A scheme for storing binary trees in an array X is as follows. Indexing of X starts at 1 instead of 0. the root is stored at X[1]. For a node stored at X[i], the left child, if any, is stored in X[2i] and the right child, if any, in X[2i+1]. To be able to store any binary tree on n vertices the minimum size of X should be

The following function computes the value of ^mC_n correctly for all legal values m and n (m≥1,n≥0 and m>n)

int func(int m, int n) 
{ 
     if (E) return 1; 
     else return(func(m -1, n) + func(m - 1, n - 1)); 
} 

In the above function, which of the following is the correct expression for E?

An implementation of a queue Q, using two stacks S1 and S2, is given below:

void insert(Q, X){
  push(S1, X);
}

void delete(Q){
 if(stack - empty(S1)) then {
   print("Q is empty");
   return;
 }else while (!(stack - empty(S1))){
   X = pop(S1);
   push(S2, X);
 }
 X = pop(S2);
}

Let n insert and $$m( \le n)$$ delete operations be performed in an arbitrary order on an empty queue Q. Let x and y be the number of push and pop operations performed respectively in the process. Which one of the following is true for all m and n?

Which of the following relational query languages have the same expressive power?

I) Relational algebra
II) Tuple relational calculus restricted to safe expressions
III) Domain relational calculus restricted to safe expressions