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Data Structures & Algs. " Lecture 1O =a4%Intro to Data Structures & AlgorithmsWagner Truppel Lecturer, Dept. of Computer Science & Engineering UC Riverside wagner@cs.ucr.edu http://www.cs.ucr.edu/~wagner http://www.cs.ucr.edu/cs14zO  O`a~Today s TopicsOverview of Data Structures & Algorithms The  bookstore example Abstraction: Interface Implementation`) ) >3Overview of DS & AsThe  bookstore example How do you find the book you re looking for ? You need to use some kind of algorithm and& *ZZZZ?4Overview of DS & AsPThe  bookstore example How do you find the book you re looking for ? You need to use some kind of algorithm and& & of course, we want the best algorithm possible, but& *ZZ@5Overview of DS & AsThe  bookstore example How do you find the book you re looking for ? You need to use some kind of algorithm and& & of course, we want the best algorithm possible, but& & what  best means will depend on how the books are organized (stored)*ZZRFMessyBookPile, Inc. This bookstore keeps its books all in one big pile, with no organization of any kind Your algorithm is then: For each book If it is not the book I want, continue searching If the bookstore has 1,000,000 books, and if it takes 10 secs for you to check each book, it may take you as long as 4 months to find the book you want Not a very good algorithm, is it ? Note: search time is directly proportional to number of books: O(n)mZZ1ZZm1        8    >    ;            SGLongBookShelf, Inc. This competitor bookstore keeps its books all in one very long array sorted by ISBN One possible algorithm is then (linear search): For each book If it is not the book I want, continue searching This is the same algorithm used with MessyBookPile,Inc. Again& search time is directly proportional to number of books: O(n) Note that the algorithm did not make use of the fact that the books are sortedZZ1ZZ?! 1y              0   YKLongBookShelf, Inc. &Another possible algorithm is then (binary search): Look at the middle book If it is the book I want, stop If the book I want comes before the middle book, search the first half of the array using this same algorithm If the book I want comes after the middle book, search the second half of the array using this same algorithm This does make use of the fact that the books are sorted Note: recursive algorithm ! Now& search time is proportional to the logarithm of the number of books: O(log2 n) 1,000,000 books, 10 secs/book = ???r4ZZZZ$ 8 A (    0    @               "       ZLLongBookShelf, Inc. Another possible algorithm is then (binary search): Look at the middle book If it is the book I want, stop If the book I want comes before the middle book, search the first half of the array using this same algorithm If the book I want comes after the middle book, search the second half of the array using this same algorithm This does make use of the fact that the books are sorted Note: recursive algorithm ! Now& search time is proportional to the logarithm of the number of books: O(log2 n) 1,000,000 books, 10 secs/book = 200 s < 4 min !!! [ 220 = 1,048,576 so log2(1,000,000) H" 20 ]4ZZZZ-Z$ 8 A (    0    @               "            GVJBinaryBooks, Inc. This bookstore keeps its books organized in a binary search tree It s suing LongBookShelf, Inc. because they stole the idea of a binary search from BinaryBooks,Inc. The algorithm is binary search: Look at a node of the tree If it contains the book I want, stop If the book I want comes before the book in this node, search this node s left child, using this same algorithm If the book I want comes after the book in this node, search this node s right child, using this same algorithm2ZZ ZZZ.A >    +    ;    +    !    ,M ; HMBCategoriesRUs, Inc. <This other competitor bookstore keeps its books all organized by sections The search algorithm is now: For each section If it is the section of the book I want Search each book in that section using one of the previous algorithms This is a little faster than the corresponding algorithm used in the previous slideshZZ(ZFZ ZUZA (F  ULABottom line& 8The choice and efficiency of an algorithm depends on how the data it accesses is organized Likewise, how you re going to store your data depends on what you want to do with it. If you don t care about searching, you might not care if the algorithm is linear search or binary search. In addition, a data structure depends on the properties of the data they store Pile of books: equality Sorted books: less thanLZ  NCInterface x Implementation:Consider an int variable int is a data type It could be that the computer you re using stores int s in 1 s complement or 2 s complement format When you use it, you don t care how it s really implemented inside the computer All you care is that the following operations are defined for that particular data type: +, -, *, /, <, >, <=, >=, ==, !=, ++, -- A data type like that is called an Abstract Data Type or ADT8Z)Z=Z  2#> @:ODInterface x ImplementationxSo what you really care about is the interface of an ADT, not its implementation The interface of an ADT is the set of operations defined for it So, in the bookstore example, you could create a general interface for your bookstore, and then have as many individual implementations as you wanted This sounds like OOP& 8=Z% PEInterface x Implementation :0$That s all, folks& ( Questions ?  n 0/PsxHH@Rg(HH(dh   ` www3ff` 3fff` ___>?" dF@,?n<d@uA @ " d`  n?" dd@   @@``PR   @ ` `P0p>> -"2003 W L Truppel bCS 14: Intro. 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