The document discusses hash tables as an efficient data structure for implementing dictionary operations. It describes how hash tables work by using a hash function to map keys to array indices, allowing for fast lookup times of O(1) on average. When collisions occur where two keys map to the same index, techniques like chaining can be used to resolve them. Hash tables are preferable to direct address tables when the key universe is very large relative to the actual number of keys, as they avoid wasting large amounts of memory when most array slots would be empty.

1. Zahoor Jan
Lecture-05
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2.  Tables
 Direct address tables
 Hash tables
 Collision and collision resolution
 Chaining
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3.  Many applications require a dynamic set that
supports dictionary operations.
 Example: a compiler maintaining a symbol
table where keys correspond to identifiers
 Hash table is a good data structure for
implementing dictionary operations
 Although searching can take as long as a
linked list implementation i.e. O(n) in worst
case.
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4.  With reasonable assumptions it can take O(1)
time.
 In practice hashing performs extremely well.
 A hash table is a generalization of an ordinary
array where direct addressing takes O(1) time.
 When the actual keys are NOT small relative to
the total number of keys, hashing is an effective
alternative.
 A key can be accessed using an array index, or is
computed.
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5.  Table is an abstract storage that contains table
entries
 Each table entry contains a unique key k.
 Each table entry may also contain some
information, I, associated with its key.
 A table entry is an ordered pair (K, I)
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6.  Suppose:
◦ The range of keys is 0..m-1
◦ Keys are distinct
 The idea:
◦ Set up an array T[0..m-1] in which
 T[i] = x if x T and key[x] = i
 T[i] = NULL otherwise
◦ This is called a direct-address table
 Operations take O(1) time!
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7. 8
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8.  Direct Addressing is the most efficient way to
access the data since.
 It takes only single step for any operation on
direct address table.
 It works well when the Universe U of keys is
reasonable small.
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9. When the universe U is very large…
 Storing a table T of size U may be impractical,
given the memory available on a typical computer.
 The set K of the keys actually stored may be so
small relative to U that most of the space
allocated for T would be wasted.
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10.  A table, 50 students in a class.
 The key, 9 digit SSN, used to identify each
student.
 Number of different 9 digit number=109
 The fraction of actual keys needed. 50/109,
0.000005%
 Percent of the memory allocated for table
wasted, 99.999995%
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11.  The table should be of small fixed size.
 Any key in the universe should be able to be
mapped in the slot into table, using some
mapping function
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