### Welcome to Data Structure Quiz, Randomly Selected !!

Question 1. In a complete k-ary tree, every internal node has exactly k children. The number of leaves in such a tree with n internal nodes is:

nk

(n - 1) k + 1

n( k - 1) + 1

n(k - 1)

Question 2. 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

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 3. In the worst case, the number of comparisons needed to search a singly linked list of length n for a given element is

log 2 n

n/2

log 2 n - 1

n

Question 4. Consider the function f defined below.
```struct item
{
int data;
struct item * next;
};

int f(struct item *p)
{
return (
(p == NULL) ||
(p->next == NULL) ||
(( P->data <= p->next->data) && f(p->next))
);
}```

For a given linked list p, the function f returns 1 if and only if

the list is empty or has exactly one element

the elements in the list are sorted in non-decreasing order of data value

the elements in the list are sorted in non-increasing order of data value

not all elements in the list have the same data value.

Question 5. Consider the following algorithm for searching for a given number x in an unsorted array A[1..n] having n distinct values:
1) Choose an i uniformly at random from 1..n;
2) If A[i] = x then Stop else Goto 1;
Assuming that x is present in A, what is the expected number of comparisons made by the algorithm before it terminates?

n

n - 1

2n

n/2

Question 6. Consider the following C program that attempts to locate an element x in an array Y[] using binary search. The program is erroneous.
```f(int Y[10], int x) {
int i, j, k;
i = 0; j = 9;
do {
k = (i +  j) /2;
if( Y[k] < x) i = k; else j = k;
} while(Y[k] != x && i < j);
if(Y[k] == x) printf ("x is in the array") ;
else printf ("x is not in the array") ;
}```

On which of the following contents of Y and x does the program fail?

Y is [1 2 3 4 5 6 7 8 9 10] and x < 10

Y is [1 3 5 7 9 11 13 15 17 19] and x < 1

Y is [2 2 2 2 2 2 2 2 2 2] and x > 2

Y is [2 4 6 8 10 12 14 16 18 20] and 2 > ?x < 20 and x is even

Question 7. Consider a hash table of size seven, with starting index zero, and a hash function (3x + 4)mod7. Assuming the hash table is initially empty, which of the following is the contents of the table when the sequence 1, 3, 8, 10 is inserted into the table using closed hashing? Note that '_' denotes an empty location in the table.

8, _, _, _, _, _, 10

1, 8, 10, _, _, _, 3

1, _, _, _, _, _,3

1, 10, 8, _, _, _, 3

Question 8. A set X can be represented by an array x[n] as follows:

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 9. Let S be a stack of size n >= 1. Starting with the empty stack, suppose we push the first n natural numbers in sequence, and then perform n pop operations. Assume that Push and Pop operation take X seconds each, and Y seconds elapse between the end of one such stack operation and the start of the next operation. For m >= 1, define the stack-life of m as the time elapsed from the end of Push(m) to the start of the pop operation that removes m from S. The average stack-life of an element of this stack is

n(X + Y)

3Y + 2X

n(X + Y)-X

Y + 2X

Question 10. Consider a binary max-heap implemented using an array. Which one of the following array represents a binary max-heap?

25,12,16,13,10,8,14

25,14,13,16,10,8,12

25,14,16,13,10,8,12

25,14,12,13,10,8,16