1
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Consider the process of inserting an element into a Max Heap, where the Max Heap is represented by an array. Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element, the number of comparisons performed is:
A
$$\Theta(\log_2n)$$
B
$$\Theta(\log_2\log_2n)$$
C
$$\Theta(n)$$
D
$$\Theta(n\log_2n)$$
2
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Consider the following C code segment:
int IsPrime(n){
 int i, n;
 for(i=2; i<=sqrt(n);i++){
  if(n % i == 0){
    printf("No prime\n"); return 0;
  }
  return 1;
 }
}
Let T(n) denote the number of times the for loop is executed by the program on input n. Which of the following is TRUE?
A
T(n) = O ($$\sqrt n $$) and T(n) = $$\Omega \,(\sqrt n )$$
B
T(n) = O ($$\sqrt n $$) and T(n) = $$\Omega \,(1)$$
C
T(n) = O (n) and T(n) = $$\Omega \,(\sqrt n )$$
D
None of the above
3
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
What is the time complexity of the following recursive function?
int DoSomething(int n){
 if(n <= 2)
     return 1;
 else
     return (floor(sqrt(n)) + n);
}
A
$$\Theta \,({n^2})$$
B
$$\Theta \,(n\,{\log _2}\,n)$$
C
$$\Theta \,({\log _2}\,n)$$
D
$$\Theta \,({\log _2}\,{\log _2}\,n)$$
4
GATE CSE 2007
MCQ (Single Correct Answer)
+1
-0.3
Which of the following sorting algorithms has the lowest worst-case complexity?
A
Merge sort
B
Bubble sort
C
Quick sort
D
Selection sort
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