Consider the following C function.

int fun1 (int n) { 
     int i, j, k, p, q = 0; 
     for (i = 1; i < n; ++i) 
     {
        p = 0; 
       for (j = n; j > 1; j = j/2) 
           ++p;  
       for (k = 1; k < p; k = k * 2) 
           ++q;
     } 
     return q;
}

Which one of the following most closely approximates the return value of the function fun1?

The number of elements that can be stored in $$\Theta (\log n)$$ time using heap sort is

Which of the given options provides the increasing order of asymptotic Complexity of functions f₁, f₂, f₃ and f₄?
f₁ = 2ⁿ f₂ = n^3/2
f₃(n) = $$n\,\log _2^n$$
f₄ (n) = n ^log₂n

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];
}

f1(8) and f2(8) return the values