Problem of the Day

Bezout acquired 19 camels through his trading skill,“Of the collected camels,” it said in the late merchant’s will,“Exactly half go to my first son, Abdul,One-fourth to Wasim, one-fifth to Rasul,Call a wise man to distribute — don’t sell or kill.”

How does the Wise Man do it?

Problem of the Day

Bezout acquired 19 camels through his trading skill,“Of the collected camels,” it said in the late merchant’s will,“Exactly half go to my first son, Abdul,One-fourth to Wasim, one-fifth to Rasul,Call a wise man to distribute — don’t sell or kill.”

How does the Wise Man do it?The Wise Man adds his own camel (making 20 to distribute)

Abdul gets 10 (20 * 0.5)Wasim gets 5 (20 * 0.25)Rasul gets 4 (20 * 0.2)

& Wise Man gets his camel back (20 – 10 – 5 – 4 = 1)

LECTURE 26: DEQUES

CSC 212 – Data Structures

Stack Memory Aid

Roses are red and violets are blue

Implement push, pop , & top

And you’re a Stack too!

Stack Interface

public interface Stack<E> extends Collection {public E top() throws EmptyStackException;

public E pop() throws EmptyStackException;

public void push(E element);

}

Queue Memory Aid

Queue Memory Aid

It’s hard writing rhymes with

enqueue, dequeue, and

front

Queue Memory Aid

public interface Queue<E> extends Collection {

public E front() throws EmptyQueueException;

public E dequeue() throws EmptyQueueException;

public void enqueue(E element);

}

Queue ADT

Stacks vs. Queues

Access data with Stack in LIFO order

Last In-First Out ordering is unfair (unless late)

Data accessed in Queue using FIFO order

First In-First Out is first-come, first-served

Stacks vs. Queues

Access data with Stack in LIFO order

Last In-First Out ordering is unfair (unless late)

Data accessed in Queue using FIFO order

First In-First Out is first-come, first-served

Ord

er r

ead

if

Qu

eue

Stacks vs. Queues

Access data with Stack in LIFO order

Last In-First Out ordering is unfair (unless late)

Data accessed in Queue using FIFO order

First In-First Out is first-come, first-served

Ord

er r

ead

if

Qu

eue O

rder read

if Stack

Cannot access both sides of either Collection Transplant waiting lists Help center phone banks My Grandpa dealing cards for money

Stack only works with one end Add & remove from top of the Stack

Queue limits how each side used Front provides access & removal of elements Must use the Queue’s end to add elements

Still Have Limits

Pronounced “deck” (like on a house) Mnemonic for Double Ended QUEue dequeue ≠ deque and do not sound alike

Structure that provides access to both ends Combines Stack & Queue concepts Is also able to add elements to start

Deque ADT

public interface Deque<E> extends Collection { /* front() */ public E getFirst() throws EmptyDequeException;

/* top() */ public E getLast() throws EmptyDequeException;

/* dequeue() */ public E removeFirst() throws EmptyDequeException;

/* pop() */ public E removeLast() throws EmptyDequeException;

/* push() or enqueue() */ public addLast(E elem);

/* brand new method! */ public addFirst(E elem);

}

Deque Interface

VIPs versus Losers

Class defines fields aliased to first & last nodes Doubly-linked list enables O(1) time for all

methods Add elements by adding new Node at end Update sentinel’s next or previous to

remove element

Linked-list based Deque

head rear

Class defines fields aliased to first & last nodes Doubly-linked list enables O(1) time for all

methods Add elements by adding new Node at end Update sentinel’s next or previous to

remove element

Linked-list based Deque

rear

retVal

head

Class defines fields aliased to first & last nodes Doubly-linked list enables O(1) time for all

methods Add elements by adding new Node at end Update sentinel’s next or previous to

remove element

Linked-list based Deque

retVal

head rear

Class defines fields aliased to first & last nodes Doubly-linked list enables O(1) time for all

methods Add elements by adding new Node at end Update sentinel’s next or previous to

remove element

Linked-list based Deque

retVal

head rear

Class defines fields aliased to first & last nodes Doubly-linked list enables O(1) time for all

methods Add elements by adding new Node at end Update sentinel’s next or previous to

remove element

Linked-list based Deque

newElem

head rear

Class defines fields aliased to first & last nodes Doubly-linked list enables O(1) time for all

methods Add elements by adding new Node at end Update sentinel’s next or previous to

remove element

Linked-list based Deque

newElem

newNode

head rear

Class defines fields aliased to first & last nodes Doubly-linked list enables O(1) time for all

methods Add elements by adding new Node at end Update sentinel’s next or previous to

remove element

Linked-list based Deque

newElem

newNode

head rear

Class defines fields aliased to first & last nodes Doubly-linked list enables O(1) time for all

methods Add elements by adding new Node at end Update sentinel’s next or previous to

remove element

Linked-list based Deque

head rear

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qfr

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qf r

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qf r

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qf r

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qf r

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qf r

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qfr

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qfr

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qfr

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qfr

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qf r

DEQUES, like QUEUES, have both ends move addFirst & removeFirst moves its front

index rear index moved by addLast & removeLast

Ends of a array-based DEQUE like clock time Identical to Queue and how it works,

except… …occasionally need to subtract from index,

also

Circular Access

qf r

Array-based DEQUE Operations

Uses property of clock math Remainder of result is all that matters But the values sign is also important -1 % 4 == -1, for example

Array-based DEQUE Operations

To get this to work, use a cheap trick Adding size of the array does not change

result

(-1 + 6) % 6 (3 + 6) % 6= 5 % 6 = 9 % 6= 5 = 3

Your Turn

Get into your groups and complete activity

For Next Lecture

Midterm #2 will be in class on Wednesday