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 gets10 (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)

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 extends Collection { public E top() throws EmptyStackException; public E pop() throws EmptyStackException; public void push(E element); }

Queue Memory Aid

It’s hard writing rhymes with enqueue, dequeue, and front

Queue Memory Aid

public interface Queue extends Collection { public E front() throws EmptyQueueException; public E dequeue() throws EmptyQueueException; public void enqueue(E element); } Queue ADT

Stacks vs. Queues

Order read if Queue

Stacks vs. Queues Order read if Queue Order 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) DEQUE  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 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

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

 D EQUES, like Q UEUES, have both ends move f  addFirst & removeFirst moves its f ront index  r  r ear index moved by addLast & removeLast  Ends of a array-based D EQUE like clock time  Identical to Queue and how it works, except…  …occasionally need to subtract from index, also Circular Access q f r

Array-based D EQUE 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 D EQUE 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  Midterm #2 will be in class on Wednesday