An algorithm performs $${\left( {\log N} \right)^{1/2}}$$ find operations, N insert operations, $${\left( {\log N} \right)^{1/2}}$$ delete operations, and $${\left( {\log N} \right)^{1/2}}$$decrease-key operations on a set of data items with keys drawn from a linearly ordered set. For a delete operation, a pointer is provided to the record that must be deleted. For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?

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];
}

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