PESIT Bangalore South Campus Hosur road, 1km before Electronic City, Bengaluru -100 Department of Computer Science and Engineering

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1 USN 1 P E PESIT Bangalore South Campus Hosur road, 1km before Electronic City, Bengaluru -100 Department of Computer Science and Engineering SOLUTION FOR INTERNAL ASSESSMENT TEST 2 Date : 6/10/2017 Marks: 40 Subject & Code : Data Structures and Applications (15CS33) Class : III CSE A, B & C Name of Faculty : Prof. Sandesh B J & Ms. Sai Prasanna Time : :30 am to 10 am Note: Answer FIVE full questions, selecting any ONE full question from each part. PART 1 1 Write the algorithm to implement a stack using dynamic array whose initial capacity is 1 and array doubling is used to increase the stack s capacity whenever an element is added to a full stack. Implement the operations-push, pop and display. 2 a What are the disadvantages of Linear Queue? Explain how it is overcome in Circular Queue. 2 In linear queue, when rear index equals MAX_QUEUE_SIZE 1, the queuefull condition should move the entire queue to the left so that the first element is again at queue[0] and front is at -1. Shifting anarray is very time consuming and the worst case complexity is O(MAX_QUEUE_SIZE). In Circular queue we permit the queue to wrap around the end of array.

2 b Write the functions for insertion, display and doubling the capacity in circular queue using Dynamic array. 6

3 PART 2 3 Write the function to convert the infix expression to postfix. Trace and illustrate the status of stack for the expression: ((a/(b-c+d))*(e-a)*c) char stack[size]; int top = -1; /* define push operation */ void push(char item) if(top >= SIZE-1) printf("\nstack Overflow."); top = top+1; stack[top] = item; /* define pop operation */ char pop() char item ; if(top <0) printf("stack under flow: invalid infix expression"); /* underflow may occur for invalid expression */ /* where ( and ) are not matched */ exit(1); item = stack[top]; top = top-1; return(item); /* define function that is used to determine whether any symbol is operator or not (that is symbol is operand) * this fucntion returns 1 if symbol is opreator return 0 */ int is_operator(char symbol) if(symbol == '^' symbol == '*' symbol == '/' symbol == '+' symbol =='- ') return 1;

4 return 0; int precedence(char symbol) if(symbol == '^')/* exponent operator, highest precedence*/ return(3); if(symbol == '*' symbol == '/') return(2); if(symbol == '+' symbol == '-') /* lowest precedence */ return(1); return(0); void InfixToPostfix(char infix_exp[], char postfix_exp[]) int i, j; char item; char x; push('('); /* push '(' onto stack */ strcat(infix_exp,")"); /* add ')' to infix expression */ i=0; j=0; item=infix_exp[i]; /* initialize before loop*/ while(item!= '\0') /* run loop till end of infix expression */ if(item == '(') push(item); if( isdigit(item) isalpha(item)) postfix_exp[j] = item; j++; if(is_operator(item))// == 1) /* means symbol is operator */

5 */ stack */ j++; x=pop(); while(precedence(x)>= precedence(item)) postfix_exp[j] = x; x = pop(); /* add them to postfix expresion push(x); /* because just above while loop will terminate we have popped one extra item for which condition fails and loop terminates, so that one*/ push(item); /* push current operator symbol onto if(item == ')') /* if current symbol is ')' then */ x = pop(); /* pop and keep popping until */ while(x!= '(') /* '(' encounterd */ postfix_exp[j] = x; j++; x = pop(); printf("\ninvalid infix Expression.\n"); getchar(); exit(1); i++; if(top>=0) item = infix_exp[i]; printf("\ninvalid infix Expression.\n"); exit(1); getchar(); postfix_exp[j] = '\0'; /* add sentinel puts() fucntion */ /* will print entire postfix[] array upto SIZE */ Enter Infix expression : ((a/(b-c+d))*(e-a)*c) Stack ( Stack ((

6 Stack ((( Stack (( Stack ((( Stack (((/ Stack (((/( Stack (((/ Stack (((/( Stack (((/(- Stack (((/( Stack (((/ Stack (((/( Stack (((/(+ Stack (((/( Stack (((/ Stack ((( Stack (( Stack ( Stack (( Stack ((* Stack ((*( Stack ((* Stack ((*( Stack ((*(- Stack ((*( Stack ((* Stack (( Stack ( Stack (( Stack ((* Stack (( Stack ( Stack Postfix Expression: abc-d+/ea-*c* 4 Write a program to determine if the parentheses in an expression are properly nested using Stacks. Example: (2+(3*6)) : Valid, as equal no of open and close parenthesis. (2+(3*6) : Invalid, as unequal no of open and close parenthesis. //Valid if the student has written the code to check for ( and ) only #include < stdio.h > #include < conio.h > #define max 50

7 void main() char stk[max],exp[100]; int top,i; clrscr(); top = -1; printf("\nenter an infix expression "); gets(exp); for(i=0; exp[i]!= '\0'; i++) if( exp[i]=='(' exp[i] =='[' exp[i] == '' ) top++; stk[top]= exp[i]; if ( exp[i] == ')' ) if( stk[top] == '(' ) top--; printf("unbalanced exp"); exit(0); if ( exp[i] == ']' ) if( stk[top] == '[' ) top--; printf("unbalanced exp"); exit(0); if ( exp[i] == '' ) if( stk[top] == '' ) top--; printf("unbalanced exp"); exit(0); // for if( top == -1 ) printf("exp is balanced"); printf("exp is not balanced"); // main

8 PART 3 5 Write and explain the recursive functions for: (i)towers of Hanoi void hanoi(int n,char from,char other,char to) if(n!=0) hanoi(n-1,from,to,other); printf("\nmove DISK FROM %c TO %c",from,to); hanoi(n-1,other,from,to); (ii) Ackerman s Function. ack(m,n) if (m == 0) return n+1 if (n == 0) return ack( m - 1, 1 ) return ack( m - 1, ack( m, n - 1 ) ) 6 Write a program to implement multiple stacks using arrays. Also, write the functions to add/delete an item in i th stack. #define MEMORY_SIZE 100 /* size of memory */ #define MAX_STACK_SIZE 100 /* max number of stacks plus 1 */ /* global memory declaration */ element memory [MEMORY_SIZE]; int top [MAX_STACKS]; int boundary [MAX_STACKS]; int n; /* number of stacks entered by the user */ //To divide the array into roughly equal segments : top[0] = boundary[0] = -1; for (i = 1; i < n; i++) top [i] =boundary [i] =(MEMORY_SIZE/n)*i; boundary [n] = MEMORY_SIZE-1; Add an item to the stack stack-no void add (int i, element item) /* add an item to the ith stack */ if (top [i] == boundary [i+1]) stack_full (i); may have unused storage memory [++top [i] ] = item; Delete an item from the stack stack-no element delete (int i) /* remove top element from the ith stack */ if (top [i] == boundary [i])

9 return stack_empty (i); return memory [ top [i]--]; PART 4 7 Write a program that creates a Singly Linked List (Use insert at front) consisting of n students data with fields - name, roll no, semester. Search and print the record of student whose name is given by the user. (Print all the occurrences if multiple entries for same name exist) main( ).. // printf("enter the number of nodes to create : "); scanf("%d", &n); create(n); //read the name to be read display(name); void display(char *name) if(head == NULL) printf("linked List is empty.\n"); Node *temp; temp = head; while(temp!= NULL) if(strcmp(name, temp->name)==0) printf("node %d USN : %s Name : %s Branch : %s Semester : %d Phone No. : %ld\n", n + 1, temp -> usn, temp -> name, temp -> branch, temp -> sem, temp -> phno); temp = temp -> link; void create(int n) int i; for(i = 1; i <= n; i++) printf("enter details for node %d :\n", i);

10 insertfront(); void insertfront() char usn1[10], name1[50], branch1[3]; int sem1; long phno1; Node *temp = (Node*)malloc(sizeof(Node)); printf("enter USN : "); scanf("%s", usn1); printf("enter name : "); scanf("%s", name1); printf("enter branch : "); scanf("%s", branch1); printf("enter semester : "); scanf("%d", &sem1); printf("enter phone number : "); scanf("%ld", &phno1); strcpy(temp -> usn, usn1); strcpy(temp -> name, name1); strcpy(temp -> branch, branch1); temp -> sem = sem1; temp -> phno = phno1; if(head == NULL) head = temp; temp -> link = NULL; temp -> link = head; head = temp; count++; a Explain the need for Linked List when Arrays provide similar functionality? 2 In an array, elements are one after the another (successive memory allocation). But in linked list, memory is not contiguous. Advantages : Addition/Deletion of an element from the list at any index which is an O(1) operation in Lists as compared to Arrays.

11 b Write the functions for the following operations on Singly Linked List: (i)inserting a node at the end of SLL void append(struct Node** head_ref, int new_data) struct Node* new_node = (struct Node*) malloc(sizeof(struct Node)); 6 struct Node *last = *head_ref; /* used in step 5*/ new_node->data = new_data; new_node->next = NULL; if (*head_ref == NULL) *head_ref = new_node; while (last->next!= NULL) last = last->next; last->next = new_node; (ii) Deleting n th Node void deletenode(struct Node **head_ref, int position) // If linked list is empty if (*head_ref == NULL) // Store head node struct Node* temp = *head_ref; // If head needs to be removed if (position == 0) *head_ref = temp->next; // Change head free(temp); // free old head // Find previous node of the node to be deleted for (int i=0; temp!=null && i<position-1; i++) temp = temp->next; // If position is more than number of ndoes if (temp == NULL temp->next == NULL) // Node temp->next is the node to be deleted // Store pointer to the next of node to be deleted struct Node *next = temp->next->next; // Unlink the node from linked list free(temp->next); // Free memory temp->next = next; // Unlink the deleted node from list

12 PART 5 9 Write a program to implement the Insertion of an element at Front, Rear and n th position of a Doubly Linked List with a Header Node. (Node in 1 st Position is the one after the Header Node) //modify for header node based on code snippet below /* TO create an empty node */ void create() int data; temp =(struct node *)malloc(1*sizeof(struct node)); temp->prev = NULL; temp->next = NULL; printf("\n Enter value to node : "); scanf("%d", &data); temp->n = data; count++; /* TO insert at beginning */ void insert1() if (h == NULL) create(); h = temp; temp1 = h; create(); temp->next = h; h->prev = temp; h = temp; /* To insert at end */ void insert2() if (h == NULL) create(); h = temp; temp1 = h; create(); temp1->next = temp; temp->prev = temp1; temp1 = temp; /* To insert at any position */ void insert3() int pos, i = 2; printf("\n Enter position to be inserted : ");

13 scanf("%d", &pos); temp2 = h; if ((pos < 1) (pos >= count + 1)) printf("\n Position out of range to insert"); if ((h == NULL) && (pos!= 1)) printf("\n Empty list cannot insert other than 1st position"); if ((h == NULL) && (pos == 1)) create(); h = temp; temp1 = h; while (i < pos) temp2 = temp2->next; i++; create(); temp->prev = temp2; temp->next = temp2->next; temp2->next->prev = temp; temp2->next = temp; 10 Write a program to add two Polynomials using Linked List. typedef struct poly_node *poly_pointer; typedef struct poly_node int coef; int expon; poly_pointer link; ; poly_pointer a, b, c; poly_pointer padd(poly_pointer a, poly_pointer b) poly_pointer front, rear, temp; int sum; rear =(poly_pointer)malloc(sizeof(poly_node)); if (IS_FULL(rear)) fprintf(stderr, The memory is full\n ); exit(1);

14 front = rear; while (a && b) switch (COMPARE(a->expon, b->expon)) case -1: /* a->expon < b->expon */ attach(b->coef, b->expon, &rear); b= b->link; break; case 0: /* a->expon == b->expon */ sum = a->coef + b->coef; if (sum) attach(sum,a->expon,&rear); a = a->link; b = b->link; break; case 1: /* a->expon > b->expon */ attach(a->coef, a->expon, &rear); a = a->link; for (; a; a = a->link) attach(a->coef, a->expon, &rear); for (; b; b=b->link) attach(b->coef, b->expon, &rear); rear->link = NULL; temp = front; front = front->link; free(temp); return front; void attach(float coefficient, int exponent, poly_pointer *ptr) /* create a new node attaching to the node pointed to by ptr. ptr is updated to point to this new node. */ poly_pointer temp; temp = (poly_pointer) malloc(sizeof(poly_node)); if (IS_FULL(temp)) fprintf(stderr, The memory is full\n ); exit(1); temp->coef = coefficient; temp->expon = exponent; (*ptr)->link = temp; *ptr = temp; *******

Fall, 2015 Prof. Jungkeun Park

Data Structures t and Algorithms Circular lists / Doubly linked lists Fall, 2015 Prof. Jungkeun Park Copyright Notice: This material is modified version of the lecture slides by Prof. Rada Mihalcea in