Introduction to data structures

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Introduction to data structures
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Data and Information

• Data are raw facts
• Data are aggregated and summarized to form
  meaningful information
• The result of decision is action, which in turn
  generate more data

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Data and Information
Decision
Information
Data
Action
4
Kind of Decisions

• There are 3 levels of decisions
• Operational decisions, which govern the daily
  activities of the organization.
• Control decisions or tactical decisions, which
  determine the way the organization executes
  designated mission.
• Planning decisions or strategic decisions, which
  develop and define the organizations mission.

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Data Management

• Data must be managed in such a way that they are
  correct and are available to produce needed
  information.

• Storage
• Aggregation
• Update
• Retrieval
• Protection

• Measurement
• Collection
• Transcription
• Validation
• Organization

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Data Management Objectives

• To make data resilient, flexible, and adaptable
  to supporting decision making process.
• Data must be represented and stored so that they
  can be accessed later.
• Data must be organized so that they can be
  selectively and efficiently accessed.
• Data must be processed and presented so that they
  support the user environment effectively.
• Data must be protected and managed so that they
  retain their value.

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What is Data Structures?

• A data structure is a class of data that can be
  characterized by its organization and the
  operations that are defined on it.
• Sometimes called data type

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Classification of Data Structures

• Primitive data structures i.e.integers, booleans,
  and characters
• Simple data structures constructed from one or
  more primitives i.e. strings, arrays, and records
• Linear data structures i.e. stacks, queues, and
  linear linked list
• Nonlinear data structures i.e. trees and graphs
• File organizations i.e. sequential, relative,
  indexed sequential, and multikey file
  organizations

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Integers

• Operation
• Binary operators i.e. addition, subtraction,
  multiplication, division, exponentiation, etc.
• Unary operators i.e. negation

, -3 ,-2 ,-1 ,0 ,1 ,2 ,3 ,
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Booleans

• Also called a logical
• Have one of the two values true or false
• Operation
• Binary operators i.e. or and and
• Unary operator i.e. not
• Not has precedence over or and and
• Relational operators i.e. ,They do not have boolean operands rather they
  are operators with boolean results, e.g. 3
  true

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Booleans
Applied to first operand.
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Characters

• is an element taken from a set of symbols, which
  include the numeric digits, the alphabetic
  characters and some special characters.

0,1,2,3,4,5,6,7,8,9,A,B,C,D,,X,Y,Z,
,?,.,,,-,/
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Strings

• is a finite sequence of symbols taken from a
  character set which is called alphabet.
• e.g. alphabet A C,D,1
• A set of strings derived from alphabet A are
  CD1, CD, DDC, 1D111, and so forth.
• Three major operations on strings are
• Length
• Concatenation
• Substring

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Strings

• String length
• Length operator has one operand, of type string,
  and produce a result of type integer.

N Length(S)
e.g. S computer Length(S) 8
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Strings

• String concatenation
• Concatenation operates on two strings, placing
  them end to end to produce a resultant string.
• Concatenation operator has two operands, both of
  type string, and produces a result of type string.

Concat(String1,String2)
e.g. A sale B person Concat(A,B) is
saleperson
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Strings

• Substring
• Substring has a single string as one of its
  operands and generates a new string as its
  result.
• Substring operator has one operand of type
  string, two operands of type integer, and
  produces a result of type string.

String
Number of characters to take
Substr(S,i,j)
Starting point
e.g. S representation Substr(S,3,7) is
present
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Strings (Composite Operations)

• Insertion
• Insertion operator has two operands of type
  string, one operand of type integer, and produces
  a result of type string.
• Insert the string S0 into the string S, such
  that the first character of S0 is the ith
  character of the result

Insert(S,S0,i)
e.g. S comment S0 ple Insert(S,
S0,4) is complement
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Strings (Composite Operations)

• Deletion
• Deletion operator has one operands of type
  string, two operands of type integer, and
  produces a result of type string.

Delete(S,i,j)

• To delete substring of length j that starts at
  the ith character from string S.

e.g. S database Delete(S, 5,4)
??? data
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Strings and Integers

• Strings with
• Integer without or
• So 1234 and 1234 are different.

Integer value
String value

• String operators length, concatenation,
  substring- cannot be applied to variables that
  are of integer data type

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Mapping to Storage Integers

• One characteristic of logical data structure is
  that it may have several possible storage mapping
  or physical representation.
• Sign and Magnitude Representation
• Positive integers are identified by a plus sign
  and a string of digits which represent the
  magnitude.
• Negative integers are identified by a minus sign
  and a string of digits which represent the
  magnitude.
• e.g. 250, -100, 7, -7
• e.g. 500 (-200) ?

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Mapping to Storage Integers

• Ones-Complement Representation
• Ones-complement can be used to represent
  negative numbers.
• Ones complement of X can be formed by
  subtracting from a long string of one. (Reverting
  bits of positive X from 1 to 0 and 0 to 1)
• e.g. The ones complement form of 0101 (5) is
  represented as 1 1 1 1
• 0 1 0 1-
• 1 0 1 0 (-5)

• e.g. 7 (5) ?

1
1
1
0111
1010
0010
1
0
0
0
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Mapping to Storage Integers

• Twos-Complement Representation

• An easier method to get the two's complement of a
  number is as follows
• 1. Starting from the right, find the first '1
• 2. Invert all of the bits to the left of that
  one
• Example
• 0101001
• 1010111

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Mapping to Storage Integers

• Twos-Complement Representation
• To convert to -5 in twos complement notation,
  locate the first 1 in binary representation of 5
  (0101), and reverse all remaining left bits
• 1011 (-5)

• e.g. 7 (5) ?

1
1
1
1
ignored
0111
1011
0010
0
1
0
0
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Mapping to Storage Characters

• The two most prevalent encoding schemes are
• Extended Binary Coded Decimal Interchange Code
  (EBCDIC)
• 8 bits are required to represent any character in
  the character set.
• American Standard Code for Information
  Interchange (ASCII)
• 7 bits are required to represent any character in
  the character set.
• Consume less storage and can be transmitted more
  quickly.

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Mapping to Storage Characters

• Special purpose schemes
• Huffman Code
• Characters are represented by a variable number
  of bits depending upon the relative frequency of
  occurrence of the character in the vocabulary of
  the application.
• e.g.

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Mapping to Storage Strings

• To store string in storage, pointer which
  identifies a storage location is required.
• e.g. string1ABCDEFG, string2BCD
• There are 3 simple ways to store string variable
  in contiguous space.
• 1.Keep string name, starting address, and length

• The corresponding storage format could be
• A B C D E F G B C D

PTR1S
PTR2S
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Mapping to Storage Strings

• 2.Keep strings name, its starting address, and
  terminating address

• The corresponding storage format could be
• A B C D E F G B C D
• OR (overlaying the strings)

PTR1S
PTR1T
PTR2T
PTR2S
A B C D E F G
PTR1S
PTR1T
PTR2S
PTR2T
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Mapping to Storage Strings

• 3.Keep strings name and its starting address. Use
  an end of string marker in storage to delimit the
  string.

• The corresponding storage format could be
• A B C D E F G B C D

PTR1S
PTR2S
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Mapping to Storage Strings

• Packed-String Representation
• Placing each of the successive codes for the
  characters in successive storage words, with as
  many of the characters as possible in any given
  word.
• e.g. string BINDERSTWINE with four
  character-per-word packing

word i
word i1
word i2
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Mapping to Storage Strings

• Packed-String Representation
• Number of words required to store string S is
  Length(S)/K, where K represents characters per
  word.
• For example, String S decisionmaker with 32
  bits per word.
• Number of words required is 13/4 4 words

• Sometimes the character codes fit words evenly
  If there are 16 bits per word, EBCDIC with 8 bits
  per character fits very well. However, ASCII,
  with 7 bits per characters, will allow two
  characters in a 16-bit word with two unusable
  bits remaining.

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Mapping to Storage Strings

• Unpacked-String Representation
• Storing one to a word the character codes for
  each of the successive characters.
• e.g. string BINDERSTWINE stored in unpacked
  format as follow

• The number of words required to store string S in
  unpacked format is Length(S).