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!
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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.
- a) Find a path from the root node to n1 and store it in an array.
- b) Find a path from the root node to n2 and store it in an array.
- 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:
- a) A node can have a key that is greater than all the keys in the node’s left subtree.
- 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:
- Create a temporary array that stores the inorder traversal of the tree
- Sort the temporary array. You can use any sorting algorithm here.
- Again perform an inorder traversal on the tree.
- 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:
- Node to be deleted is a leaf node.
Simply remove the node.
- Node to be removed has one child.
In this case, copy the child to the node and delete the child.
- 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.
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:
- Each node has a colour either red or black.
- The root is always black.
- A red node cannot have a red parent or red child.
- 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:
- Check data of root node ( tree1 data ==tree2 data)
- Check left subtree recursively. call sameTree( tree1-> left subtree, tree2-> left subtree)
- Similarly, check right subtree
- 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.
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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