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:

In the following C function, let n $$ \ge $$ 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?

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?

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);
}