Final Quiz-4 Time-1hr :30min UE:101-Algorithms & Programming

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1 Final Quiz-4 Time-1hr :30min UE:101-Algorithms & Programming Please read carefully the following instructions mentioned below: 1)In some questions you have to explain your answer (Overall Idea) and procedure on the Answersheet provided to you during exam. 2)You have to attempt all questions in Answer-sheet given to you during Exam. Do not write anything on Question Paper,for calculation you can use rough-sheet. 3) Partial marks will be given if you donot explain your response correctly. 4)Plagiarism or any cheating will lead to penalty of marks or decision as per invigilators. 5)Section A & B are 5 Marks each, Section C is 10 marks. 6)You have to return your Answer-sheet & Rough-sheet to invigilators. ******************************************************************************** Section-A(Programming) Q1(a) Assume a 3x3 array named myarray is initialized with value-'a','b','c','d','e','f', 'g','h','i'.assume all variables are declared appropriately.what will be the values of myarray after the following code runs on myarray?(explain) for(i=0;i<3;i++) for(j=0;j<3;j++) myarray[i][j]=myarray[j][i]; 'a','b','c','d','e','f','g','h','i' 'a','d','g','b','e','h','c','f','i' 'a','d','g','d','e','h','g','h','i' 'a','d','c','b','e','i','e','f','h' (V) None.

2 Q1(b) In the following declaration which statement exactly define 's'? struct node int i; float j; ; struct node *s[10]; An array,each element of which is a pointer to a structure of type node. A structure of 2 fields,each filed being a pointer to an array of 10 elements. A structure of 3 fields: an integer,a float, an array of 10 elements. An array, each element of which is a strucutre of type node. Q2.Consider the following recursive function: void fun1(int n) int i=0; if(n>1) fun1(n-1); for(i=0;i<n;i++) printf( * ); if we call fun1(4),then (a) How many times fun1() will be called,including the first call itself?(explain) (b) How many times will the character '*' be printed?(explain) Section B(Data-Structures) Q3(a).Which data structure represent a waiting line and limits insertions to be made at the back of the data structure and limits removals to be made from the front? Stack Queue Binary Tree None Q3(b).Which of the following statement about stack is incorrect? Stacks can be implemented using linked lists. Stacks are first in, first out (FIFO) data structures. New nodes can only be added to the top of the stack. The last node(at the bottom) of a stack has null(0) link.

3 Q4(a).Consider the following function to traverse a linked list. Which among the following statement is incorrect about given function(explain) void traverse(struct node *head) while(head-->next!= NULL) printf( %d,head-->data); head=head-->next; The function may crash when the linked list is empty. The function doesnot print the last node when the linked list is not empty. The function is implemented incorrectly because it changes the head. None. Q4(b)The following C function takes a singly linked list as input argument. It modifies the list by moving the last element to the front of the list and returns the modified list. Some part of the code left blank. typedef struct node int value; struct node* next; Node; Node* move_to_front(node* head) Node* p, *q; if((head==null) (head->next==null)) return head; q=null; p=head; while(p->next!= NULL) q=p; p=p->next; (blank-line) return head; Choose the correct alternative to replace the blank line q=null; p->next=head; head =p ; q->next=null; head =p; p->next = head; head=p; p->next=q; q->next=null; q->next=null; p->next=head; head=p;

4 Q5.Suppose that we have numbers between 1 and 1000 in a binary search tree and want to search for the number 363. which of the following sequences could not be the sequences of nodes examined?(explain) 2,252,401,398,330,344,397, ,220,911,244,898,258,362, ,202,911,240,912,245,363. 2,399,387,219,266,382,381,278,363. (V) 935,278,347,621,299,392,358,363. Section C(Algorithms) Q6(a)Calculate the time complexity(big-oh) of the following source code:(explain) main() for (i=1;i<=n^2;i++) for(j=1;j<=i^2;j++) for(k=1;k<=n^2;k=5*k) x=y+z; Q6(b)Check which of the following is/are True: where O is Big-Oh Notation only. (n+a)^m= O(n^m) where a&&m are +ve Constants. 2^(n+1) = O(2^n) 2^(2n) = O(2^n) None. Q7(a)Let P be a QuickSort Program to sort numbers in ascending order using the first element as pivot. Let t1 and t2 be the number of comparisons made by P for the inputs 1, 2, 3, 4, 5 and 4, 1, 5, 3, 2 respectively. Which one of the following holds?(explain) t1=5 t1<t2 t1>t2 t1=t2 Q7(b)Assume that the algorithms considered here sort the input sequences in ascending order. If the input is already in ascending order. A. Quicksort runs in Θ(n 2 ) time B. Bubblesort runs in Θ(n 2 ) time C. Mergesort runs in Θ(n) time D. Insertion sort runs in Θ(n) time which of the following are TRUE? (Explain with Example) A and B Only A and C Only B and D Only A and D Only

5 Q8(a)The Breadth First Search algorithm has been implemented using the queue data structure. One possible order of visiting the nodes of the following graph is(explain) MNOPQR NQMPOR QMNPRO QMNPOR Q8(b) Let G be a graph with n vertices and m edges. What is the tightest upper bound(big- Oh) on the running time on Depth First Search of G? Assume that the graph is represented using adjacency matrix(explain) O(n) O(m+n) O(n^2) (Iv) O(mn) Q9(a)Suppose we run Dijkstra s single source shortest-path algorithm on the following edge weighted directed graph with vertex P as the source. In what order do the nodes get included into the set of vertices for which the shortest path distances are finalized?(explain) P-Q-R-S-T-U P-Q-R-U-S-T P-Q-R-U-T-S P-Q-T-R-U-S

6 Q9(b)Let G be an undirected connected graph with distinct edge weight. Let emax be the edge with maximum weight and emin the edge with minimum weight. Which of the following statements is false? Every minimum spanning tree of G must contain emin. If emax is in a minimum spanning tree,then its removal must disconnect G. No minimun spanning tree contains emax. G has a unique minimum spanning tree. Q10(a)Consider the undirected graph below: Using Prim's algorithm to construct a minimum spanning tree starting with node A, which one of the following sequences of edges represents a possible order in which the edges would be added to construct the minimum spanning tree? (E, G), (C, F), (F, G), (A, D), (A, B), (A, C) (A, D), (A, B), (A, C), (C, F), (G, E), (F, G) (A, B), (A, D), (D, F), (F, G), (G, E), (F, C) (A, D), (A, B), (D, F), (F, C), (F, G), (G, E) Q10(b)Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? In adjacency list representation, space is saved for sparse graphs. DFS and BSF can be done in O( V + E ) time for adjacency list representation. These operations take O( V ^2) time in adjacency matrix representation. Here is V and E are number of vertices and edges. Adding a vertex in adjacency list representation is easier than adjacency matrix representation. All of the above. ********************************************************************************

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