How many distinct BSTs can be constructed with 3 distinct keys?

You are given the postorder traversal, P, of a binary search tree on the n elements 1, 2,..........., n. You have to determine the unique binary search tree that has P as its postorder traversal. What is the time complexity of the most efficient algorithm for doing this?

A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. If L = 41, and I = 10, what is the value of n?

Consider the following C program segment where CellNode represents a node in a binary tree:

struct CellNode 
{ 
     struct CellNOde *leftChild; 
     int element; 
     struct CellNode *rightChild; 
}; 

int GetValue(struct CellNode *ptr) 
{ 
     int value = 0; 
     if (ptr != NULL) 
     { 
       if ((ptr->leftChild == NULL) && 
        (ptr->rightChild == NULL)) 
       value = 1; 
       else 
         value = value + GetValue(ptr->leftChild) 
             + GetValue(ptr->rightChild); 
     } 
     return(value); 
} 

The value returned by GetValue() when a pointer to the root of a binary tree is passed as its argument is: