Chapter 8 Stacks and Queues 1

Chapter 8 Stacks and Queues 1

This is a stack of books. 2

This is a queue of people. 3

Chap. 8 Contents 8. 1 Stacks 8. 1. 1 The Pure. Stack Interface 8. 1. 2 Implementations of the Pure. Stack Interface 8. 1. 3 Stack Application 1: How Compilers Implement Recursion 8. 1. 4 Stack Application 2: Converting from Infix to Postfix 8. 1. 5 Prefix Notation 8. 2 Queues 8. 2. 1 The Pure. Queue Interface 8. 2. 2 Implementations of the Pure. Queue Interface 8. 2. 3 Computer Simulation 8. 2. 4 Queue Application: A Simulated Car Wash 4

8. 1 Stacks 5

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Object-Oriented (O-O) Terms Stack, Queue 是特別的 List. 以O-O 術語, 它們 EXTEND (延伸) List (不論是 Array. List 或是 Linked. List) General concepts (通用觀念) are Super classes such as Array. List Specialized concepts (專用觀念 ) are Sub classes such as Stack 7

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8. 1. 1 The Pure. Stack Interface 15

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8. 1. 2 實作Pure. Stack Interface 18

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寫出下列的輸出結果: Linked. List. Pure. Stack my. Stack = new Linked. List. Pure. Stack( ); for (int i = 0; i < 10; i++) my. Stack. push (i * i); while (!my. Stack. is. Empty( )) System. out. println (my. Stack. pop( )); ANS: 81 (9*9), 64 (8*8), 49, 36, 25, 16, 9, 4, 1, 0 24

8. 1. 3 Stack 的應用 1: Compiler如何實作Recursion 25

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Run-time stack 處理 activation records. Push: When method is called Pop: When execution of method is completed (returned) 27

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Run-time Stack: n=1 return “ 1” n=2 return “ 10” n =5 return “ 101” 29

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8. 1. 4 Stack 應用 2: 轉換Infix(中置式) 到 Postfix(後置式) 在 infix 表示法中, operator(運算子) 放置於 operands(運算元) 之間. For example: a + b c – d + (e * f – g * h) / i 34

Old compilers: Infix Machine language 這會因為parentheses(小括號)而產生混亂. Newer compilers: Infix Postfix Machine language 35

在 postfix 表示法中, an operator 直接地放置 於他的operands之後. No parenthesis needed. Infix a + b Postfix ab+ a + b * c abc*+ a * b + c ab*c+ (a + b) * c ab+c* 36

postfix 不必使用 Parentheses 很棒! 37

Let’s convert an infix string below to a postfix string. x – y * z ANS: xyz*38

Postfix 保留 operands的先後順序, so an operand can be appended to postfix as soon as that operand is encountered in infix. 39

Infix x – y * z Postfix x 40

Infix x – y * z Postfix x The operands for ‘-’ 尚未在 postfix, 所以 ‘ - ’ 一定要先暫存在某地方. 41

Infix x – y * z Postfix xy 42

Infix x – y * z Postfix xy The operands for ‘*’ 未在postfix, 所以‘*’ 一定要暫存在某地方, 且在‘-’之前 取出 (後存先取). 43

Infix x – y * z Postfix xyz 44

Infix x – y * z Postfix xyz* – ANS. 45

As another test case, we start with x*y-z. After moving ‘x’ to postfix, ‘*’ is temporarily saved, and then ‘y’ 被加到postfix. What happens when ‘-’ is accessed? Infix x * y – z Postfix xy 46

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暫時儲存處是: Stack! Here is the strategy (pseudo-code) for maintaining the stack: 48

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口 訣 : if Infix Greater, Push 50

Convert from infix to postfix: Infix a + b * c / d - e Postfix 51

Infix Postfix a + b * c / d – e abc*d/+e – * + Operator stack 52

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Convert to postfix: x * (y + z) 54

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59 Infix token

Tokens 60

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8. 1. 5 Prefix(前置式) Notation 63

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8. 2 Queues 70

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回想一下； STACK: (Last-In-First-Out) LIFO 72

Enqueue “張三” 73

張三 Front Back 74

Enqueue “李四” 75

張三 Front 李四 Back 76

Enqueue “王五” 77

張三 Front 李四 王五 Back 78

Dequeue 79

李四 Front 王五 Back 80

8. 2. 1 The Pure. Queue Interface 81

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8. 2. 2 Implementations of the Pure. Queue Interface 85

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Heavy Inheritance Tax 在 class reuse 實務上， 被reuse的class要有完整method description developers 清楚了解後， 再寫dummy code (如上述get) 來override 不能reuse的methods. 這是相當沉重的負擔，有如稅負，故叫 Inheritance Tax. 88

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Determine the output from the following: Linked. List. Pure. Queue my. Queue = new Linked. List. Pure. Queue(); for (int i = 0; i < 10; i++) my. Queue. enqueue (i * i); while (!my. Queue. is. Empty( )) System. out. println (my. Queue. dequeue( )); ANS: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 91

8. 2. 3 Computer Simulation(模擬) SYSTEM 是由互動的部分 (interacting parts) 所組成 92

model 是 system的簡化. 建構model 是為了研究 system 93

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8. 2. 4 Queue Application: A Simulated Car Wash 101

car. Wash • Minimal waiting time is 0 min. • Maximal waiting time: 10 min*5 car= 50 min arrival queue departure to queue from queue Wash Station car car car 102

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Car class • • • /* Car * 初始化 Car object * 為指定的下次到達時間 */ public Car (int next. Arrival. Time) /* get. Arrival. Time • /* 記錄 the just dequeued car 的 arrival time. • * @return the arrival time of this car • */ • public int get. Arrival. Time() 116

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public class Car{ protected int arrival. Time; public Car(){}//default constructor, //for the sake of sub-classses of Car public Car (int next. Arrival. Time){ arrival. Time=next. Arrival. Time; }// constructor with int parameter public int get. Arrival. Time(){ return arrival. Time; }/*get. Arrival. Time*/ }/*Car*/ 128

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A Deque is a “double ended queue” (pronounced as “deck”) that allows inserting and removing from both ends. As a real-world example, a ticket purchasing line acts like a queue, but sometimes somebody who purchased the ticket suddenly comes back to ask something. Because he/she already purchased the ticket, he/she got the privilege to come to the front and ask further questions. Here we need a data structure to add data from front. Also, user can also leave the queue from rear. [edited from web site “stackoverflow”] 132

Python List It is implemented as array, written in C. list 1 = ['physics', 'chemistry', 1997, 2015] list 2 = [1, 2, 3, 4, 5, 6, 7 ] print (list 1[0]) physics print (list 2[1: 5]) [2, 3, 4, 5] print (list 2[-1]) 7 133

Python Tuple is a special list whose elements cannot be changed. tuple 1= (12, 26, 12, 54) print (tuple 1[0]) 12 print (tuple 1[1: 3]) 26 12 print (tuple 1[-1]) 54 tuple 1[0] = 15 Type Error: ‘tuple’ object does not support item assignment. 134

Python Set set 1 = set ( [12, 26, 12, 54] ) print (set 1) set ([12, 26, 54]) set 1. add(32) set ([32, 12, 26, 54]) print (12 in set 1) True print (13 in set 1) False 135

Python Dictionary It is similar to Java Map with key: value pairs. dict 1= { ‘a’: 1, ‘b’: 2, ‘c’: 1} print (dict 1) { ‘a’: 1, ‘b’: 2, ‘c’: 1} print (dict 1. get(‘a’) ) 1 del dict 1[‘c’] print (dict 1) { ‘a’: 1, ‘b’: 2} 136