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COM212 Data Structures

COM212 Data Structures. Intro to Abstract Data Structures 4 Weeks ~7 Homework Problems Implementation of Abstract Data Structures 7 Weeks ~7 Programming Assignments Test Advanced Java Programming 3 Weeks Project. Today. Complexity Abstract Data Structures Lists Recursion.

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COM212 Data Structures

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  1. COM212 Data Structures • Intro to Abstract Data Structures • 4 Weeks • ~7 Homework Problems • Implementation of Abstract Data Structures • 7 Weeks • ~7 Programming Assignments • Test • Advanced Java Programming • 3 Weeks • Project

  2. Today • Complexity • Abstract Data Structures • Lists • Recursion

  3. Complexity • How long functions take to run • Can be counted in number of instructions executed • Growth rate of functions • How much longer they take to run as size of the input increases

  4. Example Function One example(n) print x print y x = y2 What is the run time?

  5. Example Function One example(n) print x print y x = y2 The run time is 3.

  6. Example Function Two example(n) loop n times y = x + 1 x = y2 print x What is the run time?

  7. Example Function Two example(n) loop n times y = x + 1 x = y2 print x The run time is 4n

  8. Example Function Three example(n) print x print y loop n times y = x + 1 x = y2 print x What is the run time?

  9. Example Function Three example(n) print x print y loop n times y = x + 1 x = y2 print x The run time is 4n + 2

  10. Complexity Notation • We need some notation to help us categorize functions by how long they take to run. • Since the second two example functions will take about the same time to run, they should be in the same category. • Even functions with run times of 2n and 3n take similar time to run. • They are much more dependent on n than a function that takes constant time to run.

  11. Example A large n affects ex1() but not ex2() ex1(n) loop n times print x ex2(n) print x

  12. Big O f(n)≤cg(n) for all n≥n0

  13. Example f(n) = 4n + 2 using g(n) = n and c = 5 and n0 = 2 f(n)≤cg(n) for all n≥n0 is 4n + 2 ≤ 5n when n ≥2 So g(n) is n. The complexity of f(n) is O(n)

  14. Other Examples O(n) O(1) 4n+8 16 ¼(n-8) 296 200n+56801 1000302 O(n2) 4n2+18

  15. Others 56n + 7 0.34n – 455 0.003n2 + 3 14 5(lg n) + 5 98n4 + 2

  16. Data Structures • Data Types • A way of representing or organizing data • Examples • integer 5 • float 6.543 • character a • array

  17. Array 5 9 34 3 10 6 • Contiguous section of memory • Fixed size • Containing all one data type

  18. Abstract Data Structures • Independent of implementation • User does not care about the implementation • Set of operations to access / manipulate data • Examples: • FIFO queue • Return the largest from a set • List

  19. Abstract Data Structure • The user has a need for a specific DS, but the actual implementation is not of their concern. • The actual implementation is hidden from the user. • The programmer needs to ensure that the means of implementation allows the user to do everything that is required.

  20. Lists List L = x0 x1 x2 x3 … xn-1 n = # elements If a list is ordered than the key of xi-1 <= the key of xi for all i where 0 < i < n. The sort symbol <= can be replaced by >= or any other function that determines ordering in the keys. An unordered list does not have this restriction. Functions: access(L, i) returns xi length(L) returns n concat(L1, L2) returns a new list with L2 concatenated on to L1 createEmptyList() returns a newly created empty list isEmptyList(L) returns true if L is empty and false if it is not searchFor(L, key) returns i where key of xi = key remove(L, i) returns a list with xi removed; the old xi+1 is now xi, etc. inserti(L, i, x) returns a list with x inserted as xi; the old xi is now xi+1, etc. insert(L, x) returns a list with x added to L sort(L) returns the list in sorted order

  21. A Node NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95

  22. Problem • We need a list that has a maximum of 100 nodes. • How can you implement this kind of list?

  23. Homework 0 • Describe how to use an array to implement an unordered list (assume a max size of 100 elements). • Determine how to do the following functions: access, length, concat, createEmptyList, isEmptyList, searchFor, remove, and insert. • How would any of these functions change if the list was to be ordered?

  24. COM212 Java Tutorial Link: https://www.codecademy.com/learn/learn-java • Unit 1: Introduction to Java Due on 2/6/19 • Unit 2: Conditionals and Control Flow Due on 2/13/19 • Unit 3: Object-Oriented Java Due on 2/20/19

  25. Recursion

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