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# Most Common Binary Tree Interview Questions & Answers [For Freshers & Experienced]

Updated on 04 July, 2024

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## Introduction

Data structures are one of the most fundamental concepts in object-oriented programming. To explain it simply, a data structure is a particular way of organizing data in a computer so that it can be effectively processed. There are several data structures like stacks, queues, and trees that have their own unique properties.

Trees allow us to organize data in a hierarchical fashion. Such a data structure is very different from linear data structures like linked lists or arrays. A tree consists of nodes that carry information.

A binary tree is a special type of tree that can only have up to two children. This means that a particular node in a binary tree can have no child, one child, or two children but not more. A binary tree is an important data structure that can enable us to solve difficult problems and build complex codes.

If you are applying for a job as a Java Developer or a software engineer, your interview may contain several questions revolving around this concept. Often, candidates find it hard to answer questions based on binary trees, binary search trees, and related programs. In this article, we will explore some of the most frequently asked interview questions related to binary trees. This article will help you better understand the concept and prepare you so that you can land your dream job!

## What is a Binary Tree Interview Question?

A common binary tree interview question involves tasks such as traversing the tree (pre-order, in-order, post-order), finding the height of the tree, checking if the tree is balanced, finding the lowest common ancestor (LCA) of two nodes, or implementing specific operations like insertion, deletion, or searching for a node based on certain criteria.

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## Top Binary Tree Interview Questions & Answers

The following section contains a catalog of questions and their expected answers based on the binary tree concept.

1) What is a leaf node?

Any node in a binary tree or a tree that does not have any children is called a leaf node.

2) What is a root node?

The first node or the top node in a tree is called the root node.

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3) How do you find the lowest common ancestor (LCA) of a binary tree in Java?

Let us consider two nodes n1 and n2 that are part of a binary tree.

The lowest common ancestor (LCA) of n1 and n2 is the shared ancestor of n1 and n2 that is located farthest from the root.

You can follow the following method to find the LCA.

1. a) Find a path from the root node to n1 and store it in an array.
2. b) Find a path from the root node to n2 and store it in an array.
3. c) Traverse both paths until the value is the same in both the arrays.

4) How do you check if a given binary tree is a subtree of another binary tree?

Consider we have a binary tree T. We now want to check if a binary tree S is a subtree of T.

To do this, first, try to check if you find a node in T that is also in S.

Once you find this common node, check if the following nodes are also a part of S.

If yes, we can safely say that S is a subtree of T.

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5) How do you find the distance between two nodes in a binary tree?

Consider two nodes n1 and n2 that are part of a binary tree.

The distance between n1 and n2 is equal to the minimum number of edges that need to be traversed to reach from one node to the other.

It is important to note that you traverse the shortest distance between the nodes.

6) What is a binary search tree?

A binary search tree (BST) is a special type of binary tree in which each internal node contains a key. For a binary search tree, the rule is:

1. a) A node can have a key that is greater than all the keys in the node’s left subtree.
2. b) A node can have a key that is smaller than all the keys in the node’s right subtree.

Thus, if n1 is a node that has a key 8, then every node in the left subtree of n1 will contain keys lesser than 8, and every node in the right subtree of n1 will contain keys greater than 8.

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7) What is a self-balanced tree?

Self-balanced binary search trees automatically keep their height as small as possible when operations like insertion and deletion take place.

For a BST to be self-balanced, it is important that it consistently follows the rules of BST so that the left subtree has lower-valued keys while the right subtree has high valued keys.

This is done using two operations:

– Left rotation

– Right rotation

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8) What is an AVL tree?

The AVL tree is named after its inventors: Adelson, Velski, and Landis. An AVL tree is a self-balancing binary tree that checks the height of its left subtree and right subtree and assures that the difference is not more than 1. This difference is called the balance factor

Thus, BalanceFactor = height (Left subtree) – height (Right subtree)

If the balance factor is more than 1, the tree is balanced using some of the following techniques:

– Left rotation

– Right rotation

– Left-Right rotation

– Right-Right rotation

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9) How do you convert a binary tree into a binary search tree in Java?

The main difference between a binary tree and a binary search tree is that the BST follows the left subtree should have lower key values and the right subtree should have higher key values rule. This can be done using a series of traversal techniques as follows:

1. Create a temporary array that stores the inorder traversal of the tree
2. Sort the temporary array. You can use any sorting algorithm here.
3. Again perform an inorder traversal on the tree.
4. Copy the array elements one by one to each tree node.

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10) How do you delete a node from a binary search tree in Java?

The deletion operation for a BST can be tricky since its properties need to be preserved post the operation. Here’s a look at all three possible cases:

1. Node to be deleted is a leaf node.
Simply remove the node.
2. Node to be removed has one child.

In this case, copy the child to the node and delete the child.

1. Node to be removed has two children.

In this case, find the inorder successor of the node. You can then copy its content to the node and delete the inorder successor.

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11) What is the Red-Black tree data structure?

The Red-Black tree is a special type of self-balancing tree that has the following properties:

1. Each node has a colour either red or black.
2. The root is always black.
3. A red node cannot have a red parent or red child.
4. Every path from the root node to a NULL node has the same number of black nodes.

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12) How do you find if two trees are identical?

Two binary trees are identical if they have the same data and arrangement. This can be done by traversing both trees and comparing their data and arrangements.

Here’s the algorithm that can enable us to do this:

1. Check data of root node ( tree1 data ==tree2 data)
2. Check left subtree recursively. call sameTree( tree1-> left subtree, tree2-> left subtree)
3. Similarly, check right subtree
4. if a,b,c are true, return1

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13) What are the types of traversal of binary trees?

It is one of the common tree questions. The traversal of a binary tree has three types. They are discussed below. i) Inorder tree traversal: In this type, the left subtree is visited first, then the root, and lastly, the right subtree. Remember that any node may be a subtree in itself. The output of this type in sequence generates sorted key values in ascending order. ii) Preorder tree traversal: In this type, the root node is first visited, and then the left subtree is visited. Finally, the right subtree is visited. iii)Postorder tree traversal: The root node is visited at the end, and therefore its name is “Postorder tree traversal. The traversal order is the left subtree, the right subtree, and then the root node.

14) How are binary trees represented in memory?

You must prepare for such binary tree questions to crack your interview. A small and nearly complete binary tree can be stored in a linear array.  The linear array is used because a linear array’s search process is costly. You have to consider the nodes’ positional indexes to store the binary tree in a linear array. This indexing should be considered beginning with 1 from the root node and moving from left to right as you go move from one level to another. The binary trees are widely used to store decision trees that represent decisions i.e. true or false, yes or no, or 0 or 1. They are often used in gaming applications wherein a player is allowed to take only two moves.

15) What are the common applications of binary trees?

It is one of the trendiest tree questions. Binary trees are used for classification purposes. A decision tree represents a supervised machine-learning algorithm. The binary tree data structure is used to imitate the decision-making process. Usually, a decision tree starts with a root node. The internal nodes are dataset features or conditions. The branches represent decision rules whereas the leave nodes show the decision’s outcome. Another major application of binary trees is in expression evaluation. The binary tree’s leaves are the operands whereas the internal nodes signify the operators. Binary trees are also used in database indexing for sorting data for easy searching, insertion, and deletion.

16) How are binary trees used for sorting?

Such binary tree questions denote the versatility of binary trees. Binary search trees are variants of binary trees. They used to implement sorting algorithms to order items. Basically, a binary search tree is a sorted or ordered binary tree in which the value in the left child is lesser than that in the parent node. The values in the right node are more than that in the parent node. The items to be ordered are first inserted into a binary search tree to fulfill a sorting process. The tree is traversed via the in-order traversal to access the sorted items.

17) How are binary trees used for data compression?

It is one of the intermediate-level tree questions. Huffman coding is used to create a binary tree that can compress data. Data compression encodes data to use fewer bits. Firstly, Huffman coding builds a binary tree based on the text to compress. It then inserts the characters’ encodings in the nodes depending on their frequency within the text. A character’s encoding is achieved by traversing the tree from its root to the node. Recurrently occurring characters will boast a shorter path than the less occurring characters. The purpose is to decrease the number of bits for frequent characters and ascertain maximum data compression.

18) How to handle duplicate nodes in a binary search tree?

It is one of the top 50 tree interview questions because it specifies your ability to handle binary trees. You can store the inorder traversal of a specific binary tree in an array to handle duplicate nodes. Subsequently, you need to check whether the array includes any duplicates. You can prevent the use of an array and solve this issue in O(n) time. Hashing is used for the same. You can traverse the given tree, for each node to check if it already occurs in the hash table. The result is true (duplicate found) if it exists, else you insert it into the hash table.

19) Can binary search be used for the linked list?

You can prepare for such top 50 tree interview questions to easily crack your interviews. Binary search is allowed on the linked list if you have an ordered list and you know the number of elements in a list.  You can access a single element at a time via a pointer to that node when sorting the list. The pointer is either to a previous node or the next node. Consequently, it increases the traversal steps for each element in the linked list to search for the middle element.  This process makes it inefficient. On the other hand, the binary search on an array is efficient and fast. You can access the array’s middle by command “array[middle]”. You can’t do the same with a linked list because you have to write your algorithm to obtain the middle node’s value of a linked list.

20) Why binary tree is a recursive data structure?

Preparing for the frequently asked binary tree questions increases your chances of getting hired. A recursive data structure is partially composed of smaller instances of the same data structure. A binary tree is a recursive data structure because it can be correspondingly defined in two ways. They are either using an empty tree or a node pointing to two binary trees (its left child and its right child). The binary tree’s recursive relationships that are used to define a structure offer a natural model for working any recursive algorithm on the data structure.

21) What is the difference between a general tree and a binary tree?

These types of top 50 tree interview questions test the candidates’ in-depth knowledge of binary trees. In a general tree, every node can have either zero or multiple child nodes. It can’t be empty. There is no upper limit on a node’s degree. The topmost node is known as the root node. Several subtrees exist in a general tree.

A binary tree is the specific version of the General tree. In a binary tree, every node can have a maximum of two nodes. There is a limitation on a node’s degree. This is because the nodes in a binary tree can have a maximum of two child nodes. Two subtrees exist i.e. left-subtree and right-subtree. The binary tree can be empty, unlike the general tree. Contrasting the general tree, a binary tree’s subtree is ordered because its nodes can be ordered based on specific criteria.

22) How can the balance of a binary tree be determined?

If there is a maximum one difference in height between the left and right subtrees of a node, the binary tree is said to be balanced. You can over time determine the height of the left and right subtrees for each node in a binary tree to see if it is balanced. The tree is not balanced if there is ever a height differential greater than one.

23) Describe the binary tree traversal process by utilizing the breadth-first search (BFS) method.

For binary trees, a level-order traversal approach is called breadth-first search. Before going to the next level, BFS investigates every node at the current level, starting at the root. It tracks nodes using a queue data structure.

24) How can the maximum element be found In a binary tree?

In order to determine the maximum element in a binary tree, follow the maximum value you have encountered thus far while traversing the tree in a depth-first way (e.g., in-order, pre-order, or post-order).

25) Describe what threaded binary trees are.

A threaded binary tree is a binary tree in which some pointers are used to move across the tree without the requirement for recursion or a stack. The efficient traversal of the tree is made possible by these pointers, often referred to as threads, which connect nodes in a particular order.

26) What is a complete binary tree?

This is one of the most asked binary search tree questions. A binary tree that has every level—possibly the final one—is completely filled and every node as far to the left is said to be complete. There are no gaps in the last level’s node filling from left to right.

27) How is a binary tree mirrored or inverted?

Recursively swapping the left and right subtrees of each node will mirror or invert the binary tree. The tree is reflected along its vertical axis by this process.

28) Describe what a binary heap is.

A whole binary tree that complies with the heap property is called a binary heap. Every node in a max heap has a value that is greater than or equal to the values of its offspring. Each node in a min heap has a value that is either less than or equal to the values of its offspring.

29) How difficult is it to find an element in a binary search tree in terms of time?

In a binary search tree, the temporal complexity of looking for an element is O(h), where h is the tree’s height. Finding an element in a binary search tree is one of the biggest binary tree problems but is overcomeable. Since the height of a balanced BST is log(n), the search operation is O(log n). On the other hand, the time complexity may be O(n) in the worst scenario (unbalanced tree).

30) How do you discover the kth smallest/largest entry in a binary search tree?

In an in-order traversal of a binary search tree, note the items encountered in order to get the kth smallest element. Stop when you reach the kth element. Similarly, run a reverse in-order traverse for the kth greatest element.

31) Explain the concept of a trie.

Prefix trees, or tries, are tree-like data structures that are effectively used for storing and querying associative arrays or dynamic sets. It is very helpful for word representation in dictionaries.

32) What distinguishes binary search trees from binary trees?

A binary search tree (BST) is a particular kind of binary tree in which the left subtree of a node only contains nodes with keys less than the node’s key, and the right subtree contains nodes with keys greater than the node’s key. A binary tree is a hierarchical structure in which each node has at most two children.

33) How is the diameter of a binary tree determined?

The length of the longest path connecting any two nodes in a binary tree is its diameter. Add together the heights of each node’s left and right subtrees to determine the diameter. The largest of these sums represents the diameter.

34) What makes a heap different from a stack?

A stack is a type of data structure that adheres to the Last In, First Out (LIFO) principle, whereas a heap is a section of computer memory used for dynamic memory allocation. Whereas stacks are used for local variable storage and function calls, heaps are used for dynamic memory allocation.

35) How does one locate the lowest common ancestor (LCA) in a binary search tree?

The node where two nodes’ routes diverge is referred to as their lowest common ancestor (LCA) in a binary search tree. Navigate the tree beginning at the root. Proceed with the search on the same side of the current node if both nodes are on it; if not, the LCA is the current node.

36) Describe the idea of binary tree Morris Traversals.

A quick and effective method for traversing binary trees in sequence without the need of a stack or recursion is the Morris Traversal. Through threading nodes and establishing a temporary connection to a predecessor or successor, it alters the structure of the tree.

37) In what ways can a binary tree be serialized and deserialized?

A binary tree is converted into a string representation through the technique of serialization; the opposite procedure is known as deserialisation. Either level-order or pre-order traversals of the tree are performed during serialization. During deserialization, the serialized string is then utilized for recreation. Tree coding questions frequently involve these processes.

38) What distinguishes a B-tree from a binary tree?

A B-tree is a self-balancing tree data structure that allows each node to have more than two children, whereas a binary tree is a tree data structure where each node can have up to two children. Databases and file systems frequently use b-trees to efficiently retrieve data.

39) How can a binary tree’s cycle be found?

Use depth-first search (DFS) or breadth-first search (BFS) traversal to find a cycle in a binary tree. A cycle is identified during traversal if a node that is already on the current path—the stack for DFS or the queue for BFS—is found.

40) Describe the idea behind an AVL tree question and their applications.

Self-balancing binary search trees, or an AVL tree question, maintain each node’s balance factor at either -1, 0 or 1. In order to facilitate effective searching and retrieval, these trees dynamically modify their structure throughout insertion and deletion operations, avoiding degradation into a linked list. They come in handy in situations where searches are conducted frequently.

41) Describe the idea of a Cartesian tree.

The Cartesian tree property is adhered to by a Cartesian tree that is generated from a numerical series. Because of this trait, subarrays to the left and right of the largest element are represented by the left and right subtrees. Sequence values are mapped to node values. Cartesian trees are used in expression trees and sorting techniques, two areas that are commonly studied in the context of top 50 tree questions.

42) In a binary tree lacking parent pointers, how can the LCA (Lowest Common Ancestor) be found?

Finding the Lowest Common Ancestor (LCA) requires recursively exploring a binary tree without parent pointers. If either of the designated nodes is located, the function ought to return the identified node. When nodes are located in distinct subtrees, the active node assumes the role of the LCA. The search proceeds within the same subtree if both nodes are present. Binary tree Interview questions concerning binary trees frequently address this technique.

43) What is the process for creating a balanced binary search tree from a sorted array?

Use these procedures to create a balanced binary search tree from a sorted array:

1. a) Locate the array’s middle element.
2. b) Make a node where the root is the middle element.
3. c) Recursively repeat the process for the left and right halves of the array, assigning the middle element of each half as the root of the associated subtree.

44) Explain Huffman coding and how it relates to binary trees.

With shorter encodings for more often occurring characters, Huffman coding, a compression technique, builds a binary tree depending on character frequency in a text. Characters are shown as leaves in Huffman trees, and merging is shown as an internal node. This is not the same as a binary search question, which looks for values within a binary search tree.

45) What is the process for determining a binary tree’s maximum depth or height?

Use a depth-first traversal (such as post-order, pre-order, or in-order) and recursively determine the depth of each subtree to determine the maximum depth of a binary tree. The higher value between the depths of the left and right subtrees plus one for the current node is the maximum depth.

## Final Thoughts

In this article, we explored some of the most commonly asked binary search tree interview questions. Exploring more about data structures can help you get a better grasp of logic and programming. You can try looking at examples mentioned in this article and practice by changing values to build your fundamentals. With some practice, you will be in a great position to crack your interview.

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### 1. What are the real-life examples of Binary Tree data structure?

The binary tree is one of the most used data structures. It also acts as a base algorithm for many other user-defined data structures. There are many real-life applications that use this data structure and its implementation directly or indirectly.

Many compression algorithms use binary trees for their implementations such as the Huffman coding. Binary trees are also used in networking. Decision trees also use binary trees internally. Heap data structure uses binary trees to implement priority queues.

### 2. How should I practice binary tree coding questions after preparing these theoretical interview questions?

After you are thorough with the theoretical concepts of binary tree and preparing all the interview questions, you can start practising coding questions starting from easy, then medium, and then finally hard level problems.

You can start approaching topic wise questions, and then after becoming confident in those, you can do problems from mixed topics. There are tons of websites like GFG, LeetCode, which have quality questions to practice from. Practising enough varied problems will not only boost your confidence but will also help you ace your interviews.

### 3. Why is a binary tree and its concepts so important?

Binary tree data structure and its fundamental concepts like properties, types, traversals, and operations are very crucial not only for interviews but also when you develop real-life applications. The concepts are used in implementing efficient algorithms and help you to develop sharp problem-solving skills.

This is one of the most asked data structures in interviews. The binary tree acts as a base for various other data structures and algorithms such as heaps, decision trees, heap sort and tree sort.

### 4. What are class 12 binary tree questions?

Binary tree questions class 12 typically cover fundamental operations such as insertion, deletion, searching, traversal (in-order, pre-order, post-order), and determining properties like height, depth, and whether the tree is balanced or not.

Rohit Sharma

Rohit Sharma is the Program Director for the UpGrad-IIIT Bangalore, PG Diploma Data Analytics Program.

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