In a binary tree, for every node the difference between the number of nodes in the left and right subtrees is at most 2. If the height of the tree is h > 0, then the minimum number of nodes in the tree is:

Consider the following C program segment

struct CellNode{ 
    struct CellNode *leftChild; 
    int element; 
    struct CellNode *rightChild; 
  };
 
int Dosomething (struct CellNode *ptr) { 
      int value = 0; 
      if (ptr ! = NULL) 
          { if (ptr - > leftChild ! = NULL) 
            value = 1 + DoSomething (ptr - > leftChild); 
          if (ptr - > rightChild ! = NULL) 
            value = max(value,1 + DoSomething (ptr - > rightChild)); 
          } 
      return (value); 
} 

The value returned by the function DoSomething when a pointer to the root of a non-empty tree is passed as argument is

Consider the label sequences obtained by the following pairs of traversals on a labeled binary tree. Which of these pairs identify a tree uniquely?
i) preorder and postorder
ii) inorder and postorder
iii) preorder and inorder
iv) level order and postorder

A program takes as input a balanced binary search tree with n leaf nodes and computes the value of a function g(x) for each node x. If the cost of computing g(x) is min{ no. of leaf-nodes in left-subtree of x, no. of leaf-nodes in right-subtree of x } then the worst-case time complexity of the program is