simple example Tsize is 7 Keys of items to be added are:
345, 617, 963, 712, 366
Hash function is:
Key % tsize
What is the home address of each item to be added?

6. 1 2 3 4 5 6
345 % 7  2
617 % 7  1
963 % 7  4
712 % 7  5
366 % 7  a collision

7. How to deal with collisions?
Collisions are inevitable
Home address becomes the starting point for finding
Where to add a key-value pair
Finding item with a given key
Retrieving the value associated with a given key
Finding key-value pair to be removed
A hash table Needs a collision resolution strategy

8. Two kinds of hash tables
Open hash tables
All items are stored in the array/vector
at their home address (if open)
or follow a probe sequence to find open spot
Chained hash tables
Items with the same home address are synonyms
Synonyms are stored in a list starting at the home address
For both all operations start by applying a hash function and then using the home address as the starting point for finding the item or where to store the item

9. an open hash table add the following items item home address 345 2 1 2 3 4 5 6 E E E E E E E

10. an open hash table Find: 712, 366, 49, 50 E F 617 F 345 F 366 F 963 F1 2 3 4 5 6 E F
617 F
345
Find: 712, 366, 49, 50 F
366 F
963 F
712 E

11. an open hash table Remove: 345 E E F 617 F 617 F 345 R F 366 F 366 F1 2 3 4 5 6 1 2 3 4 5 6 E E F
617 F
617 F
345
Remove: 345 R F
366 F
366 F
963 F
963 F
712 F
712 E E

12. a chained hash table add the following items item home address 345 2 1 2 3 4 5 6

13. a chained hash table Find: 712, 345, 49, 50 Remove: 345 617 366 3451 2 3 4 5 6
617
366
345
Find: 712, 345, 49, 50
Remove: 345
963
712

14. Hash table performance
Depends on
Load factor (n / tsize)
must be < 1 for open hash tale
Can be > 1 for chained hash table
Quality of the hash function
How uniformly are the home addresses produced distributed over the range 0 .. Tsize-1

15. Chained hash tables
Hash function determines which synonym list to search
With a good hash function synonym lists will be of nearly equal length
What is the average synonym list length if we add n items to a hash table with a size of tsize?
Given HT1 and ht2
Both have a load factor of 2
Ht1 holds 1000 items and ht2 holds 4000 items
How does their expected performance compare?
Time to find an item grows at the same rate as the load factor (not n)
search for an item in a chained hash table is O(1)
Search for an item in a closed hash table also increases at same rate as the load factor

16. Hash functions Simplest case
Item being hashed is an integer
Return Item % tsize
What if the item being hashed is a string?
create an integer from the string
Simplest way
Sum the characters (each is stored as an asci value)

17. hash functions Key  0 .. tSize – 1
A good hash function uniformly distributes home addresses over the range 0 .. Tsize-1
What can be done to make a hash function good?
Using a prime number for tsize helps reduce collisions
Knowledge about keys can help devise a better hash function for a given set of key values
Who uses (calls) the hash function?
The program that makes use of a set/map?
The implementer of the map?
Who should write the hash function?
The program that makes use of the map?

18. Map user writes Map implementer uses a hash function the hash function
Map Interface
Map user writes
a hash function
Map implementer uses
the hash function

19. How can the Map user pass the hash function to the map implementer?
a function (like a variable) has a type and a value
The type of a function is its prototype (arguments and return type)
The value of function is a pointer to a block of code to be executed
Typedef int(*hashfunc) (keyType key, int tsize);
Any function that has parameters of keytype and int and returns an int is of type *hashfunc
User of the map writes a hash function and passes it to the map constructor which stores it as a data member

20. MAP IMPLEMENTATION typedef int(*hashFunc)(KeyType item, int tsize);
class Map{
public:
Map(int size, hashFunc func);
private:
hashFunc hash; // the hash function };

21. MAP USER int hash(KeyType key, int tsize);
// input: size of the hash table and a key
// output: returns an int between 0 and tsize - 1
int main () {
Map myMap(size, hash); }
int hash(KeyType key, int tsize){

22. Hash table performance
Two Key factors
Load factor - n / tsize
over .75 for open hash table likely to produce long probe sequences
can be more than 1 for chained hash table
Quality of the hash function
How uniformly are the home addresses produced distributed over the range Tsize-1
Using a prime number for tsize helps reduce collisions
Knowledge about keys can help devise a better hash function for a given set of key values

23. Choosing between a bst and a hash table for a map or set
What do we know about the number of items to be stored?
Space needed for a bst is O(n)
Space needed for a chained HT is O(n + tsize)
Space for an open ht is O(tsize)
What do we know about the items or keys to be compared?
Need to be comparable for both
Need a hash function for a ht
Is it necessary to traverse elements in order of items or keys?