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## Intro to Data Structures and ADTs

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### Intro to Data Structures and ADTs

Chapter 2

Goal of Data Structures

- Organize data
- Facilitate efficient …
- storage
- retrieval
- manipulation
- Select and design appropriate data types
- This is the real essence of OOP

of data

Simplicity Tradeoff

- Simplicity of data organization versus
- Simplicity/elegance of algorithms
- Simple (unsophisticated) data structure
- may require much work for processing data.
- More complex data organization
- May yield nicer algorithms for the basic operations

Issues

- Amount of data
- phone book lookup (Hallsville vs. Dallas)
- linear search?
- Number of accesses and use required
- compiler's lookup of an identifier's type in a symbol table
- linear, binary, hash table?
- Static vs. dynamic nature of the data
- consider a text processor
- array, vector?

Abstract Data Types (ADT)

- Defn: collection of
- related data items … together with
- an associated set of operations
- Why "abstract?"
- Data, operations, and relations are studiedindependent of implementation.
- Whatnot how is the focus.

Implementation of an ADT

- Defn: storage (data) structures which
- store the data items … and
- algorithms for the basic operations
- These data structures are
- provided in a language or
- built from the language constructs (user defined)

Implementation of an ADT

- Successful software design usesdata abstraction
- We separate the
- definition of a data type from
- the implementation

Memory

- 2-state devices « bits 0 and 1
- Organized into
- bytes (8 bits) and
- words (machine dependent — e.g., 4 bytes).
- Each byte (or word) has an address
- to store and retrieve contents of any given memory location.

Simple Data Types

- The most basic form of datasequences of bits
- Simple data types
- values are atomic — can't be subdivided
- are ADTs.
- Implementations have:
- Storage structures: memory locations
- Algorithms: system hardware/software to do basic operations.

Simple Data Types

- Boolean
- values { false, true }
- could be stored in bits, usually use a byte
- operations &&, ||
- Character
- byte for ASCII, EBCDIC
- 2 bytes for Unicode (Java)
- operations ==, <, >, etc. using numeric code

Simple Data Types

- Unsigned Integer data
- non-negative unsigned integers
- stored in base-two in a fixed number of bits
- Signed integer
- stored in a fixed number of bits
- Representations
- sign-magnitude
- two's complement

Sign-magnitude Representation

- Save one bit (usually most significant) for sign(0 = +, 1 = – )
- Use base-two representation in the other bits.
- 88 = 0000000001011000
- -88 = 1 000000001011000

Cumbersome for arithmetic computations

Two's Complement Representation

- For nonnegative n:
- Use ordinary base-two representation with leading (sign) bit 0
- For n < 0
- Find w-bit base-2 representation of |n|
- Complement each bit.
- Add 1

Two's Complement Representation

- Example: –88
- 88 as a 16-bit base-two number0000000001011000
- Complement this bit string1111111110100111
- Add 11111111110101000

WHY?

Two's Complement Representation

- Works well for arithmetic computations

- 5 + –6:
- 0000000000000101
- +1111111111111010

1111111111111111

What gets done to the bits to give this answer?

Biased Representation

- Add a constant bias to the number
- typically 2w-1 (where w is number of bits)
- then find its base-two representation
- Example: 88 using w = 16 bits and bias of 215 = 32768
- Add the bias to 88, giving 32856
- Represent the result in base-two notation:1000000001011000

Biased Representation

- Example -88 usingw = 16 bits and bias of 215 = 32768
- Add the bias to -88, giving 32680
- Represent the result in base-two notation:0111111110101000
- Good for comparisons; so, it is commonly used for exponents in floating-point representation of reals.

Problems with Integer Representation

- Limited Capacity — a finite number of bits
- An operation can produce a value that requires more bits than maximum number allowed.This is called overflow .
- None of these is a perfect representation of (mathematical) integers
- Can only store a finite (sub)range of them.

Real Data

- Types float and double in C++
- Use single precision (IEEE Floating-Point)
- Store:
- sign of mantissa in leftmost bit (0 = +, 1 = – )
- biased binary rep. of exponent in next 8 bits (bias = 127)
- bits b2b3 . . .b24 mantissa in rightmost 23 bits.
- Need not store b1 — know it's 1)

Real Data

- Example: 22.625 = 10110.1012
- Floating point form:1.01101012 * 24

Problems with Real Representation

- Exponent overflow and underflow
- Round off error
- Most reals do not have terminating binary representations.

Example:

0.7 = (0.10110011001100110011001100. . .)2

Problems with Real Representation

- Round off error may be compounded in a sequence of operations.
- Recall the sums of calculated currency values
- Be careful in comparing reals
- with == and !=.
- Instead use comparison for closenessif (abs (x – 12.34) < 0.001) …

C-Style Data StructuresArrays

- Single dimension int numList [30];
- Multi dimension float realList [10][10]; int numTable [3][4][5];
- All elements of same type
- Elements accessed by
- name and [ ] operator numList[5]
- name, offset, and dereference *(numlist + 5)
- Name of the array is a pointer constant

Note you must specify number of elements used

Same call for either style of parameter list declaration

Arrays- Arrays as parameters
- Formal parameter void doIt (int list[ ], int count); / orvoid toIt (int *list, int count);
- Actual parameterdoit (numList, numUsed);

Problems with C-Style Arrays

- Capacity cannot change.
- Solution 1 (non-OOP)
- Use a "run-time array"
- Construct B to have required capacity
- Copy elements of A into B
- Deallocate A

Solution 2 (OOP) Use vector

Later

Problems with C-Style Arrays

- Virtually no predefined operations for non-char arrays.
- The Deeper Problem:
- C-style arrays aren't self-contained.

Basic Principle of OOP:

- An object should be autonomous(self-contained)
- Should carry within itself all of the information needed to describe and operate upon itself.

Aggregate Data Types

- Predefined types not always adequate to model the problem
- When objects have multiple attributes
- When objects have collections of heterogeneous elements
- C++ provides structs and classes
- Create new types with multiple attributes

Structures

- Characteristics
- has a fixed size
- is ordered
- elements may be of different size
- direct access of elements by name (not index)

struct Date {int month, day, year;char dayOfWeek [12];

};

FAQs about Structures

- structs can be nested (can contain struct objects)
- Access members with
- name of struct object
- dot (member selector operator) .
- name of struct member

Date today = { 3, 4, 2005, "Tuesday");

cout << today.month;

Procedural: ( C, FORTRAN, and Pascal )

Action-oriented — concentrates on the verbs

Programmers:

Identify basic tasks to solve problem

Implement actions to do tasks as subprograms (procedures/functions/subroutines)

Group subprograms into programs/modules/libraries,

together make up a complete system for solving the problem

Object-oriented: ( C++, Java, and Smalltalk)

Focuses on the nouns of problem specification

Programmers:

Determine objects needed for problem

Determine how they should work together to solve the problem.

Create types called classes made up of

data members

function members to operate on the data.

Instances of a type (class) called objects.

A commercial for OOP: Two programming paradigms
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