Introduction to Algorithms

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Introduction to Algorithms
Book by Thomas H. Cormen Charles E.
Leiserson Ronald L. Rivest and Clifford Stein
Powerpoint by Michael Block
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Chapter 1
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Algorithms
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Algorithms - Basic Definition

• A set procedure to process information.

• A correct algorithm is defined as

• Any algorithm that creates the desired
  relationship between the input and output values.

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Algorithms - Examples - Sorting Algorithms
Insertion Sort
Merge Sort
Grouped
Original Input
Organize
Find the first incorrect placement
Sort the next incorrect placement
Final sorted input
Final sorted input
This step takes a lot longer than the others
Insertion sort is efficient when sorting small
amounts of numbers.
Merge sort is efficient with large amounts of
numbers.
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Data Structures
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Data Structures - Basic Definition

• A means of storing data.

• Does not have to be organized.

• Usually created for a specific purpose or
  situation.

• Use the data structure best suited for your
  problem to allow your algorithm to be as
  efficient as possible.

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NP-Complete Problems
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NP-Complete Problems - Basic Definition

• A problem without an efficient algorithm.

• If an efficient algorithm exists for one it
  works for all.

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Efficiency
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Efficiency - Basic Definition

• Efficiency determines how well designed an
  algorithm is.

• Efficiency does not have to be measured in time.

• Efficiency can be found by creating a formula of
  each part in the algorithm based on a variable
  and solving for that variable.

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And now for something completely different...
We will take a short break from algorithms and
chapter 2 to work on math concepts in chapter 3.
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Chapter 3
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All Greek to me -
- Pronounced theta

• Used in graphing curves and parabolas to create
  an upper and lower bound.

Asymptotic upper bounds
Original function
Starting point for the asymptotic bind
Asymptotic lower bounds
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All Greek to me -
Because the base of both sides is (n) the
equation is asymptotically tight bound. The
coeficients of n do not matter as long as the
term stays basically the same.
Data being tested
Theta creates an upper and lower bounds so that
the data stays within an acceptable range.
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All Greek to me -
Asymptotically tight bound
Not asymptotically tight bound
Because n is on both sides of the equation.
Because one side contains n² and the other
contains n¹.
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All Greek to me - O
O - Pronounced big-oh

• Used in graphing curves and parabolas to create
  an upper bound.

Asymptotic upper bounds
Starting point for the asymptotic bind
Original function
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All Greek to me - O