Advance Data StructureReview of Chapter 3

張啟中

Queue

Queue An ordered list All insertions take place at one end, rear All deletions take place at the opposite end, front First-In-First-Out (FIFO)

Abstract Data Type for Queuetemplate <class KeyType>class Queue { //objects: a finite ordered list with zero or more elements. public: Queue(int MaxQueueSize=DefaultSize); //create an empty queue whose maximum size is MaxQueueSize Boolean IsFullQ(); //if (number of elements in queue== MaxQueueSize) return TRUE //else return FALSE void Add(const Keytype& item); //if (IsFullQ()) then QueueFull() //else insert item at rear of queue Boolean IsEmptyQ(); //if number of elements in the queue is equal to 0 then return TRUE //else return FALSE Keytype* Delete(KeyType&); //if (IsEmpty()) then QueueEmpty() and return 0 //else remove the item at front of queue and return a pointer to it

};

Representation: Queue Definition

private: int front, rear; KeyType *queue; int MaxSize;

Implementation of Queuetemplate <class KeyType>Queue<KeyType>::Queue(int MaxQueueSize):MaxSize(MaxQueueSize)

{ queue = new Keytype[MaxSize]; front = rear = -1;}

Queue 的操作

Implementation of member function IsFull() Implementation of member function IsEmpty() Implementation of member function Add() Implementation of member function Delete()

See textbook pp132-133

Queue Implementation I: Linear Array

……

0 1 2 3 4 MaxSize -1

front = rear = -1

Initially

Queue Implementation I: Linear Array

after Insert 4 elements

MaxSize -1

front = -1

……

0 1 2 3 4

rear = 3

Insert

template <class KeyType>void Queue<KeyType>::Add(const KeyType& x){ if (isFull()) QueueFull(); else queue[++rear] = x;}

Queue Implementation I: Linear Array MaxSize -1

front = 1

……

0 1 2 3 4

rear = 3

delete

template <class KeyType>KeyType* Queue<KeyType>::Delete(){ if (isEmpty()) { QueueEmpty(); return 0; } x = queue[++front]; return &x;)

after delete 2 elements

Queue Implementation I: Linear Array 如何判斷 Queue 是空的？ front == rear

如何判斷 Queue 是滿的？ rear == MaxSize-1

MaxSize -1

……

0 1 2 3 4

front = rear = 3 after delete 4 elements

after Insert MaxSize elementsfront = -1

MaxSize -1

……

0 1 2 3 4

rear = MaxSize-1

Queue Implementation I: Linear Array 用 Linear Array 實作 Queue ，在新增時會面臨兩種最壞的情況。 解決方法：依序搬移 Queue 中的元素位置（ case 2 需先刪除第

一個元素），但其代價需 O(MaxSize)

MaxSize -1

front = 3

……

0 1 2 3 4

rear = MaxSize-1

Case 1:

MaxSize -1

front = -1

……

0 1 2 3 4

rear = MaxSize-1

Case 2:

為了改善 linear array 的缺失，必須將 Queue 改成環形陣列。所謂的環形陣列，是一個普通的陣列，但在概念上將其首尾相接而成。

0 2 3 4 5 6 71

0

1

2

3 4

5

6

7front

Rear

Queue Implementation II: Circular Array

template <class KeyType>Queue<KeyType>::Queue(void):MaxSize(MaxQueueSize){ queue = new KeyType[MaxSize]; front = rear= 0;}

Queue Implementation II: Circular Array

front = rear = 0

Initially

0

1

2

3 4

MaxSize-1

●

●

Queue Implementation II: Circular Array

0

1

2

3 4

●

●

MaxSize-1

front = 0

rear = 3

after insert 3 elements

Insert

0

1

2

3 4

●

●

MaxSize-1

front = 2

rear = 3

after delete 2 elements

Delete

Queue Implementation II: Circular Array 用 circular Array 實作 Queue ，會面臨無法判斷 Queue 是空的

或是滿的問題。因為 front == rear 時 Queue 可能為空，也可能為滿。

如何解決？

0

1

2

3 4

●

●

MaxSize-1

front = rear = 3 Empty

0

1

2

3 4

●

●

MaxSize-1

front = rear = 3 Full

Queue Implementation II: Circular Array 解決方法，有二種

Method 1 ：犧牲空間 任何時候只允許 MaxSize-1 個元素在 Queue 中 Method 2 ：犧牲時間

增加一個變數，記錄上一次的動作。 因為 Queue 元素的新增與刪除非常頻繁，所

以我們較常採用 Method 1 還有沒有其他的解法？（當然有）

Circular Array : Method 1

template <class KeyType>void Queue<keyType>::Add(const KeyType& x){ int newrear =(rear+1) % MaxSize if (front == newrear) QueueFull(); else queue[rear=newrear]=x;}

0

1

2

3 4

●

●

MaxSize-1

front = 3

rear = 1

newrear = (rear + 1) % MaxSize

0

1

2

3 4

●

●

MaxSize-1

front = 3newrear = (rear + 1) % MaxSize

front == newrear

rear = 2

FullOK

Circular Array : Method 1

template <class KeyType>KeyType* Queue<keyType>::Delete(const KeyType& x){ if (front == rear) { QueueEmpty(); return; } front = (front+1) % MaxSize; x = queue[front]; return &x;}

0

1

2

3 4

●

●

MaxSize-1

rear = 2

front = 2OK 0

1

2

3 4

●

●

MaxSize-1

front = rear = 2

Empty

Circular Array : Method 2 當 add 時，令 LastOp = ‘+’ ，當 delete 時，令 LastOp = ‘-’ 。 當 front == rear 時，若 LastOp == ‘+’ 則 Queue 是滿的，反之，

若 LastOp == ‘-’ 則 Queue 為空。

Definitionprivate: int front, rear; KeyType *queue; int MaxSize; char LastOp;

Implementation of Queuetemplate <class KeyType>Queue<KeyType>::Queue(int MaxQueueSize):MaxSize(MaxQueueSize){ queue = new Keytype[MaxSize]; front = rear = -1 LastOp = ‘-’; // + add - delete}

Example: Queue

Job Scheduling String convert to Integer Recognizing palindromes Event-driven Programs Process Queue

Example Queue: Job Scheduling

front rear Q[0]

[1] [2] [3] [4] [5] …. Comments

-1 -1 queue empty initial

-1 0 J1 Job 1 joins Q

-1 1 J1 J2 Job 2 joins Q

-1 2 J1 J2 J3 Job 3 joins Q

0 2

J2 J3 Job 1 leaves Q

0 3

J2 J3 J4 Job 4 joins Q

1 3

J3 J4 Job 2 leaves Q

Example Queue ：String convert to Integer

【範例】

“bb1234” 1234 (b represents a blank)

b

bb

bb1

bb12

bb123

bb1234

b1234

1234

234 N = 0 Ch = ‘1’

34 N = 1 Ch = ‘2’

4 N = 12 Ch = ‘3’

N = 123 Ch = ‘4’

N = 1234 Ch = ‘4’

Example Queue: Recognizing palindromes

S

Q

a b c d c b a

a

S

Q

a

b c d c b a

a b

S

Q

ba

c d c b a

S

Q

d c b a

a b c

S

Q

c b a

a b c d c

S

Q

b a

cba

a b c d

dcba

cdcba

S

Q

a

a b c d c b

bcdcba S

Q a b c d c b a

abcdcba S

Q a b c d c b a

abcdcba

Example Queue: Event-driven Programs 目前流行的視窗系統（如 X

Window 、 MS Windows ）是採用事件驅動（ event-driven ）的模式。

視窗系統必須處理許多不同的事件（ event ）— 如：鍵盤輸入、滑鼠移動、壓下滑鼠按鍵、放開滑鼠按鍵等等使用者的動作，以及視窗遮蓋、視窗浮現等等螢幕狀態的改變。這些事件依序地擺放在所謂的事件佇列（ event queu

e ）中，然後用循覆的方式依序處理（稱為事件迴路（ eve

nt loop ））。

取出下一個事件

判斷是何事件

front rear

event queue

e1 e2 en

呼叫該事件的處理函式

eventloop

加入新事

件

Example Queue: Process Queue 現代作業系統（ operating system ）為了不浪費電腦的強大能力，通常具有多工（ multi-processing ）的能力。 程序 (processes) 指的是正在執行的程式 多工 (multi-tasking) 指的是電腦在一個時段內能夠

同時執行多個程式。 Example: Windows 2000/XP 、 Linux 、 Mac OS

等

Example Queue: Process Queue 作業系統如何做到多工？

作業系統只要同時載入若干的程式，然後在這些程式間迅速切換執行即可，由於 CPU 運算的速度和人認知的速度比較起來快了許多，因此造成了這些程式是「同時執行」的感覺。

在任一刻 CPU 仍然只能執行一個程序。

程序在整個的執行過程中，可能處於下列的狀態： 新生（ new ） 執行（ running ） 預備（ ready ） 等待（ waiting ） 結束（ terminated ）

new

ready running

waiting

terminated

admittedinterrupt

schedulerdispatchI/O or event

completionI/O or event

wait

exit

Example Queue: Process Queue

Multiple Stacks and Queues12

n

m1

n

mM0 m-1

b[0]t[0]

b[1]t[1]

b[2]t[2]

b[n]

niin

mitib

0,1][][initially

range b[i]+1 到 b[i+1] for stack i, 0 <= i < nb[n] = m-1

full See book p.156