Consider the following statements:

I. The smallest element in a max-heap is always at a leaf node.
II. The second largest element in a max-heap is always a child of the root node.
III. A max-heap can be constructed from a binary search tree in Θ(n) time.
IV. A binary search tree can be constructed from a max-heap in Θ(n) time.

Which of the above statements are TRUE?

Let T be a full binary tree with 8 leaves. (A full binary tree has every level full). Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _____.

Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:

The pre-order traversal of a binary search tree is given by 12, 8, 6, 2, 7, 9, 10, 16, 15, 19, 17, 20. Then the post-order traversal of this tree is:

Consider the following New-order strategy for traversing a binary tree:

• Visit the root;
• Visit the right subtree using New-order;
• Visit the left subtree using New-order;

The New-order traversal of the expression tree corresponding to the reverse polish expression 3 4 * 5 - 2 ˆ 6 7 * 1 + - is given by:

A binary tree T has 20 leaves. The number of nodes in T having two children is _________.

Consider a binary tree T that has 200 leaf nodes. Then, the number of nodes in T that have exactly two children are ____.

The height of a tree is defined as the number of edges on the longest path in the tree. The function shown in the pseudocode below is invoked as height (root) to compute the height of a binary tree rooted at the tree pointer root.

The appropriate expression for the two boxes B1 and B2 are

We are given a set of n distinct elements and an unlabeled binary tree with n nodes. In how many ways can we populate the tree with the given set so that it becomes a binary search tree?

In a binary tree with n nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree that have exactly one child?

The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height h is:

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

The inorder and preorder traversal of a binary tree are d b e a f c g and a b d e c f g, respectively. The postorder traversal of the binary tree is:

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:

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.

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 

Consider the following C program segment

struct CellNode
{
  struct CelINode *leftchild;
  int element;
  struct CelINode *rightChild;
}
 
int Dosomething(struct CelINode *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

Draw all binary trees having exactly three nodes labeled A, B and C on which Preorder traversal gives the sequence C, B, A.

Consider the following nested representation of binary trees: (X Y Z) indicates Y and Z are the left and right sub stress, respectively, of node X. Note that Y and Z may be NULL, or further nested. Which of the following represents a valid binary tree?

Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a postorder, inorder and preorder traversal. Respectively, of a complete binary tree. Which of the following is always tree?

Which of the following statements is false?

A binary search tree contains the value 1, 2, 3, 4, 5, 6, 7, 8. The tree is traversed in pre-order and the values are printed out. Which of the following sequences is a valid output?

In the balanced binary tree in the below figure, how many nodes will become unbalanced when a node is inserted as a child of the node “g”?

Which of the following sequences denotes the post order traversal sequence of the tree of question 14?

A binary search tree is generated by inserting in order the following integers:

 50, 15, 62, 5, 20, 58, 91, 3, 8, 37, 60, 24  

The number of nodes in the left subtree and right subtree of the root respectively is

The preorder traversal of a binary search tree is 15, 10, 12, 11, 20, 18, 16, 19.

Which one of the following is the postorder traversal of the tree?

What is the worst case time complexity of inserting n² elements into an AVL-tree with n elements initially?

In a balanced binary search tree with n elements, what is the worst case time complexity of reporting all elements in range [a,b]? Assume that the number of reported elements is k.

The weighted external path length of the binary tree in figure is _____

Choose the correct alternatives (More than one may be correct). The number of rooted binary trees with n nodes is,

Choose the correct alternatives (More than one may be correct).

It is possible to construct a binary tree uniquely whose pre-order and post-order traversals are given?

If the number of leaves in a tree is not a power of 2, then the tree is not a binary tree.

The following three are known to be the preorder, inorder and postorder sequences of a binary tree. But it is not known which is which.

MBCAFHPYK
KAMCBYPFH
MABCKYFPH

A Binary Search Tree (BST) stores values in the range 37 to 573. Consider the following sequence of keys.

I. 81, 537, 102, 439, 285, 376, 305
II. 52, 97, 121, 195, 242, 381, 472
III. 142, 248, 520, 386, 345, 270, 307
IV. 550, 149, 507, 395, 463, 402, 270

Suppose the BST has been unsuccessfully searched for key 273. Which all of the above sequences list nodes in the order in which we could have encountered them in the search?

A Binary Search Tree (BST) stores values in the range 37 to 573. Consider the following sequence of keys.

 I. 81, 537, 102, 439, 285, 376, 305
II. 52, 97, 121, 195, 242, 381, 472
III. 142, 248, 520, 386, 345, 270, 307
IV. 550, 149, 507, 395, 463, 402, 270

Which of the following statements is TRUE?

A Binary Search Tree (BST) stores values in the range 37 to 573. Consider the following sequence of keys.

 I. 81, 537, 102, 439, 285, 376, 305
II. 52, 97, 121, 195, 242, 381, 472
III. 142, 248, 520, 386, 345, 270, 307
IV. 550, 149, 507, 395, 463, 402, 270

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

A binary tree with n > 1 nodes has n₁, n₂ and n₃ nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors. n₃ can be expressed as

A binary tree with n > 1 nodes has n₁, n₂ and n₃ nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors. Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?

When searching for the key value 60 in a binary search tree, nodes containing the key values 10, 20, 40, 50, 70 80, 90 are traversed, not necessarily in the order given. How many different orders are possible in which these key values can occur on the search path from the root to the node containing the value 60?

In a binary tree, the number of internal nodes of degree 1 is 5, and the number of internal nodes of degree 2 is 10. The number of leaf nodes in the binary tree is

Suppose that we have numbers between 1 and 100 in a binary search tree and want to search for the number 55. Which of the following sequences CANNOT be the sequence of nodes examined?

An array X of n distinct integers is interpreted as a complete binary tree. The index of the first element of the array is 0. The index of the parent of element X[i],i≠0 is?

An array X of n distinct integers is interpreted as a complete binary tree. The index of the first element of the array is 0. If only the root node does not satisfy the heap property, the algorithm to convert the complete binary tree into a heap has the best asymptotic time complexity of

An array X of n distinct integers is interpreted as a complete binary tree. The index of the first element of the array is 0. If the root node is at level 0, the level of element X[i], i ≠ 0, is

An array of integers of size n can be converted into a heap by adjusting the heaps rooted at each internal node of the complete binary tree starting at the node ⌊(n - 1) /2⌋, and doing this adjustment up to the root node (root node is at index 0) in the order ⌊(n - 1)/2⌋, ⌊(n - 3)/2⌋, ....., 0. The time required to construct a heap in this manner is

Which of the following data structures is used in level order traversal of a binary tree?

In a full binary tree of height 10, the number of nodes with degree 0,1, and 2 will be ____,____ and ____ respectively.

Note: Consider height of a tree as the number of nodes in the longest path from root to any leaf node

Consider an AVL tree constructed by inserting the elements 18, 10, 5, 3, 27, 7, 35, 43, 32 one by one. Which of the following options give the number of comparisons to search the key value 45 in this AVL tree?

A full binary tree with n leaves contains

The maximum height of a binary tree with 'n' nodes is ____

Consider the following two statements.
1. A binary tree T is full if each node is either a leaf or possesses exactly two child nodes.
2. A binary tree with n levels is complete if all levels except possibly the last are completely full, and the last level has all its nodes to the left side.
Which statement is/are TRUE?

In ____balance factor of a node is the difference between left subtree and right subtree.

The following is the sequence of insertion in a binary search tree.

45, 65, 35, 40, 33, 70, 60, 75, 69 

Consider the following Inorder and Preorder traversal of a tree

Inorder- D B E F A G H C
Pre Order- A B D E F C G H 

Which one from the following is a true statement about Binary trees (BST)?