1. Richard Anderson (instead of Martin Tompa)
CSE 326 Hashing
Richard Anderson
(instead of Martin Tompa)

2. Chaining review H(k) = k mod 17 k H(k) A B C D E F G H I J K1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 k
H(k) A B C D E F G H I J K
H(k) = k mod 17
Collect twelve birthdays from students and hash into the table with chaining

3. Open address hashing Store all elements in table
If a cell is occupied, try another cell.
Linear probing, try cells
H(k), H(k) + 1 mod m, H(k) + 2 mod m, . .

4. Open Address Hashing H(k) = k mod 17 k H(k) A 53 2 B 41 7 C 91 6 D 751 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 A 3 I 4 J 5 6 C 7 B 8 D 9 F 10 K 11 12 13 E 14 15 16 H k
H(k) A 53 2 B 41 7 C 91 6 D 75 E 13 F G 43 H 67 16 I 88 3 J 36 K 40
H(k) = k mod 17
Collect twelve birthdays from students and hash into the table with chaining
Step through example
Emphasize the growing regions

5. Open address hashing Lookup (K) { p = H(K); loop {
if (A[p] is empty) return false;
if (A[p] == K) return true;
p = (p + 1) mod m; }

6. Open address hashing issues
Clumping
Cost per operation
Deletion

7. Double hashing
Use separate hash functions for the first probe and the collision resolution
H1(k), H1(k) + H2(k) mod m, H1(k) + 2H2(k) mod m, H1(k) + 3H2(k) mod m , . . .
Return to earlier slide to update the access code

8. Double hashing example1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
month
day
H1(k) A B C D E F G H I J K
H1(k) = day mod 17
H2(k) = month
Collect twelve birthdays (month and day) from students and hash into the table with chaining
WRITE MONTHS AS NUMBERS

9. Double hashing vs. Single hashing
Load factor a, cost per operation
Single hashing
Double hashing
Single
Double a

10. Trade offs between chaining and open addressing
Chaining Open Addressing
Space
Time
Deletions
Coding complexity
High load factor

11. Hash Functions Function Efficient Uniform mapping to range
Avoids systematic collisions

12. Hashing strings
String
Suppose

13. Fact:
So: