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?

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 - function:

double foo(int n){
 int i;
 double sum;
 if(n == 0) return 1.0;
 sum = 0.0;
 for (i = 0; i < n; i++){
  sum += foo(i);
 }
 return sum;
}

The space complexity of the above function is:

Consider the following C - function:

double foo(int n){
 int i;
 double sum;
 if(n == 0) return 1.0;
 sum = 0.0;
 for (i = 0; i < n; i++){
  sum += foo(i);
 }
 return sum;
}

Suppose we modify the above function foo() and store the values of foo(i), $$0 \le i \le n$$, as and when they are computed. With this modification, the time complexity for function foo() is significantly reduced. The space complexity of the modified function would be: