CS 2430
Day 34
Announcements
• No office hours tomorrow
• Lab tomorrow (graphics, keyboard, mouse
input)
• Quiz this Friday
• Exam #3: 12/12/12
Agenda
• Linear probe (review)
• Quadratic probe
• Double hash
Linear probe
•
•
•
•
Table size = 11
Hash function: H(x) = x % 11
Next index function: f(n) = n
In the event of a collision, we use: H(x + n) =
(x + n) % 11, where we increment n for each
collision (starting from 0)
Linear probe example
H(x
H(x
H(x
H(x
H(x
H(x)
+ 1)
+ 2)
+ 3)
+ 4)
+ 5)
=
=
=
=
=
=
(x
(x
(x
(x
(x
+
+
+
+
+
x
1)
2)
3)
4)
5)
%
%
%
%
%
%
11
11
11
11
11
11
55
23
45
86
0
1
2
3
8
23
32
45
55
75
86
8
1
10
1
2
0
9
9
10
0
1
2
3
8
75
32
8
9
10
4
5
6
7
Next: quadratic probing
Quadratic probe
•
•
•
•
Table size = 11 (should always be prime)
Hash function: H(x) = x % 11
Next index function: f(n) = n2
For collisions, we use H(x + n2) = (x + n2) %
11
Quadratic probe example
H(x)
H(x + 12)
H(x + 22)
H(x + 32)
=
=
=
=
x
(x + 1)
(x + 4)
(x + 9)
55
23
45
0
1
2
%
%
%
%
11
11
11
11
3
8
23
32
45
55
75
86
8
1
10
1
2
0
9
9
10
2
7
86
8
75
32
7
8
9
10
4
5
6
A full table!
• For linear probing, it is a bad idea to let the
hash table get nearly full
• For quadratic probing, the situation is much
more drastic!
A drastic situation
• Fact: if quadratic probing is used and the table
size is prime, then a new object can always be
added if the table is at least half empty
• That is, if the table is more than half full, then
it is not always possible to add a new object.
• Why?
• Think about it…
Go to THE THING:
https://xray.ion.uwplatt.edu/summerss
Double hashing
• Table size = 11
• Hash function: H(x) = x % 11
• Next index function: f(n) = cn, where c is the
“hashing constant”
• For collisions, we use H(x + cn) = (x + cn) %
11
• In our example, we will let c = 3
Double hash example
H(x)
H(x + 3*1)
H(x + 3*2)
H(x + 3*3)
=
=
=
=
x
(x + 3)
(x + 6)
(x + 9)
55
23
0
1
%
%
%
%
11
11
11
11
8
23
32
45
55
75
86
8
1
10
1
4
0
9
9
1
4
7
86
8
75
32
7
8
9
10
45
2
3
4
5
6
Important
• For double hashing, the table size and the
hashing constant, c, must be relatively prime
• Why?
• Not every array location will be searched!
Double hash disaster!!
H(x
H(x
H(x
H(x
H(x
H(x
+
+
+
+
+
+
H(x)
3*1)
3*2)
3*3)
3*4)
3*5)
3*6)
=
=
=
=
=
=
=
x
(x + 3)
(x + 6)
(x + 9)
(x + 12)
(x + 15)
(x + 18)
%
%
%
%
%
%
%
11
11
11
11
11
11
11
2
5
8
11
2
5
8
2
5
8
2
5
8
2
2
0
1
2
5
3
4
5
8
6
7
8
Go to THE THING:
https://xray.ion.uwplatt.edu/summerss