Hashing

CSCE 3110 Data Structures & Algorithm Analysis Rada Mihalcea http://www.cs.unt.edu/~rada/CSCE3110 Hashing Reading: Chap.5, Weiss

How to Implement a Dictionary? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Hashing ,[object Object],[object Object],[object Object]

Basic Idea ,[object Object],[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],[object Object],... 0 1 2 3 1000 hash table buckets

Analysis (Ideal Case) ,[object Object],[object Object]

Ideal Case is Unrealistic ,[object Object],[object Object],[object Object],[object Object],[object Object]

Hash Functions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Collision Resolution Policies ,[object Object],[object Object],[object Object],[object Object]

Closed Hashing ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example Linear (Closed) Hashing ,[object Object],0 2 3 4 5 6 7 1 b a c ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],d

Operations Using Linear Hashing ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Performance Analysis - Worst Case ,[object Object],[object Object],[object Object]

Performance Analysis - Avg Case ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Improved Collision Resolution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 0 1 2 3 4 5 6 7 8 9 10 1001 9537 3016 9874 2009 9875 h(k) = k%11 0 1 2 3 4 5 6 7 8 9 10 1001 9537 3016 9874 2009 9875 1. What if next element has home bucket 0?  go to bucket 3 Same for elements with home bucket 1 or 2! Only a record with home position 3 will stay.  p = 4/11 that next record will go to bucket 3 2. Similarly, records hashing to 7,8,9 will end up in 10 3. Only records hashing to 4 will end up in 4 (p=1/11); same for 5 and 6 I II insert 1052 (h.b. 7) 1052 next element in bucket 3 with p = 8/11

Hash Functions - Numerical Values ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Hash Function – Strings of Characters ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Hash Function – Strings of Characters ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Open Hashing ,[object Object],[object Object],[object Object],[object Object]

Open Hashing Data Organization 0 1 2 3 4 D-1 ... ... ...

Analysis ,[object Object],[object Object],[object Object],[object Object]

Analysis Cont’d ,[object Object],[object Object],[object Object],[object Object],[object Object]

Comparison with Closed Hashing ,[object Object],[object Object],[object Object],[object Object],[object Object]

Hashing Problem ,[object Object],[object Object]

Hashing

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