GATE CS 2020

Question 61

What is the worst case time complexity of inserting n² elements into an AVL-tree with n elements initially ?

• Θ(n⁴)
• Θ(n²)
• Θ(n² log n)
• Θ(n³)

Question 62

Consider a graph G=(V, E), where V = { v1,v2,…,v100 }, E={ (vi, vj) ∣ 1≤ i < j ≤ 100} and weight of the edge (vi, vj)  is ∣i–j∣. The weight of minimum spanning tree of G is ________. Note - This question was Numerical Type.

• 99

• 100

• 98

• 101

Question 63

For parameters a and b, both of which are ω(1), T(n)=T(n^1/a)+1, and T(b)=1. Then T(n) is

• Θ(log_alog_bn)
• Θ(log_abn)
• Θ(log_blog_an)
• Θ(log₂log₂n)

Question 64

The figure below shows an annular ring with outer and inner as b and a, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum n number of circles can be painted, then the unpainted area available in annular space is _________ .

• π[(b²−a²)−(n/4)(b−a)²]
• π[(b²−a²)−n(b−a)²]
• π[(b²−a²)+(n/4)(b−a)²]
• π[(b²−a²)+n(b−a)²]

Question 65

Consider the following C functions.

C

int fun1(int n) {
    static int i= 0;
    if (n > 0) {
       ++i;
      fun1(n-1);
   }
  return (i);
}
int fun2(int n) {
   static int i= 0;
   if (n>0) {
      i = i+ fun1 (n) ;
      fun2(n-1) ;
  }
return (i);
}

The return value of fun2(5) is ________ . Note - This question was Numerical Type.

• 55
• 45
• 50
• 52