1. Abstract Data Types (ADT)
TECHNICAL UNIVERSITY OF CRETE DEPT OF ELECTRONIC AND COMPUTER ENGINEERING
DATA STRUCTURES
AND
FILE STRUCTURES
Euripides G.M. Petrakis
Chania, 2007
E.G.M. Petrakis
Abstract Data Types (ADT)

2. Abstract Data Types (ADT)
Introduction
We study data structures and we learn how to write efficient programs
this hasn’t to do with programming tricks but rather with
good organization of information and good algorithms that save
computer memory and running time
E.G.M. Petrakis
Abstract Data Types (ADT)

3. Abstract Data Types (ADT)
Data Structures
Representation of data in the memory
file structure: representation of data on the disk
e.g., collection of records (list, tree, etc)
Efficient programs require efficient data structures
a problem has to be solved within the given time and space constraints
E.G.M. Petrakis
Abstract Data Types (ADT)

4. Abstract Data Types (ADT)
Problem Constraints
Each problem puts constraints on time and space
e.g., bank example:
start account: a few minutes
transactions: a few seconds
close account: overnight
A solution is efficient if it solves the problem within its space and time constraints
Cost of solution: amount of resources consumed
E.G.M. Petrakis
Abstract Data Types (ADT)

5. Abstract Data Types (ADT)
Goals of this course
Teach data structures for main memory and disk
Teach algorithms for different tasks and data structures
Teach the idea of trade-offs
there are costs and benefits associated with each data structure and each algorithm
Teach how to measure effectiveness of each algorithm and data structure
E.G.M. Petrakis
Abstract Data Types (ADT)

6. Selecting Data Structures
Analyze the problem to determine the resource constraints a solution must meet
Determine the operations that must be supported
e.g., record search, insertion, deletion etc.
Quantify the constraints for each operation
e.g., search operations must be very fast
Select data structure that best meet these requirements
E.G.M. Petrakis
Abstract Data Types (ADT)

7. Abstract Data Types (ADT)
Costs & Benefits
Each data structure requires:
space for each data item it stores
time to perform each operation
programming effort to implement it
Each data structure has costs and benefits
rarely one data structure is better than another in all situations
one may permit faster search (or insertion or deletion) operations than another
are all operations the same important?
E.G.M. Petrakis
Abstract Data Types (ADT)

8. Abstract Data Type (ADT)
ADT: definition of a data type in terms of
a set of values and
a set of operations allowed on that data type.
Each ADT operation is defined by its inputs and outputs
ADTs hide implementation details
A data structure is the implementation of an ADT
operations associated with the ADT are implemented by one or more functions
E.G.M. Petrakis
Abstract Data Types (ADT)

9. Logical and Physical forms
Data items have both a logical and a physical form
Logical form: definition of the data item within an ADT
e.g., integers in mathematical sense: +, -
Physical form: implementation of the data item
e.g., 16 or 32 bit integers
E.G.M. Petrakis
Abstract Data Types (ADT)

10. Abstract Data Types (ADT)
ADT:Type +
Operations
Data Items:
Logical Form
Data Structure:
Storage Space +
functions
Data Items:
Physical Form
E.G.M. Petrakis
Abstract Data Types (ADT)

11. ADT String: Sequence of chars
ADT function length (s: string): integer;
post condition : length = len(s);
ADT function concat (s1,s2: string): string;
post condition: concat = s1 + s2;
ADT function substr (s: string, i, j: integer): string;
precondition: 0 < i < len(s), 0 < j < len(s) – i + 1
post condition: substr(s, i, j);
ADT function pos (s1, s2): integer;
precondition …
post condition …
E.G.M. Petrakis
Abstract Data Types (ADT)

12. Abstract Data Types (ADT)
Definition of an ADT
Depends on the application
Different definitions for the same application
An ADT hides implementation details
different implementations for the same ADT
When the ADT is given, its data type can be used by the programmer
e.g., string, math libraries in C
when the implementation changes the programs need not be changed
E.G.M. Petrakis
Abstract Data Types (ADT)

13. Abstract Data Types (ADT)
Algorithms
The method that solves a problem
An algorithm takes the input to a problem and transforms it to the output
a mapping of input to output
a problem can have many algorithms
A program is the implementation of an algorithm in some programming language
E.G.M. Petrakis
Abstract Data Types (ADT)

14. Properties of Algorithms
Effectiveness: the algorithm can be written as a program
there are problems for which no algorithm exists
Correctness: finds the correct solution for every input
Termination: terminates after a finite number of steps
each step requires a finite amount of time
Efficiency: makes efficient use of the computer’s resources
Complexity: it must be easy to implement, code and debug
E.G.M. Petrakis
Abstract Data Types (ADT)

15. Abstract Data Types (ADT)
Tiling Problem
The algorithm inputs a finite set T of tiles
it is assumed that an unlimited number of cards of each type is available
asks whether any finite area, of any size, can be covered using tiles in T so that
the colors in any two touching edges are the same
For any algorithm there can be inputs T for which the algorithm never terminates or finds a wrong answer
E.G.M. Petrakis
Abstract Data Types (ADT)

16. Abstract Data Types (ADT)
Tile tile types that
can tile any area
Tile tile types that
cannot tile any area
From “Algorithmics”, David Harel,
E.G.M. Petrakis
Abstract Data Types (ADT)

17. Abstract Data Types (ADT)
A Termination Problem
An algorithm must terminate with the correct solution for any input
No one has been able to prove that the algorithm terminates for any positive n although most people believe that it does!!
int OddEven( int n ) {
while ( n > 1 )
if (( n % 2 ) == 0) n = n / 2;
else n = 3n + 1;
return n; }
E.G.M. Petrakis
Abstract Data Types (ADT)

18. Taxonomy of Algorithms
An algorithmic problem that admits no algorithm is termed “non-computable”
If it is a decision problem it is termed “undecidable”
E.G.M. Petrakis
Abstract Data Types (ADT)

19. Abstract Data Types (ADT)
Disk Model
T = Taccess + Trotation + Tread
Block: unit memory size for disk
size of data transferred in main memory per disk access
In most cases page=block=track
e.g., 1, 2, 4, 8Kbytes
E.G.M. Petrakis
Abstract Data Types (ADT)

20. Abstract Data Types (ADT)
Disk Model (cont.)
Taccess > Trotation > Tread  increase the amount of data which is transferred to the main memory per disk access
large blocks, compression, data in memory
in multi-user systems, the disk head can be anywhere
distance covered by disk head
time
E.G.M. Petrakis
Abstract Data Types (ADT)