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Data Structure

Data Structure. Spring Semester 2012 School of Computer Science & Engineering Chung-Ang University. Sang Yong Han (Professor) Office hour: Tuesday 14:00 – 14:50 eMail: hansy@cau.ac.kr. Administrative Matters. http://ec.cse.cau.ac.kr (web site). Teaching Assistant

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Data Structure

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  1. Data Structure Spring Semester 2012 School of Computer Science & Engineering Chung-Ang University Chung-Ang University Spring 2012

  2. Sang Yong Han (Professor) • Office hour: Tuesday 14:00 – 14:50 • eMail: hansy@cau.ac.kr Administrative Matters • http://ec.cse.cau.ac.kr (web site) • Teaching Assistant • 최승진 (02-824-1187, 010-9071-7598) Chung-Ang University Spring 2012

  3. Grading • 10% - Class attitude and attendance • 25% - Assignments • 65% - Mid and Final Exams Chung-Ang University Spring 2012

  4. Administrative Matters • 지각 2번은 결석 1번과 동일하게 처리 • BreakTime 이후의 출석은 결석으로 처리 • Due date를 넘긴 과제물은 받지 않습니다. Chung-Ang University Spring 2012

  5. Prerequisites • C Chung-Ang University Spring 2012

  6. Tentative Class Schedule • Week 1 – course introduction • Week 2 – Performance Analysis • Week 3 – Array and Stack • Week 4 – Stack • Week 5 – Queue • Week 6 – Linked List • Week 7 - Review • Midterm Chung-Ang University Spring 2012

  7. Tentative Class Schedule (Cont.) • Week 9 – Tree (binary tree, etc) • Week 10 – Tree (Heap, etc) • Week 11 – Graph (ADT, etc) • Week 12 – Graph (BFS, DFS, etc) • Week 13 – Graph • Week 14 – Graph (maybe on Saturday) • Week 15 - Review • Week 16 - Final Exam Chung-Ang University Spring 2012

  8. What The Course Is About • We shall study ways to represent data and algorithms to manipulate these representations. • The study of data structures is fundamental to Computer Science & Engineering. Chung-Ang University Spring 2012

  9. What The Course Is About • Data structures is concerned with the representation and manipulation of data. • All programs manipulate data. • So, all programs represent data in some way. • Data manipulation requires an algorithm. Chung-Ang University Spring 2012

  10. Data Structures and Algorithms Algorithm Program Data Structure • Algorithm: Outline the essence of a computational procedure • Program: an implementation of an algorithm in some programming language • Data Structure: Organization of data needed to solve the problem Chung-Ang University Spring 2012

  11. Algorithmic Problem • Infinite number of input instances satisfying the specifications. For eg: A sorted, non-decreasing sequence of natural numbers of non-zero, finite length • 1, 20, 908, 909, 10000, 20000 Specification of input Specification of output as a function of input Chung-Ang University Spring 2012

  12. Algorithmic Solution • Algorithm describes actions on the input instance • Infinitely many correct algorithms for the same algorithmic problem Chung-Ang University Spring 2012

  13. What is a Good Algorithm ? • Efficient: • Running Time • Space Used • Data Structure: Organization of data needed to solve the problem Chung-Ang University Spring 2012

  14. Performance Analysis Chung-Ang University Spring 2012

  15. Problem Solving: Main Steps • Problem definition • Algorithm design / Algorithm specification • Algorithm analysis • Implementation • Testing • [Maintenance] Chung-Ang University Spring 2012

  16. 1. Problem Definition • What is the task to be accomplished? • Calculate the average of the grades for a given student • Understand the talks given out by politicians and translate them in Chinese • What are the time / space / performance requirements ? Chung-Ang University Spring 2012

  17. 2. Algorithm Design / Specifications • Algorithm: Finite set of instructions that, if followed, accomplishes a particular task. • Describe: in natural language / pseudo-code / diagrams / etc. • Criteria to follow: • Input: Zero or more quantities (externally produced) • Output: One or more quantities • Definiteness: Clarity, precision of each instruction • Finiteness: The algorithm has to stop after a finite (may be very large) number of steps • Effectiveness: Each instruction has to be basic enough and feasible Chung-Ang University Spring 2012

  18. 4,5,6: Implementation, Testing, Maintainance • Implementation • Decide on the programming language to use • C, C++, Lisp, Java, Perl, Prolog, assembly, etc. , etc. • Write clean, well documented code • Test, test, test • Integrate feedback from users, fix bugs, ensure compatibility across different versions  Maintenance Chung-Ang University Spring 2012

  19. 3. Algorithm Analysis • Space complexity • How much space is required • Time complexity • How much time does it take to run the algorithm • Often, we deal with estimates! Chung-Ang University Spring 2012

  20. Space Complexity • Space complexity = The amount of memory required by an algorithm to run to completion • Some algorithms may be more efficient if data completely loaded into memory • Need to look also at system limitations • E.g. Classify 2GB of text in various categories [politics, tourism, sport, natural disasters, etc.] – can I afford to load the entire collection? Chung-Ang University Spring 2012

  21. Space Complexity (cont’d) • Fixed part: The size required to store certain data/variables, that is independent of the size of the problem: • Variable part: Space needed by variables, whose size is dependent on the size of the problem: Chung-Ang University Spring 2012

  22. Space Complexity (cont’d) • S(P) = c + S(instance characteristics) • c = constant • Example: void float sum (float* a, int n) { float s = 0; for(int i = 0; i<n; i++) { s+ = a[i]; } return s; } Space? one word for n, one for a [passed by reference!], one for i  constant space! Chung-Ang University Spring 2012

  23. Time Complexity • Often more important than space complexity • space available (for computer programs!) tends to be larger and larger • time is still a problem for all of us • 3-4GHz processors on the market • still … • researchers estimate that the computation of various transformations for 1 single DNA chain for one single protein on 1 TerraHZ computer would take about 1 year to run to completion • Algorithms running time is an important issue Chung-Ang University Spring 2012

  24. Experimental Approach • Write a program that implements the algorithm • Run the program with data sets of varying size. • Determine the actual running time using a system call to measure time (e.g. system (date) ); • Problems? Chung-Ang University Spring 2012

  25. Experimental Approach • It is necessary to implement and test the algorithm in order to determine its running time. • Experiments can be done only on a limited set of inputs, and may not be indicative of the running time for other inputs. • The same hardware and software should be used in order to compare two algorithms. – condition very hard to achieve! Chung-Ang University Spring 2012

  26. Use a Theoretical Approach • Based on high-level description of the algorithms, rather than language dependent implementations • Makes possible an evaluation of the algorithms that is independent of the hardware and software environments  Generality Chung-Ang University Spring 2012

  27. Some Uses of a Theoretical Approach • determine practicality of algorithm • predict run time on large instance • compare 2 algorithms that have different asymptotic complexity • e.g.,O(n) and O(n2) Chung-Ang University Spring 2012

  28. Algorithm Description • How to describe algorithms independent of a programming language • Pseudo-Code = a description of an algorithm that is • more structured than usual prose but • less formal than a programming language • (Or diagrams) • Example: find the maximum element of an array. Algorithm arrayMax(A, n): Input: An array A storing n integers. Output: The maximum element in A. currentMax A[0] for i 1 to n -1 do ifcurrentMax < A[i] thencurrentMax A[i] returncurrentMax Chung-Ang University Spring 2012

  29. Pseudo Code • Expressions: use standard mathematical symbols • use  for assignment ( ? in C/C++) • use = for the equality relationship (? in C/C++) • Method Declarations: -Algorithm name(param1, param2) • Programming Constructs: • decision structures: if ... then ... [else ..] • while-loops while ... do • repeat-loops: repeat ... until ... • for-loop: for ... do • array indexing: A[i] • Methods • calls: object method(args) • returns: return value • Use comments • Instructions have to be basic enough and feasible! Chung-Ang University Spring 2012

  30. Low Level Algorithm Analysis • Based on primitive operations (low-level computations independent from the programming language) • E.g.: • Make an addition = 1 operation • Calling a method or returning from a method = 1 operation • Index in an array = 1 operation • Comparison = 1 operation etc. • Method: Inspect the pseudo-code and count the number of primitive operations executed by the algorithm Chung-Ang University Spring 2012

  31. Example Algorithm arrayMax(A, n):Input: An array A storing n integers.Output: The maximum element in A.currentMax A[0]fori  1to n -1 doif currentMax < A[i] then currentMax  A[i]return currentMax How many operations ? Chung-Ang University Spring 2012

  32. Sorting • Rearrange a[0], a[1], …, a[n-1] into ascending order. When done, a[0] <= a[1] <= … <= a[n-1] • 8, 6, 9, 4, 3 => 3, 4, 6, 8, 9 Chung-Ang University Spring 2012

  33. Sort Methods • Insertion Sort • Bubble Sort • Selection Sort • Count Sort • Shaker Sort • Shell Sort • Heap Sort • Merge Sort • Quick Sort Chung-Ang University Spring 2012

  34. Insert An Element • Given a sorted list/sequence, insert a new element • Given 3, 6, 9, 14 • Insert 5 • Result 3, 5, 6, 9, 14 Chung-Ang University Spring 2012

  35. Insert an Element • 3, 6, 9, 14 insert 5 • Compare new element (5) and last one (14) • Shift 14 right to get 3, 6, 9, , 14 • Shift 9 right to get 3, 6, , 9, 14 • Shift 6 right to get 3, , 6, 9, 14 • Insert 5 to get 3, 5, 6, 9, 14 Chung-Ang University Spring 2012

  36. Insert An Element /* insert t into a[0:i-1] */ int j; for (j = i - 1; j >= 0 && t < a[j]; j--) a[j + 1] = a[j]; a[j + 1] = t; Chung-Ang University Spring 2012

  37. Insertion Sort • Start with a sequence of size 1 • Repeatedly insert remaining elements Chung-Ang University Spring 2012

  38. Insertion Sort • Sort 7, 3, 5, 6, 1 • Start with 7 and insert 3 => 3, 7 • Insert 5 => 3, 5, 7 • Insert 6 => 3, 5, 6, 7 • Insert 1 => 1, 3, 5, 6, 7 Chung-Ang University Spring 2012

  39. Insertion Sort for (i = 1; i < n; i++) {/* insert a[i] into a[0:i-1] */ /* code to insert comes here */ } Chung-Ang University Spring 2012

  40. Insertion Sort for (i = 1; i < n; i++) {/* insert a[i] into a[0:i-1] */ int t = a[i]; int j; for (j = i - 1; j >= 0 && t < a[j]; j--) a[j + 1] = a[j]; a[j + 1] = t; } Chung-Ang University Spring 2012

  41. Complexity • Space/Memory • Time • Count a particular operation • Count number of steps • Asymptotic complexity Chung-Ang University Spring 2012

  42. Comparison Count for (i = 1; i < n; i++) {/* insert a[i] into a[0:i-1] */ int t = a[i]; int j; for (j = i - 1; j >= 0 && t < a[j]; j--) a[j + 1] = a[j]; a[j + 1] = t; } Chung-Ang University Spring 2012

  43. Comparison Count • Pick an instance characteristic … n, n = a.length for insertion sort • Determine count as a function of this instance characteristic. Chung-Ang University Spring 2012

  44. Comparison Count for (j = i - 1; j >= 0 && t < a[j]; j--) a[j + 1] = a[j]; How many comparisons are made? Chung-Ang University Spring 2012

  45. Comparison Count for (j = i - 1; j >= 0 && t < a[j]; j--) a[j + 1] = a[j]; number of compares depends on a[]s and t as well as on i Chung-Ang University Spring 2012

  46. Comparison Count • Worst-case count = maximum count • Best-case count = minimum count • Average count Chung-Ang University Spring 2012

  47. Worst-Case Comparison Count for (j = i - 1; j >= 0 && t < a[j]; j--) a[j + 1] = a[j]; a = [1, 2, 3, 4] and t = 0 => 4 compares a = [1,2,3,…,i] and t = 0 => i compares Chung-Ang University Spring 2012

  48. Worst-Case Comparison Count for (i = 1; i < n; i++) for (j = i - 1; j >= 0 && t < a[j]; j--) a[j + 1] = a[j]; total compares = 1 + 2 + 3 + … + (n-1) = (n-1)n/2 Chung-Ang University Spring 2012

  49. Step Count A step is an amount of computing that does not depend on the instance characteristic n 10 adds, 100 subtracts, 1000 multiplies can all be counted as a single step n adds cannot be counted as 1 step Chung-Ang University Spring 2012

  50. Step Count Step Count for (i = 1; i < n; i++) {/* insert a[i] into a[0:i-1] */ int t = a[i]; int j; for (j = i - 1; j >= 0 && t < a[j]; j--) a[j + 1] = a[j]; a[j + 1] = t; } Chung-Ang University Spring 2012

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