EEE2020 Data Structures and Algorithms Abstract Data Types: Stacks and Queues

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1 EEE2020 Data Structures and Algorithms Abstract Data Types: Stacks and Queues W. Jinho Song School of Electrical & Electronic Engineering Yonsei University 1

2 Textbook Chapter and Objectives Textbook "Data Structures and Algorithm Analysis in C++ 4th Edition by Mark Weiss Chapter 3: Lists, Stacks, and Queues Objectives Stacks and Queues Data structure concepts ADT implementations Big-O analysis 2

3 Stack Stack is a type of list where insertion and removal of elements occur only at the end (or top of the stack). Newer elements are added at the top. Newest elements are removed first. The newest one The oldest one 3

4 Stack ADT Stack ADT is a Last-In, First-Out (LIFO) data structure. top is a pointer to (or index of) the newest element. A push operation adds a new element at the end. A pop operation removes the last element in the stack. push(element) pop(element) top top top top top

5 Stack ADT Functions Stack ADT functions size(); empty(); print(); push(element_t element); pop(); clear(); Descriptions Get the number of elements in the stack. Return true if the stack is empty. Print the values of all elements in the stack. Add an element at the end of stack. Remove the last element in the stack. Remove all elements in the stack. 5

6 Stack ADT Implementations Stack ADT can be implemented by using array or linked list. Array Data structure is simple. Increasing stack size incurs overhead to relocate data to new, larger memory region. Linked list Date structure is more complicated than the array. It does not have penalty for increasing stack size. push and pop of both implementations are constant-time operations; O(1). 6

7 Stack ADT Applications: Function Call Procedure Function calls in C++ programs Operating system (OS) invokes main() function. 1. Save return address and variables in memory stack. 3. Return to main(). add(2020); C++ program int main(void) { 2. Jump to the function. Memory stack Return address, variables in main() function Computer memory add(int m_number) { sum += m_number; count++; 7

8 Repeated Function Calls Function calls Return to previous functions main() {... add(); stack.push(); top Return address in main() 6. stack.pop(); main() {... add(); Memory stack 3. stack.push(); 5. stack.pop(); add() {... print();... top Return address in add() add() {... print(); Memory stack print() {... In a real system, computers provide built-in stack operations, i.e., push and pop. 8

9 Recursive Functions and Stack Overflow #include <string> #include <iostream> using namespace std; /* Recursive function to print a char at a time in the string. */ void print_char(string m_string, unsigned position) { if(position < m_string.size()) { cout << m_string[position]; /* Recursive function calls: repeated stack push/pop operations */ print_char(m_string, ++position); else { cout << endl; int main(void) { string my_string = "50 Yonsei-ro, Seoul, Seodaemun-gu 03722, Seoul, South Korea"; print_char(my_string, 0); Stack overflow: recursive function calls in an indefinite loop will eventually run out of memory. 9

10 Stack ADT Applications: Postfix Simple calculator to compute "A + B * C - (D + E) / G" How do we parse this string to calculate numbers in the correct order of operations? Postfix expressions Operators perform calculations on the two preceding variables, regardless of operator priority. Expression Types Expressions Description Infix A + B * C Operators come between variables. Postfix A B C * + Operators come after variables. A B C * + D = B * C A D + A + D 10

11 Infix to Postfix Conversion Using Stack Converting an infix expression "A+B*C-(D+E)/G" to postfix. Postfix buffer Operator stack Postfix buffer Operator stack Step 1 A + Step 5 A B C * + D E + ( - Step 2 A B * + Step 6 A B C * + D E + - Step 3 A B C * + - Step 7 A B C * + D E + G / - Step 4 A B C * + D ( - Step 8 A B C * + D E + G / - 11

12 Postfix Calculation Using Stack Step 1 Step 2 Step 3 Postfix buffer A B C * + D E + G / - * + D E + G / - + D E + G / - Calculator stack C B A H = B*C A Postfix buffer Step 6 G / - Step 7 / - Step 8 - Calculator stack J = D+E A+H G J I K = J/G I Step 4 D E + G / - I = A+H Step 9 I-K Step 5 + G / - E D I I-K = (A+(B*C))-((D+E)/G) 12

13 Queue Queue is a type of list where insertion and removal of elements occur at two opposite ends, i.e., back (tail) and front (head). First in line Last in line Next in line for service New arrival 13

14 Queue ADT Queue ADT is a First-In, First-Out (FIFO) data structure. An enqueue operation adds a new element at the end. A dequeue operation removes the oldest element. It can also be implemented by using array or linked list. Linked list Both enqueue and dequeue of linked list are O(1). Data structure is relatively complicated. Array Enqueue of array is O(1), but dequeue is O(N). Data structure is relatively simple. 14

15 Queue ADT Functions Stack ADT functions size(); empty(); print(); enqueue(element_t element); dequeue(); clear(); Descriptions Get the number of elements in the queue. Return true if the queue is empty. Print the values of all elements in the queue. Add an element at the end of queue. Remove the element at index 0 in the queue. Remove all elements in the queue. 15

16 Queue ADT by Circular Array Assume the queue size (or capacity) is fixed. front is the index of (or pointer to) the oldest element. back is the index of (or pointer to) the last element of queue. front back Index:

17 Circular Array Operations front back enqueue(20); Index: front back dequeue(); Index: front back enqueue(41); Index:

18 Circular Array Operations front back dequeue(); Index: back front enqueue(85); Index: After the back loops around, indices of (back front) + 1 is not the same as number of elements in the queue. It needs to maintain a separate counter for the element counts. 18

19 Circular Array Operations back front enqueue(29); Index: /* queue.size = number of elements in the queue */ /* queue.capacity = array size regardless of occupancy */ if(queue.size < queue.capacity) { back = ++back % queue.capacity; queue.array[back] = new_element; queue.size++; return success; else { return fail; 19

.. User N Computer server Job id Name User Time Use S ------------------------- ----------------

20 Queue ADT Applications: Computer Server Jobs Server batch processing (or job scheduling) User 1 User 2 Job queue (scheduler) User 3... User N Computer server Job id Name User Time Use S linked_list user_1 0 Q stack_postfix user_n 00:17:21 R circular_array user_3 01:37:02 E array_list user_2 00:02:42 R 20

21 Queue ADT Applications: Network Routers A network router is comprised of I/O buffers (i.e., queues), routing algorithm and control logics, crossbar, etc. Routing control I/O queues Crossbar Router Control logic 21

1 P age DS & OOPS / UNIT II

1 P age DS & OOPS / UNIT II UNIT II Stacks: Definition operations - applications of stack. Queues: Definition - operations Priority queues - De que Applications of queue. Linked List: Singly Linked List, Doubly Linked List, Circular