Data Abstraction (Chapter 1)

C-1
Introduction
- Programis written in order to solvea problem.
- Solution to a problem consists of two things
 Data structure
 Algorithm
- Data Structure - the way data are organized in a computer’s memory
- Algorithm- sequence of computational steps to solve a problem
- The first step to solvea problem is obtaining an abstractview (model) of
the problem.
- A Model defines an abstractview to the problem.
- Properties of a problem
 Affected data
 Operations involved
- Data structurecan be defined by well-defined entities created by
abstraction
- Data structures modelthe static part of the world. They are unchanging
while the world is changing.
- Quality of a data structureis related to its ability to successfully modelthe
characteristics of the world
Abstract DataTypes
- ADT is an abstraction of data structure
- ADTs specify
 What can be stored in them
 What operations can be done (on/by them)
- Data structure is a language constructthat a programmer defined in order
to implement an ADT.
- Formalized and standard ADTs: - Stacks, Queues, Trees, …
Abstraction
- Abstraction is a process of classifying characteristics as relevant and
irrelevant and ignoring the irrelevantones.

Algorithms
- Algorithm is a well-defined computational procedurethat takes some value
or a set of values as input and produces somevalue or a set of values as
output.
- Algorithms model the dynamic part of the world
- Algorithms transform data structures fromone state to another state in
two ways
 Changing the value held by a data structure
 Changing the data structureitself
- The quality of an algorithm is related to its ability to successfully simulate
the changes in the world.
- Independentof any particular world model, the quality of data structure
and algorithms is determined by their ability to work together well
Properties of anAlgorithm
1. Finiteness: mustcomplete after a finite number of steps.
2. Definiteness: Each step mustbe clearly defined
3. Sequence: Each step must havea unique defined preceding and succeeding
step
4. Feasibility: Itmustbe possibleto performeach instruction.
5. Correctness: Itmustcomputecorrect answer for all possiblelegal inputs.
6. Language Independence: Itmustnotdepend on any one programming
language.
7. Completeness: Itmustsolvethe problem completely.
8. Effectiveness: Itmustbepossibleto performeach step exactly and in a
finite amount of time.
9. Efficiency: Itmustsolvewith the least amount of computational resources
such as time and space.

10.Generality: Algorithmshould bevalid on all possibleinputs.
11.Input/Output: There mustbe a specified number of input values, and one
or moreresult values.
AlgorithmAnalysis
- Itis the process of determining the amount of computing time and storage
spacerequired by differentalgorithms.
- Itis a process of predicting the resourcerequirementof algorithms in a
given environment.
- To classify somedata structures and algorithms as good, we need precise
ways of analyzing them in terms of resourcerequirement.
- The main resources are:
 Running Time: usually treated as the most important
 Memory Usage
 Communication Bandwidth
- approaches to measurethe efficiency of algorithms:
 Empirical: Programming competing algorithms and trying them
on different instances.
 Theoretical: Determining the quantity of resources required
mathematically by each algorithm.
- Clock-time is difficult to useas a consistentmeasureof an algorithm’s
efficiency becauseit varies.
- Clock-time can vary based on:
 Specific processor speed
 Currentprocessor load
 Specific data for a particular run of the program
 InputSize
 InputProperties
 Operating Environment
- We can analyzean algorithm according to the number of operations
required.

Complexity Analysis
- Itis the systematic study of the costof computation, measured either in
time units or in operations performed, or in the amount of storage space
required.
- Two things to consider:
 Time Complexity: Determinethe approximate number of
operations required to solvea problemof size n.
 Space Complexity: Determinethe approximate memory
required to solvea problem of sizen.
- Complexity analysis involves two distinct phases:
o AlgorithmAnalysis: is the process of finding the computational
complexity of algorithms – the amount of time, storage, or other
resources needed to execute them.
o Order of Magnitude Analysis: to determine the general complexity
category to which it belongs.
-
Analysis Rules
- We assumean arbitrary time unit.
- Execution of one of the following operations takes time 1:
 AssignmentOperation
 Single Input/outputOperation
 Single Boolean Operations
 Single Arithmetic Operations
 Function Return
- Running time of a selection statement (if, switch) is the time for the
condition evaluation + the maximum of the running times for the individual
clauses in the selection.
- Loops: Running time for a loop is equal to the running time for the
statements inside the loop * number of iterations.
- The total running time of a statement inside a group of nested loops is the
running time of the statements multiplied by the productof the sizes of all
the loops. For nested loops, analyzeinside out.

- Always assumethat the loop executes the maximum number of iterations
possible.
- Running time of a function call is 1 for setup + the time for any parameter
calculations + the time required for the execution of the function body.
-
Formalapproach to analysis
Measures of times
Asymptotic Analysis

Data Abstraction (Chapter 1)

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