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Binary Trees: Properties and Traversals PYQs for GATE DA

Solve 3+ Binary Trees: Properties and Traversals previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

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Question 1

2026 PYQ

Level 3: Exam Standard

You are given the following Pre-order and In-order traversals of a Binary Tree T with nodes E, F, G, P, Q, R, S. Pre-order: P Q S E R F G In-order: S Q E P F R G Which of the following statements is/are true about the Binary Tree T?

Question 2

2024 PYQ

Level 3: Exam Standard

Let H, I, L, and N represent height, number of internal nodes, number of leaf nodes, and the total number of nodes respectively in a rooted binary tree. Which of the following statements is/are always TRUE?

Question 3

2024 PYQ

Level 3: Exam Standard

Consider the following tree traversals on a full binary tree: i Preorder ii Inorder iii Postorder Which of the following traversal options is/are sufficient to uniquely reconstruct the full binary tree?

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Binary Trees: Properties and Traversals PYQs for GATE DA

Solve 3+ Binary Trees: Properties and Traversals previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

Chapter Roadmap: Binary Trees

Master the structural and navigational foundations of the most important tree data structure.

Your Learning Journey

1. Binary Tree Traversals and Reconstruction High Importance

Master pre-order, in-order, and post-order traversals.
Learn to uniquely reconstruct a tree from traversal sequences.
Understand the Full Binary Tree exception for pre-order and post-order.

2. Binary Tree Structural Properties Moderate Importance

Explore mathematical relationships between height, internal nodes, and leaves.
Derive bounds on the number of nodes for a given height.
Solve equations relating different tree parameters.

Binary Tree Traversals and Reconstruction

Master the art of rebuilding a tree from its shadows.

Chapter Context: Binary Trees: Properties and Traversals

What you will learn here

The core depth-first traversals (Pre-order, In-order, Post-order).
The mandatory role of In-order traversal in resolving left-right ambiguity.
Step-by-step methods to reconstruct a tree.
The Full Binary Tree exception for Pre-order and Post-order.

Binary Trees: Properties and Traversals: Solved Questions with Step-by-Step Explanations (3 Problems)

Question 1 · Programming, Data Structures and Algorithms · 2026 MSQ

You are given the following Pre-order and In-order traversals of a Binary Tree T with nodes E, F, G, P, Q, R, S.
Pre-order: P Q S E R F G
In-order: S Q E P F R G
Which of the following statements is/are true about the Binary Tree T?

A.
Node P is the root of T
B. The Post-order traversal of T is:
S E Q F G R P
C.
Node Q has only one child
D.
The left subtree of node R contains the node G

Correct Answer:

["A","B"]

Step-by-Step Solution

Insight: Reconstruct the tree using the standard Pre-order and In-order split method.

Exam route: Root is P. Left In-order has 3 elements, Right has 3. Split Pre-order accordingly. Build left and right subtrees. Check options.

Learning route:

Step 1: Root is the first element in Pre-order: P.

Step 2: Find P in In-order. Left of P is S, Q, E (size 3). Right of P is F, R, G (size 3).

Step 3: Split remaining Pre-order (Q, S, E, R, F, G) into Left Pre-order (Q, S, E) and Right Pre-order (R, F, G).

Step 4: Left subtree: Pre (Q, S, E), In (S, Q, E). Root is Q. Left In is S, Right In is E. So Q has left child S, right child E.

Step 5: Right subtree: Pre (R, F, G), In (F, R, G). Root is R. Left In is F, Right In is G. So R has left child F, right child G.

Step 6: Evaluate options.

A) P is root. (True)

B) Post-order is Left Post + Right Post + Root. Left Post: S, E, Q. Right Post: F, G, R. Total: S, E, Q, F, G, R, P. (True)

C) Q has two children (S and E). (False)

D) G is in the right subtree of R. (False)

Question 2 · Programming, Data Structures and Algorithms · 2024 MSQ

Let

H, I, L,

and

N

represent height, number of internal nodes, number of leaf nodes,
and the total number of nodes respectively in a rooted binary tree.
Which of the following statements is/are always TRUE?

A.
$L \leq I + 1$
B.
$H + 1 \leq N \leq 2^{H + 1} - 1$
C.
$H \leq I \leq 2^{H} - 1$
D.
$H \leq L \leq 2^{H - 1}$

Correct Answer:

["A","B","C"]

Step-by-Step Solution

Insight: Use the fundamental edge equation and height bounds to test each inequality.

Exam route: Test each option with a skewed tree (min N, max H) and a perfect tree (max N, min H) for a given H.

Learning route:

Step 1: Recall the fundamental relations: $N = L + I$ , $L = n_{2} + 1$ , $I = n_{1} + n_{2}$ .

Step 2: Check A: $L - I = (n_{2} + 1) - (n_{1} + n_{2}) = 1 - n_{1}$ . Since $n_{1} \geq 0$ , $L - I \leq 1 ⟹ L \leq I + 1$ . Always TRUE.

Step 3: Check B: For a given height $H$ (edges), the minimum nodes occur in a skewed tree (a straight line), where $N = H + 1$ . The maximum nodes occur in a perfect binary tree, where $N = 2^{H + 1} - 1$ . Thus, $H + 1 \leq N \leq 2^{H + 1} - 1$ . Always TRUE.

Step 4: Check C: The minimum internal nodes for height $H$ occurs in a skewed tree, where the longest path has $H$ edges, meaning $H$ internal nodes. So $I \geq H$ . The maximum internal nodes occur in a perfect tree, where $I = 2^{H} - 1$ . Thus, $H \leq I \leq 2^{H} - 1$ . Always TRUE.

Step 5: Check D: For $H = 0$ (single node), $L = 1$ . The upper bound gives $2^{0 - 1} = 0.5$ . Since $1 \leq 0.5$ is false, D is FALSE.

Step 6: Correct options are A, B, C.

Question 3 · Programming, Data Structures and Algorithms · 2024 MSQ

Consider the following tree traversals on a full binary tree:

i

Preorder

ii

Inorder

iii

Postorder
Which of the following traversal options is/are sufficient to uniquely reconstruct
the full binary tree?

A.
$i$ and $ii$
B.
$ii$ and $iii$
C.
$i$ and $iii$
D.
$ii$ only

Correct Answer:

["A","B","C"]

Step-by-Step Solution

Insight: In-order is mandatory for general binary trees, but for Full Binary Trees, Pre-order and Post-order are also sufficient because no node has exactly one child.

Exam route: Pre+In and In+Post are always sufficient. Pre+Post is sufficient for Full Binary Trees. In alone is never sufficient.

Learning route:

Step 1: Recall that to uniquely reconstruct a general binary tree, In-order is mandatory because Pre-order and Post-order cannot distinguish left/right if a node has only one child. Thus, (i)+(ii) and (ii)+(iii) are always sufficient.

Step 2: For a Full Binary Tree, every node has either 0 or 2 children. There are no nodes with exactly one child.

Step 3: Because there are no single-child nodes, the ambiguity in Pre-order and Post-order disappears. The second element in Pre-order is always the root of the left subtree, which allows a unique split of the Post-order array. Thus, (i)+(iii) is sufficient.

Step 4: In-order alone provides no information about the root. Thus, (ii) only is insufficient.

Step 5: Therefore, options A, B, and C are correct.

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Binary Trees: Properties and Traversals PYQs for GATE DA

Chapter Roadmap: Binary Trees

Chapter Roadmap: Binary Trees

Your Learning Journey

Binary Tree Traversals and Reconstruction

Binary Tree Traversals and Reconstruction

What you will learn here

Binary Trees: Properties and Traversals: Solved Questions with Step-by-Step Explanations (3 Problems)

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

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