PESIT Bangalore South Campus Hosur road, 1km before Electronic City, Bengaluru -100 Department of MCA

Transcription

1 USN 1 P E PESIT Bangalore South Campus Hosur road, 1km before Electronic City, Bengaluru -100 Department of MCA INTERNAL ASSESSMENT TEST 2 (Scheme and Solution) Data Structures Using C (16MCA11) 1) A. Pointers as function arguments: (5M) When we pass addresses to a function, the parameters receiving the addresses should be pointers. The process of calling a function using pointers to pass the addresses of variable is known as Call by Reference. The following points to be remembered are: * The function parameters are declared as pointers * The dereferenced pointers are used in the function body * when the function is called, the addresses are passed as actual arguments. void main() x=10; y=20; swap(&x,&y); printf( %d%d,x,y); swap(int *a,int *b) int t; t=*a; *a=*b; *b=t; B. Functions returning pointers: (5M) (e.g.) int *max(int *x,int *y) if (*x > *y) return(x); else return(y);

2 2) Advantages of Circular Queue over Linear Queue: In circular Queue memory is utilized efficiently. The memory of a deleted element can be used again by other elements in case of circular Queue. (2M) Function to insert and delete an element from Circular Queue: (8M) # include<stdio.h> # include<conio.h> # define maxsize 5 int q[maxsize],f=-1,r=-1,ch; void insert(); void delete1(); void display(); void main() clrscr(); do printf("\n1.insert\n"); printf("2.delete\n"); printf("3.exit\n"); printf("enter ur choice\n"); scanf("%d",&ch); switch(ch) case 1: insert(); case 2: delete1(); case 3: exit(0); while(ch!=3); void insert() int item; printf("enter the item\n"); scanf("%d",&item); if((r+1)%maxsize==f) printf("queue is full\n"); break; break; return; r=(r+1)%maxsize; q[r]=item; if(f==-1) f=f+1; display(); void delete1() int item; if(f==-1) printf("queue underflow"); return; item=q[f]; printf("deleted element is %d\n",item); if(f==r) f=r=-1; else f=(f+1)%maxsize; display();

3 void display() int i; printf("contents of queue are\n"); for(i=f;i<=r;i++) printf("%d\t",q[i]); if(f>r) for(i=f;i<=maxsize-1;i++) printf("%d\t",q[i]); for(i=0;i<=r;i++) printf("%d",q[i]); 3) Binary Search Trees: (10M) * A BST is a rooted binary tree whose internal nodes each store a key and each have two distinguished sub-trees denoted by left and right. * The BST have a property which states that the key in each node must be greater than all keys stored in the left sub-tree, and not greater than all keys in the right sub-tree. * Also called as ordered or sorted binary trees. * BSTs keep their keys in sorted order, so that lookup and other operations uses the principle of binary search. * When looking for a key in a tree (or to insert a new key), they traverse the tree from root to leaf, making comparisons to keys stored in the nodes of the tree and deciding, based on the comparison, to continue searching in the left or right sub trees. Function for Creating BST and Traversals: void createbst() p=(node)malloc(sizeof(struct node)); printf("enter the element to be inserted\n"); scanf("%d",&p->info); p->left=p->right=null; if(root==null) root=p; return; prev=root; for(temp=root;temp!=null;) prev=temp; if(p->info<temp->info)

4 temp=temp->left; else temp=temp->right; if(p->info<prev->info) prev->left=p; else prev->right=p; Traversals: void preorder(node root) if(root!=null) printf("%d\t",root->info); preorder(root->left); preorder(root->right); void inorder(node root) if(root!=null) inorder(root->left); printf("%d\t",root->info); inorder(root->right); void postorder(node root) if(root!=null) postorder(root->left); postorder(root->right); printf("%d\t",root->info); 4) Queue Using Doubly Linked List: (10M) void ins_rear() p=(node)mallac(sizeof(struct nodeptr)); p->info=item; cur=head->llink; head->llink=p;

5 p->rlink=head; p->llink=cur; cur->rlink=p; head->info=head->info+1; void del_front() if (head->rlink==head) printf( List is empty ); return; cur=head->rlink; // address of first node next=cur->rlink; // address of second node head->rlink=next; next->llink=head; printf( Node to be deleted %d,cur->info); free(cur); void display() if (head->rlink==head) printf( List is empty ); return; printf( Contents of the List is\n ); for(cur=head->rlink;cur!=head;cur=cur->rlink) printf( %d,cur->info); 5) A) Priority Queue: (5M) Priority Queue is a special type of data structure in which items can be inserted or deleted based on priority. Always an element with highest priority is processed before processing any of the lower priority elements. If the elements in the queue are of same priority, then the element, which is inserted first into the queue, is processed. Priority queues are used in job scheduling algorithms in the design of operating system where the jobs with highest priorities have to be processed first. The priority queues are classified into two groups: Ascending Priority Queue: is a collection of items into which items can be inserted arbitrarily and from which only the smallest element can be removed. If apq is an ascending

6 priority queue, the operation pqinsert(apq,x) inserts element x into apq and pqmindelete(apq) removes the minimum element from apq and returns its value. Once pqmindelete has been applied to retrieve the smallest element of an ascending priority queue, it can be applied again to retrieve the next smallest element, and so on. (e.g.) A queue can be viewed as an ascending priority queue whose elements are ordered by time of insertion. Descending Priority Queue: is a collection of items into which items can be inserted arbitrarily and from which only the largest element can be removed. If apq is an descending priority queue, the operation pqinsert(apq,x) inserts element x into apq and pqmaxdelete(apq) removes the maximum element from apq and returns its value. Once pqmaxdelete has been applied to retrieve the largest element of an ascending priority queue, it can be applied again to retrieve the next largest element, and so on. (e.g.) A Stack can be viewed as a descending priority queue whose elements are ordered by time of insertion. b) Advantages of Dynamic Allocation over Static Allocation: (5M) 1) Size not fixed (Efficient memory utilization) * Dynamic data structure, which can grow or shrink depending on the data availability. * If more memory space is required, the required memory space can be allocated if available. * If certain portion of memory is not required, that memory space will be de-allocated so that some other application can use that freed memory space. 2) Data can be stored in non-contiguous block of memory: * No shortage of memory since non-contiguous blocks of memory can be used to store the data. 3) Insertion and deletion of nodes is easier: * A node can be inserted into the list and deleted from any position in the list easily by changing the links or pointers. (no need to shift the nodes) 4) Data structures such as stacks and queues can be implemented dynamically using linked list. 6) A. Function for searching an element in Circular SLL (5M) B. Insert an element before a key element using Singly Linked List (5M) 7) a. Full/complete binary tree: (5M) * Binary tree in which the number of nodes at any level i is 2 d Strictly binary tree: * If the outdegree of every node in a tree is either 0 or 2.

7 (i.e.) each node can have maximum of two children or empty left and right child. Almost Complete binary tree: * A binary tree is said to be almost complete binary tree if all levels are completely filled except possibly the last level and the last level has all keys as left as possible. Level of node: The level of any node u is given by the number of edges in the path from root node. Height of tree: The height of a tree is one more than the maximum level in the tree. The depth of a vertex v is the length of the simple path from the root to v. b. Representation of Binary Trees: (5M) * The binary trees can be represented using -- Sequential allocation (arrays) or -- Linked allocation (Linked list) Linked Allocation: * The memory for a node is allocated dynamically. * A node in linked allocation has 3 fields: info contains actual information llink contains address of left subtree rlink contains address of right subtree * A node can be represented as follows: struct node int info; struct node *llink; struct node *rlink; ; typedef struct node *NODE; Sequential Allocation (Arrays): * The nodes are numbered sequentially from 0. The node with position 0 is considered as the root node. * Given the position of the root node i, 2i+1 gives the position of the left child and 2i+2 gives the position of the right child. * If i is the position of the left child, i+1 gives the position of the right child.

8 8) Dequeue: Dequeue is a queue where insertions and deletions take place at both the ends. (2M) In Input restricted double ended queue, the insertion operation is performed at only one end and deletion operation is performed at both the ends. Functions for insert_rear, delete_front, delete_rear and display (8M)