Top 4 non linear data structures for every software engineer

Want to ace your next technical interview? Nailing nonlinear data structures could be your secret weapon. They’re not just lists or arrays to store data but also help map out complex relationships and hierarchies. Getting a grip on these can enhance your problem solving abilities and really make you stand out from other candidates.

In this blog, we will dive into four key nonlinear data structures that every software engineer should know: binary trees, heaps, tries, and graphs. We'll break down what they are, how they work, and why they’re often essential in tough interview questions. Ready to level up? Let’s get started.

What is a data structure?#

A data structure is a way of organizing and storing data to be accessed and modified efficiently. Think of it as a container that holds your data in a specific layout. There are many data structures, each with strengths and use cases. Some are simple and linear, like arrays and linked lists, while others are nonlinear, like trees and graphs.

Why do we need data structures?#

Data structures are key in managing and processing data efficiently in software development. Here’s why they are essential:

• Efficiency: Using the right data structure can significantly reduce the time complexity of your algorithms. For example, searching for an item in an unsorted array takes linear time $O(n)$, but using a binary search tree can reduce this to logarithmic time $O(\log(n))$.

• Memory management: Data structures help in organizing data in memory. For instance, a hash table can efficiently manage a large dataset by using a hash function to distribute data evenly across an array.

• Real-world applications: Data structures are used everywhere, from databases to network routing algorithms. Social media platforms, for example, use graph data structures to represent and analyze user connections.

In summary, understanding and implementing the right data structure can make your software faster, more efficient, and easier to manage. This knowledge is crucial for tackling more complex problems in your software engineering career.

Top 4 nonlinear data structures for technical interviews#

A nonlinear data structure is a type of data structure where elements are not arranged sequentially. Instead, they are organized hierarchically, allowing for more complex relationships between elements.

Let’s list the top 4 nonlinear data structures and then discuss these in detail:

1. Binary trees

2. Heaps

3. Tries

4. Graphs

Each data structure has unique properties and advantages that make it suitable for different tasks. In the following sections, we will explore each one, discussing their concepts, operations, advantages, and applications.

1. Binary trees#

A binary tree is a hierarchical data structure in which each node has at most two children, the left and right child. Binary trees are fundamental in computer science and provide a base for more complex structures like binary search trees and AVL trees.

The following are the types of binary trees:

• Binary search tree (BST): This is a binary tree in which each node follows the property that the values of all left descendants are less than the node and the values of all right descendants are greater than the node.

• AVL tree: This is a self-balancing binary search tree in which the difference between the heights of the left and right subtrees cannot be more than one for all nodes.

• Red-Black tree: This is a self-balancing binary search tree in which each node contains an extra bit denoting its color, either red or black. This helps balance the tree during insertions and deletions.

Common operations:

Here are some common operations of the binary trees:

• Insertion: Adds a node to the tree while maintaining the binary tree properties.

• Deletion: Removes a node from the tree and reestablishes the binary tree properties.

• Traversal:

  • In-order (LNR):  First, visit the left subtree, then the node, and then the right subtree.

  • Pre-order (NLR):  First, visit the left node, then the left subtree, and then the right subtree.

  • Post-order (LRN): First, visit the left subtree, then the right subtree, and then the node.

  • Level-order: Visit the nodes level by level from top to bottom.

Advantages and disadvantages#

Let’s discuss some advantages and disadvantages of the binary trees:

• Advantages:

  • Hierarchical data: Efficiently represents hierarchical relationships.

  • Flexible: Implements other data structures like heaps, tries, and binary search trees.

• Disadvantages:

  • Unbalanced trees: Becomes unbalanced, leading to degraded operation performance ($O(n)$ time complexity).

  • Complexity: Maintaining balance in trees like AVL or Red-Black can be complex.

Commonly asked interview problems of binary trees#

Now, let’s look at some commonly asked problems about binary trees. Click the problem titles in the following illustration to see more details and attempt the exercise.

2. Heaps#

A heap is a specialized tree-based data structure that satisfies the heap property. It is a complete binary tree. There are two main types of heaps:

• Min-heap: In a min-heap, the key at the root must be the minimum among all keys in the heap. The same property must be recursively true for all nodes in the heap.

• Max-heap: In a max-heap, the key at the root must be the maximum among all keys in the heap. The same property must be recursively true for all nodes in the heap.

Common operations:

Here are some common operations of the heaps:

• Insertion: Adds a new element to the heap while maintaining the heap property.

• Deletion: Removes the root element (min or max) from the heap and rearranges the elements to maintain the heap property.

• Find min/max: Retrieves the minimum element from a min-heap or the maximum element from a max-heap.

Advantages and disadvantages#

Let’s discuss the advantages and disadvantages of the heaps:

• Advantages:

  • Efficient operations: Insertion and deletion operations in a heap take $O(\log (n))$ time.

  • Access to min/max: Provides quick access to the minimum or maximum element.

• Disadvantages:

  • Memory overhead: Heaps require additional memory for the pointers in tree-based implementations.

  • Not suitable for search: Heaps are not designed for searching arbitrary elements efficiently.

Commonly asked interview problems of heaps#

Now, let’s look at some commonly asked heap problems. Click the problem titles in the following illustration to see more details and attempt the exercise.

3. Tries#

A trie, also known as a prefix tree, is a tree-like data structure that stores a dynamic set of strings, usually to provide fast retrieval. Unlike binary trees, nodes in a trie can have multiple children, each representing a single string character.

Common operations:

Here are some common operations of the tries:

• Insertion: Adds a word to the trie by creating new nodes for each character that does not already exist.

• Deletion: Removes a word from the trie by deleting nodes if they are not part of another word.

• Searching: Checks if a word exists in the trie by traversing through the nodes corresponding to each character of the word.

Advantages and disadvantages#

Let’s discuss some advantages and disadvantages of the binary trees:

• Advantages:

  • Fast lookup: Provides fast lookups, insertions, and deletions for strings, typically in $O(m)$ time, where $m$ is the length of the string.

  • Prefix searching: Efficiently supports prefix searching, making it useful for auto-complete features.

• Disadvantages:

  • Space complexity: Consumes a lot of memory for storing large sets of strings, especially if many of them share common prefixes.

  • Implementation complexity: More complex to implement compared to other data structures like arrays or linked lists.

Commonly asked interview problems of tries#

Now, let’s look at some problems of tries that are commonly asked. Click the problem titles in the following illustration to see more details and attempt the exercise.

4. Graphs#

A graph is a collection of nodes (also known as vertices) and edges that connect pairs of nodes. Graphs model relationships and connections in various fields, such as computer science, biology, and social networks.

The following are the types of graphs:

• Directed graph: This is a graph where edges have a direction, indicating a one-way relationship between nodes.

• Undirected graph: This is a graph where edges have no direction, indicating a two-way relationship between nodes.

• Weighted graph: This is a graph where edges have weights, representing the cost or distance between nodes.

• Unweighted graph: This is a graph where edges have no weights, representing a simple connection between nodes.

Graphs can be represented in the following forms:

• Adjacency list: Each node has a list of all the nodes it is connected to. This representation is space-efficient, especially for sparse graphs.

• Adjacency matrix: A 2D array where the element at row $i$ and column $j$ represents an edge’s presence (and possibly weight) of an edge between nodes $i$ and $j$. This representation is easy to implement but can be space-inefficient for large, sparse graphs.

Common operations:

Here are some common operations of the graphs:

• Traversal:

  • Depth-first search (DFS): Explores as far down a branch as possible before backtracking.

  • Breadth-first search (BFS): Explores all neighbors at the present depth before moving on to nodes at the next depth level.

• Shortest path:

  • Dijkstra’s algorithm: Finds the shortest path from a source node to all other nodes in a weighted graph.

  • Bellman-Ford algorithm: Finds the shortest paths from a source node to all other nodes in a graph with possible negative weights.

  • Floyd-Warshall algorithm: Finds shortest paths between all pairs of nodes.

Advantages and disadvantages#

Let’s discuss an advantage and a disadvantage of the graphs:

• Advantage:

  • Versatility: Represents various data structures and problems, such as networks, social relationships, and dependencies.

• Disadvantage:

  • Complexity: Graph algorithms can be complex to implement and understand.

Commonly asked interview problems of graphs#

Now, let’s look at some commonly asked graph problems. Click the problem titles in the following illustration to see more details and attempt the exercise.

Conclusion#

We have explored the most important nonlinear data structures that every software engineer should know. Mastering these data structures takes practice. Here’s where mock interviews can become a game changer. We offer a range of mock interviews, including data structures interviews, allowing you to practice with various problem types. During these mock interviews, pay close attention to the interviewer’s feedback. Use the feedback provided to identify areas for improvement and refine your skills.

Also, try implementing various data structures and solving problems on our platform to enhance your skills. Consistent practice will make your understanding of data structures more intuitive and robust.

To deepen your knowledge and assess your current proficiency, consider exploring our data structures course that is offered in different programming languages:

• Data Structures for Coding Interviews in Python

• Data Structures for Coding Interviews in C++

• Data Structures for Coding Interviews in Java

• Data Structures for Coding Interviews in JavaScript