Linear Probing (9.3)


How do you insert an item in a hash table using Linear Probing?

	sequentially scan the array until an empty cell is found
	wrap-around from the last position to the first


Show the result of inserting 2, 7, 3, 8 into a hash table of size 5.


How do you find an item in a hash table using Linear Probing?

	follow the same sequence as insert
	if you reach an empty slot, the item is not in the table


Show the result of finding 8 and 9 in the hash table.

















Classwork
You may work with a partner.

Show the result of inserting 7, 6, 1, 2 into a hash table of size 5.

















How do you delete an item from a hash table using Linear Probing?


	you must use lazy deletion

	mark cell, looks empty for insert, used for find

















Performance Analysis of Linear Probing


What's the Load Factor of a hash table?

	the number of items in the table divided by the table size

	LoadFactor = n/m
		n is the number of items in the table
		m is the size of the array used for the table


How many compares are needed (on average) to find an item
in a linear-probing hash table?

	Compares = 1/2 * (1 + 1/(1 - LoadFactor))  (Knuth, vol 3)
					(for a successful search)

	1.50 compares when Load Factor is 0.50
	2.50 compares when Load Factor is 0.75
	10.50 compares when Load Factor is 0.95
		(what happens if Load Factor is 1.0)


What's a good Load Factor to use with linear probing?

	less than 0.50

















Rehashing


What do you do when the Load Factor becomes too high?

	grow the table (like an ArrayList)


Do you copy each item from the old table to the same location in the new table?

	no, the hash function is different because the table size is different
	hash each item into the new table

















Quadratic Probing


How do you insert an item in a hash table using Quadratic Probing?

	scan cells 1, 4, 9, ... away from the original probe
	if the hash function gives H, scan H+(i^2) instead of H+i


Show the result of inserting 2, 7, 3, 8 into a hash table of size 5.

















Classwork
You may work with a partner.

Show the result of inserting 7, 6, 1, 2 into a hash table of size 5.

















Will Quadratic Probing find an empty cell?

	if the table size is prime
	and the load factor is <= 0.5
	probes will be to different locations


Why use Quadratic Probing rather than Linear Probing?

	linear probing tends to create clusters of occupied cells
	quadratic probing results in less clustering

















Double Hashing


What's Double Hashing?

	like linear probing
	but a second hash function gives the amount to increment

	H(x) + 0*H2(x)
	H(x) + 1*H2(x)
	H(x) + 2*H2(x)
	...
	H(x) + i*H2(x)


Show the result of inserting 2, 7, 3, 8 into a hash table of size 5.
(Use H(x) = x % 5 and H2(x) = x % 3 + 1.)

















Classwork
You may work with a partner.

Show the result of inserting 7, 6, 1, 2 into a hash table of size 5.
(Use H(x) = x % 5 and H2(x) = x % 3 + 1.)