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Hash Tables

Hash Tables. Chapter 12 discusses several ways of storing information in an array, and later searching for the information. Hash tables are a common approach to the storing/searching problem. Data Structures and Other Objects Using C++. Serial Search.

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Hash Tables

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  1. Hash Tables • Chapter 12 discusses several ways of storing information in an array, and later searching for the information. • Hash tablesare a common approach to the storing/searching problem. Data Structures and Other Objects Using C++

  2. Serial Search • Algorithm: step through an array, check one item at a time looking for a desired item

  3. Binary Search

  4. What is a Hash Table ? • The simplest kind of hash table is an array of records. • This example has 701 records. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700] . . . An array of records

  5. What is a Hash Table ? [ 4 ] • Each record has a special field --- unique identification value, called its key. • In this example, the key is a long integer field called Number. Number 506643548 [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700] . . .

  6. What is a Hash Table ? [ 4 ] Number 506643548 • The number might be a person's identification number, and the rest of the record has information about the person. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700] . . .

  7. Number 281942902 Number 233667136 Number 506643548 Number 155778322 . . . What is a Hash Table ? • When a hash table is in use, some spots contain valid records, and other spots are "empty". [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  8. Number 281942902 Number 233667136 Number 506643548 Number 155778322 . . . Inserting a New Record Number 580625685 • In order to insert a new record, the key must somehow be converted toan array index. • The index is called the hash valueof the key. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  9. Number 281942902 Number 233667136 Number 506643548 Number 155778322 . . . Inserting a New Record Number 580625685 • Typical way create a hash value through hash function: (Number % 701) What is (580625685 % 701) ? [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  10. Number 281942902 Number 233667136 Number 506643548 Number 155778322 . . . Inserting a New Record Number 580625685 • Typical way to create a hash value: (Number mod 701) 3 What is (580625685 mod 701) ? [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  11. [3] Number 281942902 Number 233667136 Number 506643548 Number 155778322 . . . Inserting a New Record Number 580625685 • The hash value is used for the location of the new record. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  12. Number 281942902 Number 233667136 Number 580625685 Number 506643548 Number 155778322 . . . Inserting a New Record • The hash value is used for the location of the new record. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  13. My hash value is [2]. Number 281942902 Number 233667136 Number 580625685 Number 506643548 Number 155778322 . . . Collisions Number 701466868 • Here is another new record to insert, with a hash value of 2. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  14. When a collision occurs, move forward until you find an empty spot --- open-address hashing. Number 281942902 Number 233667136 Number 580625685 Number 506643548 Number 155778322 . . . Collisions Number 701466868 • This is called a collision, because there is already another valid record at [2]. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  15. When a collision occurs, move forward until you find an empty spot. Number 281942902 Number 233667136 Number 580625685 Number 506643548 Number 155778322 . . . Collisions Number 701466868 • This is called a collision, because there is already another valid record at [2]. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  16. When a collision occurs, move forward until you find an empty spot. Number 281942902 Number 233667136 Number 580625685 Number 506643548 Number 155778322 . . . Collisions Number 701466868 • This is called a collision, because there is already another valid record at [2]. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  17. The new record goes in the empty spot. Number 281942902 Number 233667136 Number 701466868 Number 580625685 Number 506643548 Number 155778322 . . . Collisions • This is called a collision, because there is already another valid record at [2]. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  18. Number 281942902 Number 233667136 Number 701466868 Number 580625685 Number 506643548 Number 155778322 . . . A Quiz Where would you be placed in this table, if there is no collision? Use your social security number or some other favorite number. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  19. Number 281942902 Number 233667136 Number 701466868 Number 580625685 Number 506643548 Number 155778322 . . . Searching for a Key Number 701466868 • The data that's attached to a key can be found fairly quickly. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  20. My hash value is [2]. Not me. Number 281942902 Number 233667136 Number 701466868 Number 580625685 Number 506643548 Number 155778322 . . . Searching for a Key Number 701466868 • Calculate the hash value. • Check that location of the array for the key. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  21. My hash value is [2]. Not me. Number 281942902 Number 233667136 Number 701466868 Number 580625685 Number 506643548 Number 155778322 . . . Searching for a Key Number 701466868 • Keep moving forward until you find the key, or you reach an empty spot. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  22. My hash value is [2]. Not me. Number 281942902 Number 233667136 Number 701466868 Number 580625685 Number 506643548 Number 155778322 . . . Searching for a Key Number 701466868 • Keep moving forward until you find the key, or you reach an empty spot. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  23. My hash value is [2]. Yes! Number 281942902 Number 233667136 Number 701466868 Number 580625685 Number 506643548 Number 155778322 . . . Searching for a Key Number 701466868 • Keep moving forward until you find the key, or you reach an empty spot. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  24. My hash value is [2]. Yes! Number 281942902 Number 233667136 Number 701466868 Number 580625685 Number 506643548 Number 155778322 . . . Searching for a Key Number 701466868 • When the item is found, the information can be copied to the necessary location. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  25. Please delete me. Number 281942902 Number 233667136 Number 701466868 Number 580625685 Number 506643548 Number 155778322 . . . Deleting a Record • Records may also be deleted from a hash table. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  26. Number 281942902 Number 233667136 Number 701466868 Number 580625685 Number 155778322 . . . Deleting a Record • Records may also be deleted from a hash table. • But the location must not be left as an ordinary "empty spot" since that could interfere with searches. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  27. Number 281942902 Number 233667136 Number 701466868 Number 580625685 Number 155778322 . . . Deleting a Record • Records may also be deleted from a hash table. • But the location must not be left as an ordinary "empty spot" since that could interfere with searches. • The location must be marked in some special way so that a search can tell that the spot used to have something in it. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

  28. Double Hashing • Linear probing: the insertion function move forward from the calculated index until a vacant spot is found in the hash table • Double hashing: uses a second hash function to determine how to resolve a collision • Example: hash1(key) = 330; hash2(key) = 7 • If location 330 is occupied, then move forward 7 spots and try location 337. If 337 is also occupied, then move forward 7 spots to location 344, and so on. • If the calculation of the next spot beyond the end of the array, then “wrap around” to the front of the array

  29. Quadratic Probing • If there is a collision, then move to the next array index. If there is a second collision, then move forward two more spots through the array. After a third collision, move forward three more spots, and so on. • If the calculation of the next spot beyond the end of the array, then “wrap around” to the front of the array

  30. Chained Hashing • Open-address hashing: a collision is handled by probing the array for an unused position. Each array location can hold just one entry. • Chained hashing (Chaining): each location of the hash table’s array can hold more than one entry

  31. Time Analysis

  32. Summary • Hash tables store a collection of records with keys. • The location of a record depends on the hash value of the record's key. • When a collision occurs, the next available location is used. • Searching for a particular key is generally quick. • When an item is deleted, the location must be marked in a special way, so that the searches know that the spot used to be used.

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