Stacks and Queues 25 Stack In/Out LIFO: Last-in First-out Push - PowerPoint PPT Presentation

Stacks and Queues 25

Stack In/Out LIFO: Last-in First-out Push Pop Undo/Redo Back/Forward Function call/return Stack 26

Queue HPC FIFO: First-in First-out Back Front In Out Jobs Enqueue Dequeue Queue 27

Queue and Stack ADT Queue Stack Enqueue Push Dequeue Pop Front Top Size Size Empty? Empty? 28

Stack/Queue Implementation Queue List Enqueue Push_back Dequeue Pop_back Front Size Push_front Empty Pop_front Stack Front Back Push Pop Size Top Empty Size Empty 29

Queue Implementation Queue Array Impl. Linked List Impl. Enqueue O(1) O(1) Dequeue O(n) O(1) Front O(1) O(1) Memory overhead Small Big Random access O(1) O(n) 30

Circular Array Queue Front Back 31

Circular Array Queue Front Enqueue Back 32

Circular Array Queue Dequeue Front Back 33

Circular Linked List Queue Front Back 34

Queue Implementation Queue Circular Array Circular Linked Impl. List Impl. Enqueue O(1) O(1) Dequeue O(1) O(1) Front O(1) O(1) Memory overhead Small Big 35

Standard Template Library (STL) Lists, stacks, and queues are all implemented in STL In a real program, you would better use them; why? For the sake of learning, you are not allowed to use STL during this class unless otherwise mentioned 36

Stack Applications Expression evaluation Human-friendly infix expressions The operator falls between the two operands 3 + 2 × 5 = 13 Easier to read and understand Can be easily broken into pieces Machine-friendly postfix expressions The operator is placed after the two operands 325 ×+= 13 Easier to compute in one pass No need for parentheses 37

Evaluate postfix expressions Infix: 3 × 5 + 4/2 × 2 = 34 Postfix: 35 × 42/+2 × ⨉ ⨉ 3 5 4 2 / + 2 Stack of operands 38

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Stack of operands 39

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Push 3 Stack of operands 40

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Push 5 3 Stack of operands 41

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Pop 5 3 Stack of operands 42

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Pop 5 3 Stack of operands 43

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 ⨉ 5 3 Stack of operands 44

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Push 15 Stack of operands 45

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Push 4 15 Stack of operands 46

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Push 2 4 15 Stack of operands 47

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 2 4 15 Stack of operands 48

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Pop 4 2 / Pop Push 2 15 Stack of operands 49

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Pop 15 2 + Pop Push 17 Stack of operands 50

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Push 2 17 Stack of operands 51

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 Pop 17 ⨉ 2 Pop Push 34 Stack of operands 52

Postfix Evaluation Example ⨉ ⨉ 3 5 4 2 / + 2 34 Stack of operands 53

Infix to Postfix Conversion Convert the input into a sequence of operators and operands Account for operator precedence Account for parentheses Example Infix (input): 3 × 5 + 4/2 × 2 Postfix (desired output): 35 × 42/+2 × 54

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output ( Stack of operators 55

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output 3 ( Stack of operators 56

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output 3 ⨉ ( Stack of operators 57

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output 35 ⨉ ( Stack of operators 58

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output 35 ⨉ + ( Stack of operators 59

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output 35 ⨉ 4 + ( Stack of operators 60

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output 35 ⨉ 4 / + ( Stack of operators 61

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output 35 ⨉ 42 / + ( Stack of operators 62

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output 35 ⨉ 42/+ Stack of operators 63

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output 35 ⨉ 42/+ ⨉ Stack of operators 64

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output 35 ⨉ 42/+2 ⨉ Stack of operators 65

Example Input ⨉ ⨉ ( 3 5 + 4 / 2 ) 2 Output 35 ⨉ 42/+2 ⨉ Stack of operators 66