1. Algorithm. Data Structures & Algorithms. How many times you weight? Algo 2 : Half Cutting. How many times you weight? Algo.1 :Two coins at a time

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1 Data Structures & Algorithms Lecturer : Kritawan Siriboon,, Room no. 93 Text : Data Structures & Algorithm Analysis in C, C, Mark Allen Weiss, Addison Wesley. Algorithm State how to solve problem step by step. Ex: Finding a fake coin out of n real gold coins. Given a two arm scale. the fake coin is lighter. How many times you weight? Algo. :Two coins at a time est Case Worst Case n/2 Average Case How many times you weight? Algo 2 : Half Cutting est Case Worst Case Time remaining n/2 2 n/4 3 n/ d = n/2 = n/2 2 = n/ = n/2 d 2 d = n d = log 2 n ½ ½

2 2. Data Structure The Eight ueen Problem Structures of all data : how to keep related data in memory. Ex. The Eight ueen Problem. Puting eight ueens on 8 x 8 chessboard such that none of them is able to capture any other using the standard chess queen s move. The Eight ueen Problem Data Structures The Eight ueen Solutions It has 92 distinct solutions. If solutions that only differ by symmetry operatons (rotations & reflections) of the board are counted as one, the puzzle has 2 unique solutions D array -D array col row Row Coloumn

A 2 3 4 7 2 3 4 7 2-D array & -D array x A[][] <==> [3] [3] : aseadd 3 sizeof(int) A[][] : aseadd ( (8 ) () )sizeof(int) Column size x 2 3

Algorithms : recursion, complexity (algorithm analysis), hashing, searching, sorting.

3 A D array & -D array x A[][] <==> [3] [3] : aseadd 3 sizeof(int) A[][] : aseadd ( (8 ) () )sizeof(int) Column size x Data Structures & Algorithms Data Structures abstract data type: stack, queue, linked list, trees, heap, graph. Algorithms : recursion, complexity (algorithm analysis), hashing, searching, sorting. Stacks ก ก ก ก (push) ก ก กก (pop) ก ก ก(top of stack) Last In First Out List Stack Data Structure ก ก ; int item[]; Type ก ก template<class T, int MAX = > ; T item[max]; stack<int> s; stack<char,2> s2;

4 asic Operations on stack s i = s.pop() i = pop(s) pop i out off s stack s / init(s) Initialize empty s / empty(s) empty s? s.push(i) push(s, i) push i onto s i = s.top() i = top(s) look at the top without poping s.push(i) / push(s, i) template<class T, int MAX = > top = 2 C A D top = 3 D 2 C A top; item[top] = i; item[top] = i; Check Overflow i = s.pop() / i = pop(s) template<class T, int MAX = > pop C i = s.top() / i = top(s) top = 2 C A top = A template<class T, int MAX = > top = 2 C A return item[top--]; return item[top]; Check Underflow

5 ? / empty(s)? stack<char> s; / init(s)? template<class T, int MAX = > top = 2 C A top = - template<class T, int MAX = > top = 2 C A top = - return top == -; stack() : top(-) { Stack Applications Parenthesis Matching Evaluate Postfix Expression Infix to Postfix Conversion (Reverse Polish Notation) Function Call (in recursion) Parenthesis Matching Are the parenthesis correct? (ab-c)[de]/{f(gh) [(ab-c[de]/{f(gh) (ab-c [de]/{f(gh)

6 Init empty stack s Warnier-Orr Diagram Design Tool Init empty stack s Warnier-Orr Diagram Design Tool error=false read ch error=false read ch Paren matching Scan (not EOF && not error) ch = non_paren ch = open paren ch = close paren s.push(ch) error =true(no match-open-paren) open = s.pop() match(open,ch) Paren matching Scan (not EOF && not error) ch = open paren ch = close paren s.push(ch) error =true(no match-open-paren) open = s.pop() notmatch(open,ch) error = true notmatch(open,ch) error = true error no match-open-paren / missmatch (missmatch) error no match-open-paren / missmatch (missmatch) error MATCH open paren exceed error MATCH open paren exceed Infix Form Evaluate Postfix Notation Prefix Form Postfix Form (Polish notation) a b a b a b a b c a b c a b c Evaluate Postfix Notation =? input: 23 s.push() s.push() s.push(2) s.push(3) S input: o2=s.pop() =3 o=s.pop() =2 s.push(23) What s next? S

7 input: 23 s.push() s.push() s.push(2) =? input: 3 3=s.pop() 2 2=s.pop() s.push(23) Infix to Postfix Conversion abc c ===> abc s.push(3) input: 8 s.push(8) s 8 input: 8= s.pop() = s.pop() s 4 output s.push(8) input: - input: 3 4= s.pop() s.push(3) 3 = s.pop() -3-3 s.push(-4) input: 3= s.pop() -3= s.pop() -32 input: -32= s.pop() = s.pop() stack s.push(-33) s.push(-32) -92 Infix to Postfix Conversion abc ---- > abc Infix to Postfix Conversion abc abc ---- > input: stack: output: abc a abc a abc ab abc ab abc abc abc abc input: stack: output: abc a abc a abc ab abc ab abc abc abc abc

8 abc-d a abc-d a abc-d ab abc-d ab abc-d abc abc-d - abc abc-d - abcd abc-d abcd- Infix to Postfix Conversion abcd- Infix to Postfix Conversion abc-d => input: stack: output: abc-(d/ef)g => abcde/fg- abc-(d/ef)g ab abc-(d/ef)g abc abc-(d/ef)g - abc ( abc-(d/ef)g - abcd / ( abc-(d/ef)g - abcde Infix to Postfix Conversion (cont.) / ( abc-(d/ef)g - abcde ( abc-(d/ef)g - abcde/f abc-(d/ef)g - abcde/f abc-(d/ef)g - abcde/fg abc-(d/ef)g - abcde/fg- abc-(d/ef)g => abcde/fg-

Some Applications of Stack. Spring Semester 2007 Programming and Data Structure 1

Some Applications of Stack. Spring Semester 2007 Programming and Data Structure 1 Some Applications of Stack Spring Semester 2007 Programming and Data Structure 1 Arithmetic Expressions Polish Notation Spring Semester 2007 Programming and Data Structure 2 What is Polish Notation? Conventionally,