The maximum number of binary trees that can be formed with three unlabeled nodes is:

Consider the following C program:

#include 
#define EOF -1 
     void push (int); /* push the argument on the stack */ 
     int pop (void); /* pop the top of the stack */ 
     void flagError (); 
     int main () { 
       int c, m, n, r; 
       while ((c = getchar ()) != EOF) { 
         if (isdigit (c) ) 
           push (c); 
         else if ((c == '+') || (c == '*')) { 
           m = pop (); 
           n = pop (); 
           r = (c == '+') ? n + m : n*m; 
           push (r); 
         } else if (c != ' ') 
           flagError (); 
       } 
       printf("% c", pop ()); 
    } 

What is the output of the program for the following input ? 5 2 * 3 3 2 + * +

Suppose you are given an implementation of a queue of integers. The operations that can be performed on the queue are:
i. isEmpty (Q) — returns true if the queue is empty, false otherwise.
ii. delete (Q) — deletes the element at the front of the queue and returns its value.
iii. insert (Q, i) — inserts the integer i at the rear of the queue.
Consider the following function:

void f (queue Q) { 
  int i ; 
  if (!isEmpty(Q)) { 
      i = delete(Q); 
      f(Q); 
      insert(Q, i); 
  } 
} 

What operation is performed by the above function f ?

Consider the B⁺ tree in the adjoining figure, where each node has at most two keys and three links.

Keys K 15 and then K 25 are inserted into this tree in that order. Exactly how many of the following nodes (disregarding the links) will be present in the tree after the two insertions?