Chapter 11: Hash Tables.

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Presentation transcript:

Chapter 11: Hash Tables

Hash Tables

Direct Address Tables

Direct Address Tables

Hash Tables

Hashing with Chaining

Hashing with Chaining

Hashing with Chaining

Hashing with Chaining

Hashing with Chaining

Hashing with Chaining Proof is not covered in CS312.

Hash Functions

Hash Functions

Hash Functions: Division Method

Hash Functions: Multiplication Method

Hash Functions: Multiplication Method

Hash Functions: Multiplication Method 𝑚= 2 𝑝 0<𝑠< 2 𝑤 𝐴= 𝑠 2 𝑤

Hash Functions: Multiplication Method

Hash Tables: Open Addressing

Hash Tables: Open Addressing

Hash Tables: Open Addressing

Hash Tables: Open Addressing // It is a number between 0 and m-1

Hash Tables: Open Addressing

Hash Tables: Open Addressing

Hash Tables: Open Addressing

Hash Tables: Open Addressing

Hash Tables: Open Addressing Example: Hash table size 13 with h1(k)= k mod 13 and h2(k)= 1+(k mod 11) Consider k = 14. h1(14) = 1 and h2(14) =4. Therefore, we probe 1, 5, 9, …

Hash Tables: Open Addressing

Hash Tables: Open Addressing

Hash Tables: Open Addressing

Hash Tables: Open Addressing

Hash Tables: Open Addressing Proof: not covered in CS312