TCSS 342

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TCSS 342

• Data Structures Algorithms
• Autumn 2004
• Ed Hong

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Course Objectives

• (Broad) Prepare you to be a good software
  engineer
• (Specific) Learn basic data structures and
  algorithms
• Data structures how data is organized
• Algorithms unambiguous sequence of steps to
  compute something

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Software Design Goals
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Course Content

• Data Structures
• Algorithms
• Data Structures Algorithms Programs
• Algorithm analysis determining how long an
  algorithm will take to solve a problem
• Who cares? Arent computers fast enough and
  getting faster?

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An Example

• Given an array of 1,000,000 integers,
• find the maximum integer in the array.
• Now suppose we are asked to find the kth largest
  element. (The Selection Problem)

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Candidate Solutions

• Candidate solution 1
• Sort the entire array (from small to large),
  using Javas Arrays.sort() Pick out the
  (1,000,000 k)th element.
• Candidate solution 2
• Sort the first k elements.
• For each of the remaining (1,000,000 k)
  elements,
• keep the k largest in an array.
• Pick out the smallest of the k survivors.

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Is either solution good?

• Is there a better solution?
• How would you go about determining the answer to
  these questions?

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Method 1

• Code each algorithm and run them to see how long
  they take.
• Problem How will you know if there is a better
  program or whether there is no better program?
• What will happen when the number of inputs is
  twice as many? Three? A hundred?

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Method 2

• Develop a model of the way computers work and
  compare how the algorithms behave in the model.
• Goal To be able to predict performance at a
  coarse level. That is, to be able to distinguish
  between good and bad algorithms.
• Another benefit when assumptions change, we can
  predict the effects of those changes.

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Why algorithm analysis?

• As computers get faster and problem sizes get
  bigger, analysis will become more important.
• Why? The difference between good and bad
  algorithms will get bigger.

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Why data structures?

• When programming, you are an engineer.
• Engineers have a bag of tools and tricks and
  the knowledge of which tool is the right one for
  a given problem.
• Arrays, lists, stacks, queues, trees, hash
  tables, graphs.

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Software Development Practices

• Modular code
• Appropriate commenting of code
• Each method needs a comment explaining its
  parameters and its behavior.
• Debugging with integrated development environment
  (IDE)
• Incremental development
• Unified modeling language (UML)

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Mathematical Background

• Exponents
• XA XB XAB
• XA / XB XA-B
• (XA)B XAB
• XNXN 2XN
• 2N2N 2N1
• Logarithms
• Definition XA B if and only if logX B A.

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Logarithms, continued

• log AB log A log B
• Proof

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Logarithms, Series

• log A/B log A log B
• log (AB) B log A
• Series
• binary representation of numbers

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Series

• Geometric progression for agt0, a ?1

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Boolean Logic

• Let P and Q be statements.
• not P is true if P is false.
• P and Q is true if both P and Q are true.
• P or Q is true if one of or both P or Q are
  true.
• P implies Q is true if P is false or Q is true
  (or both).