CIT 594

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CIT 594
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Basic content

• CIT 594 is a continuation of CIT 591
• Java will be used throughout
• However, CIT 594 is not primarily a course about
  Java
• Topics
• Data Structures
• Supplied by Java
• How to create your own
• Algorithms
• A sampling of some better-known algorithms
• Analysis of algorithms
• Simple algebra is required

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Types of Collection

• A collection is a structured group of objects
• Java supplies several types of Collection
• Set cannot contain duplicate elements, order is
  not important
• SortedSet like a Set, but order is important
• List may contain duplicate elements, order is
  important
• Java also supplies some collection-like things
• Map a dictionary that associates keys with
  values, order is not important
• SortedMap like a Map, but order is important

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The Collections hierarchy
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Uniformity through interfaces

• Much of the elegance of the Collections Framework
  arises from the intelligent use of interfaces
• For example, the Collection interface specifies
  (among many other operations)
• boolean add(Object o)
• boolean isEmpty()
• boolean remove()
• int size()
• Object toArray()
• Iterator iterator()

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Creating lists in Java

• class Cell int value Cell next
• Cell (int v, Cell n) // constructor value
  v next n
• Cell temp new Cell(17, null)
• temp new Cell(23, temp)
• temp new Cell(97, temp)
• Cell myList new Cell(44, temp)

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A short list of categories

• Algorithm types we will consider include
• Simple recursive algorithms
• Backtracking algorithms
• Divide and conquer algorithms
• Dynamic programming algorithms
• Greedy algorithms
• Branch and bound algorithms
• Brute force algorithms
• Randomized algorithms

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Example recursive algorithms

• To count the number of elements in a list
• If the list is empty, return zero otherwise,
• Step past the first element, and count the
  remaining elements in the list
• Add one to the result
• To test if a value occurs in a list
• If the list is empty, return false otherwise,
• If the first thing in the list is the given
  value, return true otherwise
• Step past the first element, and test whether the
  value occurs in the remainder of the list

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Example backtracking algorithm

• To color a map with no more than four colors
• color(Country n)
• If all countries have been colored (n gt number of
  countries) return success otherwise,
• For each color c of four colors,
• If country n is not adjacent to a country that
  has been colored c
• Color country n with color c
• recursively color country n1
• If successful, return success
• If loop exits, return failure

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Example greedy algorithm

• Suppose you want to count out a certain amount of
  money, using the fewest possible bills and coins
• A greedy algorithm would do this would beAt
  each step, take the largest possible bill or coin
  that does not overshoot
• Example To make 6.39, you can choose
• a 5 bill
• a 1 bill, to make 6
• a 25 coin, to make 6.25
• A 10 coin, to make 6.35
• four 1 coins, to make 6.39
• For US money, the greedy algorithm always gives
  the optimum solution

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Time and space

• To analyze an algorithm means
• developing a formula for predicting how fast an
  algorithm is, based on the size of the input
  (time complexity), and/or
• developing a formula for predicting how much
  memory an algorithm requires, based on the size
  of the input (space complexity)
• Usually time is our biggest concern
• Most algorithms require a fixed amount of space

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y x2 3x 5, for x1..20
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The End