Welcome to Data Structure Quiz, Advanced Level !!

Question 1. An undirected graph G(V, E) contains n ( n > 2 ) nodes named v1 , v2 , .. vn. Two nodes vi , vj are connected if and only if 0 < |i - j| <= 2. Each edge (vi, vj ) is assigned a weight i + j. A sample graph with n = 4 is shown below
Graph
What will be the cost of the minimum spanning tree (MST) of such a graph with n nodes?

1/12(11n^2 - 5n)

n^2 - n + 1

6n - 11

2n + 1

Question 2. Consider the following recurrence:
recurrence
Which one of the following is true?

T(n) = Theta(loglogn)

T(n) = Theta(logn)

T(n) = Theta(sqrt(n))

T(n) = Theta(n)

Question 3. In the following C function, let n >= m.
 
int gcd(n,m) 
{ 
      if (n%m ==0) return m;  
      n = n%m; 
      return gcd(m,n); 
} 

How many recursive calls are made by this function?

Theta(logn)

Omega(n)

Theta(loglogn)

Theta(sqrt(n))

Question 4. An undirected graph G has n nodes. Its adjacency matrix is given by an n * n square matrix whose (i) diagonal elements are 0's and (ii) non-diagonal elements are 1's. which one of the following is TRUE?

Graph G has no minimum spanning tree (MST)

Graph G has a unique MST of cost n-1

Graph G has multiple distinct MSTs, each of cost n-1

Graph G has multiple spanning trees of different costs

Question 5. A single array A[1..MAXSIZE] is used to implement two stacks. The two stacks grow from opposite ends of the array. Variables top1 and top2 (topl < top 2) point to the location of the topmost element in each of the stacks. If the space is to be used efficiently, the condition for "stack full" is

(top1 = MAXSIZE/2) and (top2 = MAXSIZE/2 + 1)

top1 + top2 = MAXSIZE

(top1= MAXSIZE/2) or (top2 = MAXSIZE)

top1= top2 -1

Question 6. A Priority-Queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is given below:
    10, 8, 5, 3, 2
Two new elements "1" and "7" are inserted in the heap in that order. The level-order traversal of the heap after the insertion of the elements is:

10, 8, 7, 5, 3, 2, 1

10, 8, 7, 2, 3, 1, 5

10, 8, 7, 1, 2, 3, 5

10, 8, 7, 3, 2, 1, 5

Question 7. A set X can be represented by an array x[n] as follows:
array pic
Consider the following algorithm in which x,y and z are Boolean arrays of size n:
algorithm zzz(x[] , y[], z []) 
{ 
    int i; 
    for (i=O; i<n;   ++i) 
    z[i] = (x[i] ^ ~y[i]) U (~x[i] ^ y[i]) 
}

The set Z computed by the algorithm is:

(X Intersection Y)

(X Union Y)

(X-Y) Intersection (Y-X)

(X-Y) Union (Y-X)

Question 8. A hash table of length 10 uses open addressing with hash function h(k)=k mod 10, and linear probing. After inserting 6 values into an empty hash table, the table is as shown below.
hash_table
Which one of the following choices gives a possible order in which the key values could have been inserted in the table?

46, 42, 34, 52, 23, 33

34, 42, 23, 52, 33, 46

46, 34, 42, 23, 52, 33

42, 46, 33, 23, 34, 52

Question 9. An array of n numbers is given, where n is an even number. The maximum as well as the minimum of these n numbers needs to be determined. Which of the following is TRUE about the number of comparisons needed?

At least 2n - c comparisons, for some constant c, are needed.

At most 1.5n - 2 comparisons are needed.

At least nLog2n comparisons are needed.

none of the above

Question 10. A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be represented by an array as follows: The root is stored in the first location, a[0], nodes in the next level, from left to right, is stored from a[1] to a[3]. The nodes from the second level of the tree from left to right are stored from a[4] location onward. An item x can be inserted into a 3-ary heap containing n items by placing x in the location a[n] and pushing it up the tree to satisfy the heap property.
Which one of the following is a valid sequence of elements in an array representing 3-ary max heap?

1, 3, 5, 6, 8, 9

9, 6, 3, 1, 8, 5

9, 3, 6, 8, 5, 1

9, 5, 6, 8, 3, 1