Introduction to Data Structures and Algorithms

1
Introduction to Data Structures and Algorithms
2
Areas of Focus

• How do we represent data internally for use with
  our programs?
• How do we select the best representation for our
  problem?
• How do we measure the efficiency of our algorithm
  or solution?

3
Terms

• type
• simple type
• composite type
• data type
• data item

• efficiency
• resource constraints
• storage space
• time
• cost
• file structure

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Abstract Data Type

• ADT - a collection of data together with a
  defined set of operations to manipulate the data.
• type of data
• set of operations

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Data Structures

• data structure organization or structure for the
  collection of data stored in an ADT.
• data abstraction i.e. encapsulation
• data item forms
• logical
• physical

6
Selecting a Data Structure

• Analyze the problem to determine constraints.
• Determine basic operations quantify resource
  constraints.
• Select the data structure.

7
Ask Questions

• Is all data inserted into the data structure
• at the beginning?
• or interspersed?
• Can data be deleted?
• Is all data processed in
• some well-defined order?
• or is random access allowed?

8
Cost and Benefits

• Each data structure has costs and benefits.
• Seldom is one data structure better than another
  in all situations.
• There are many different data structures.

9
Data Structure Requirements

• A data structure requires
• space for each data item it stores
• time to perform each basic operation
• programming effort
• Selecting the right data structure requires
  careful analysis of the problem.

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Problems

• problem a task to be performed.
• The problem definition
• should not include any constraints on how the
  problem should be solved.
• Should include constraints on the resources that
  may be used.
• constraints - stated or implied.

11
Viewed as Functions

• Problems can be viewed as functions
  (mathematical)
• function - a matching between inputs and outputs.
• input - can be a single value or a collection.
• parameters - the input(s) to the function.
• A particular input must always result in the same
  output.

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Algorithms

• algorithm a process followed to solve a problem.
• Takes the input and transforms it to the output.
• Must be well defined.

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Algorithms Properties

• Must possess the following properties
• be correct
• composed of concrete steps
• have no ambiguity
• composed of a finite number of steps
• Must terminate

14
Programs

• program - an implementation of an algorithm or a
  solution to a problem using a computer
  programming language.

15
Choosing an Algorithm

• A problem can have many algorithms.
• Our goal is to choose an algorithm
• simplicity - easy to understand, code, and debug.
• efficient - makes efficient use of resources.
• Often these two goals conflict.

16
Course Goals

• Learn the commonly used data structures,
  algorithms, and algorithm design techniques.
• Learn how to measure the effectiveness and
  efficiency of a data structure or algorithm.
• Study the trade-offs between the conflicting
  goals of simplicity and efficiency.