Consider the following C functions:

int f1(int n){
 if(n == 0 || n == 1){
    return n;
 }
 return (2 * f1(n - 1) + 3 * f1(n - 2));
}
int f2(int n){
 int i;
 int X[N], Y[N], Z[N];
 X[0] = Y[0] = Z[0] = 0;
 X[1] = 1; Y[1] = 2; Z[1] = 3;
 for(i = 2; i <= n; i++){
  X[i] = Y[i - 1] + Z[i - 2];
  Y[i] = 2 * X[i];
  Z[i] = 3 * X[i];
 }
 return X[n];
}

The returning time of f1(n) and f2(n) are

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?

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);
}