Data Structures & Algorithms

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 We shall study ways to represent data and algorithms to manipulate these representations. The study of data structures is fundamental to Computer Science & Engineering.

Functions of Data Structures s Add –Index –Key –Position –Priority s Get s Change s Delete

Common Data Structures s Array s Stack s Queue s Linked List s Tree s Heap s Hash Table s Priority Queue

How many Algorithms? s Countless

Algorithm Strategies s Greedy s Divide and Conquer s Dynamic Programming s Exhaustive Search s Approximation Algorithms s Randomized Algorithms

Which Data Structure or Algorithm is better? s Must Meet Requirement s High Performance s Low RAM footprint s Easy to implement –Encapsulated

Prerequisites s Asymptotic Complexity  Big Oh, Theta, and Omega notations sCsC

Web Site s programming.im.ncnu.edu.tw s 管 5047 s Handouts, syllabus, text, source codes, exercise solutions, lectures, assignments, past exams, past exam solutions, TAs, etc.

Assignments s Moodle.ncnu.edu.tw s Assignment guidelines

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

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; }