CIT 594 28-Nov-18

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

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

The Collections hierarchy

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()

Creating lists in Java 44 97 23 17 myList: 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);

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

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

Example backtracking algorithm To color a map with no more than four colors: color(Country n): If all countries have been colored (n > 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 n+1 If successful, return success If loop exits, return failure

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 be: At 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 3

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

y = x2 + 3x + 5, for x=1..20

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