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Midterm 1 on Friday February 12 Closed book, closed notes No computer can be used 50 minutes 4 questions

Write a function Write program fragment Explain how to do things using stacks,

queues, lists etc

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Stack

The Stack Metaphor

• A stack is a data structure in which the elements are accessible only in a last-in/first-out order.

• The fundamental operations on a stack are push, which adds a new value to the top of the stack, and pop, which removes and returns the top value.

• One of the most common metaphors for the stack concept is a spring-loaded storage tray for dishes. Adding a new dish to the stack pushes any previous dishes downward. Taking the top dish away allows the dishes to pop back up.

Implementation of Stack#define elements int #define stacksize 100

typedef struct { int top; elements items[stacksize]; } stack;

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Implementation of Stackint empty ( stack s ); /* postcondition: empty(s) == 1 if s is empty, == 0 otherwise */ int full ( stack s ); /* postcondition: full(s) == 1 if s is full, == 0 otherwise */ elements pop ( stack *s ); /* precondition: not empty(*s); postcondition: push(*s, pop(*s)) == *s */

void push ( stack *s, elements e ); /* precondition: full(*s) == 0; postcondition: push(*s,e); pop(*s) == e */ 5

Implementation of Stack II#define elements int

typedef struct { int top; int size; elements *items; } stack;

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Implementation of Stack IIstack create ( int n ); /* postcondition: create(n) is a stack which can hold n items */int empty ( stack s ); /* postcondition: empty(s) == 1 if s is empty, == 0 otherwise */ int full ( stack s ); /* postcondition: full(s) == 1 if s is full, == 0 otherwise */ int pop ( stack *s, elements *e ); /* precondition: not empty(*s); postcondition: pop(*s,*e) == 0 if not empty(*s), == 1 otherwise, check = push(*s,*e) restores the stack */

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Queues and Lists

QUEUES Very similar to stacks The only difference between them is in

the order in which elements are processed.

A stack uses a last-in/first-out (LIFO) discipline

A queue adopts a first-in/first-out (FIFO) model that more closely resembles a waiting line.

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Queue ADTabstract typedef <<elements>> queue;/* a queue is a sequence of elements, FIFO = First In First Out */

abstract int empty ( queue q );postcondition: empty(s) == 1 if queue is empty, == 0 otherwise;

abstract int full ( queue q );postcondition: full(s) == 1 if queue is full, == 0 otherwise;

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Queue ADT

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abstract elements delete ( queue q ); /* dequeue */precondition: empty(q) == 0;postcondition: first element is removed from queue q;

abstract void insert ( queue q, elements e ); /* enqueue */precondition: full(q) == 0;postcondition: element e is added to the end of queue q;

Implementation of Queue

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#define elements int

typedef struct{ int size,front,rear; elements *items;} queue;

Implementation of Queue

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0 1 2 3 4

0 -1

Front Rear

A B C

0 1 2 3 4

0 2

Front Rear

F C D E

0 1 2 3 4

2 0

Front Rear

C

0 1 2 3 4

2 2

Front Rear

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Linked List Group of nodes connected by pointers A node consists of

Data Pointer to next node

6 5 3 8Head Null

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Declaration of a nodestruct node{

int info;struct node *next;

};typedef struct node node;

6 5 3 8Head Null

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Linked List Structure

6 5 3 8Head

6 5 3 8Head Null

Some addressIn memory

Points back toInternal node

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Dynamic allocation of a nodenode *ptr;ptr = (node *)malloc(sizeof(node));

?ptr

free(ptr)

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Inserting at the Head1. Allocate a new node2. Insert new element3. Make new node point to old head4. Update head to point to new node

6 5 3 8Head Null

2 6 5 3 8 NullHead

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Inserting at the Headnode *inserthead(node *head, int a){ node *ptr; ptr = (node*)malloc(sizeof(node)); ptr->info = a; ptr->next = head; return(ptr);}

6 5 3 8Head Null

2 6 5 3 8 NullHead

head = inserthead(head,2);

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Removing at the Head1. Update head to point to next node in the list2. Allow garbage collector to reclaim the former

first node

6 5 3 8Head Null

5 3 8Head Null

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Inserting at the Tail1. Allocate a new node2. Insert new element3. Have new node point to null4. Have old last node point to new node

6 5 3 8Head Null

6 5 3 8Head Null1

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Print a linked listvoid printlist (node *head){ while (head !=NULL) { printf("%d ",head->info); head = head->next; } printf("\n");}

6 5 3 8Head Null

printlist(head);

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Find length of a linked listint length(node *head){ if (head == NULL) return 0; else return 1 + length(head-

>next);}

6 5 3 8Head Null

x=length(head);

Linked List Implementation of Queue

typedef struct{ int size,front,rear; elements *items;} queue;

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6 5 3 8Head Null

Linked List Implementation of Queue

struct node{ elements info; struct node *next; };

typedef struct node node;

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6 5 3 8

front

Null

struct queue{ node *front; node *rear; } ;

typedef struct queue queue

rear

Linked List Implementation of Queue

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6 5 3 8

front

Null

int empty ( queue q );/* postcondition: empty(q) == 1 if queue q is empty, * == 0 otherwise; */elements delete ( queue *q );/* precondition: empty(*q) == 0; * postcondition: first element is removed from queue *q; */

void insert ( queue *q, elements e );/* precondition: full(*q) == 0; * postcondition: element e is inserted to end of queue *q; */

rear

Linked List Implementation of Queue

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6 5 3 8 Null

queue *q;

q

front rear

struct

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Doubly Linked List Group of nodes connected by pointers A node consists of

Data Pointer to next node Pointer to previous node

6 5 3 8Head

NullNull

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Doubly Linked Liststruct cnode{

int info;struct cnode *next;

struct cnode *previous;};typedef struct cnode cnode;

6 5 3 8Head

NullNull

Circular Lists Linked lists have some limitations

Given a pointer p, we can not reach preceding nodes In circular lists, next field of last node points to

first node A node consists of

Data Pointer to next node

6 5 3 8Head Null

6 5 3 8Head

Circular Lists Keep a pointer to the last node How can we add or remove an element from either the front

or the rear of the list? How can we check if the list is empty?

6 5 3 8

list

First node Last node