CSCI 62Data Structures

Dr. Joshua StoughOctober 7, 2008

Today• Linear Structures

– Grow and Shrink in predetermined manner.

– Stacks – Last In – First Out – Queues – First In – First Out

• http://www.cs.williams.edu/JavaStructures/Documentation.html

Linear Interface

AbstractLinear

Stacks• Like a stack of paper (or cafeteria trays)

– “last-in first-out” (LIFO) • can only add to the top - push• can only remove from the top - pop

• Why?– Often used to keep track of execution in a

program• when returning from a method call, the computer

has to remember where it last was

AbstractStack• push()• pop()• peek()• That’s it!

– All the rest is complication that can be abstracted away.

Stack

Stack

topNodeNodeNodeNodeNode

Node Only need access to the top of the stack

Everything O(1)How about with Vector?

May be implemented as a linked list

push – addFirst()pop – removeFirst()peek – getFirst()

Stacks• Interesting idea

– Vector O(1) add time, sometimes O(1) sometimes O(n)• If that lack of reliability is offputing, then

need list implementation

StacksExample

10 public shuffle() {11 int ind1 = nextInt(NUM_CARDS); }

1 public static void main (String[] args) {2 deck = new Deck();3 deck.shuffle();4 System.out.println (deck); }

20 public int nextInt (int num) {21 return 0; }

Call Stack33

11top

Stacks used to simulate recursion• CallFrame• CallStack to organize the CallFrames

• CallFrame contains– Local variables– Method parameters– Program counter – declaring location

within routine

Recursive QuickSort

Iterative QuickSort CallFrame

Iterative QuickSort

Stack Question• Suppose you wish to fill a stack

with a copy of another, maintaining the order of elements. Using only Stack operations, describe how this would be done. How many additional stacks are necessary?

• public static void copy(Stack s, Stack t)

Stack copy answer

Stack Question• Suppose you wish to reverse the

order of elements of a stack. Using only Stack operations, describe how this would be done. Assuming you place the result in the original stack, how many additional stacks are necessary?

• public static void reverse(Stack s)

Stack: as List or Vector.• What’s required of a Stack?

– Add to top, remove from top.

• As a List– Complexity of push, peek, pop?

• As a Vector– Complexity of push, peek, pop?

Post-Fix Notation• 6 4 + (10)• 3 2 – 4 + (5)• 1 2 3 4 5 6 + + + + + (21)

• Quick: Backus-Naur Form• E := L | E E O• O := + | - | / | * | ^ | %• L := some number

Solving Postfix Notation using a Stack• The expression to evaluate is

either a L or a E. • Push all the tokens onto the stack:• Take the top:

– If L, then we know the value.– If O,

• Get two more E off the stack.• Perform the appropriate operation and

return that value.

Queues• Standing in line

– “first-in first-out” (FIFO)• add to the “tail” of the list (back of line) - enqueue• remove from the “head” (head of line) - dequeue

• Why?– often used to keep things in the order that

they arrived– processes to be scheduled on the CPU– packets arriving to a router

Queue – as Linked List – using a Linked

ListQueue

headNodeNodeNodeNodeNode

Node Only have access to the head and tail of the queue

May be implemented as a linked list

-add to tail-remove from head-SinglyLinked with tail would be fine.

tail

Queue – as a Vector• Add elements to the back

– Complexity?

• Get elements from the front– Complexity?

• Cost of adding elements?

Queue – as Array• Keep ints for head and count• Use % to keep track of head upon

remove

Stack vs Queues• Stacks depth-first,

• Queues breadth-first.