Data Structures, Algorithms, & Applications Instructor: Babak Alipour Slides and book: Sartaj Sahni

Clip Art Sources s s s s

What The Course Is About s Data structures is concerned with the representation and manipulation of data. s All programs manipulate data. s So, all programs represent data in some way. s Data manipulation requires an algorithm.

What The Course Is About Algorithm design methods needed to develop programs that do the data manipulation. The study of data structures and algorithms is fundamental to Computer Science.

Prerequisites s Asymptotic Complexity  Big Oh, Theta, and Omega notations s C++ / Java

Web Site For Book s

Source Codes s Download source codes from Web site and make sure you can compile and execute at least one code. s Use the readme file to map text programs to file names. s X.cpp is C++ program; X.output is output generated by X.cpp; and X.input is the input data (if any is required).

Organization of Text s Three parts s Part I … Chapters 1-4, Background s Part 2 … Chapters 5-16, Data Structures s Part 3 … Chapters 17-21, Algorithms s Each chapter … concepts + applications

Sorting s Rearrange a[0], a[1], …, a[n-1] into ascending order. When done, a[0] <= a[1] <= … <= a[n-1] s 8, 6, 9, 4, 3 => 3, 4, 6, 8, 9

Sort Methods s Insertion Sort s Bubble Sort s Selection Sort s Count Sort s Shaker Sort s Shell Sort s Heap Sort s Merge Sort s Quick Sort

Insert An Element s Given a sorted list/sequence, insert a new element s Given 3, 6, 9, 14 s Insert 5 s Result 3, 5, 6, 9, 14

Insert an Element s 3, 6, 9, 14 insert 5 s Compare new element (5) and last one (14) s Shift 14 right to get 3, 6, 9,, 14 s Shift 9 right to get 3, 6,, 9, 14 s Shift 6 right to get 3,, 6, 9, 14 s Insert 5 to get 3, 5, 6, 9, 14

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;

Insertion Sort s Start with a sequence of size 1 s Repeatedly insert remaining elements

Insertion Sort s Sort 7, 3, 5, 6, 1 s Start with 7 and insert 3 => 3, 7 s Insert 5 => 3, 5, 7 s Insert 6 => 3, 5, 6, 7 s Insert 1 => 1, 3, 5, 6, 7

Insertion Sort for (int i = 1; i < n; i++) {// insert a[i] into a[0:i-1] // code to insert comes here }

Insertion Sort for (int 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; }