The most important thing for interviews in product-based companies is data structures. The data structure is a way of storing and organizing the available data for further use. Data structures are of two types, Linear and Non-linear. Let us discuss non-linear data structures and their complexity.

Non-Linear Data Structures

Non - Linear Data Structures are those Data Structures in which data is not stored linearly or sequentially, and due to which each element is not connected to the previous or next element so that they can be accessed in a single run. Non-linear data structures are more complex and memory-efficient with respect to linear data structures.

Some examples of non-linear data structures are trees, graphs, etc.

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Time Complexity

Time complexity can be understood as a concept that constitutes the quantification of time taken by an algorithm or code snippet to execute. The time complexity is also a measure of the efficiency, such that the lesser the time is taken by the algorithm, the more its efficiency will be.

We will be discussing only the worst-case time complexity in this article.

Space Complexity

Space Complexity can be understood as the amount of memory space occupied by a code snippet or algorithm. It is one of the two measures of the efficiency of an algorithm. The lesser the space it takes, the more efficient it is.

Now let’s discuss the complexities of some non-linear Data structures.

Binary Tree

A tree in which all the nodes do not have more than two children is called a Binary Tree.

For Example:

For a binary tree consisting of N nodes:

Time Complexity

The time complexity for accessing any specific node:

Average Complexity: O(log N)

Worst Complexity: O(N)

The time complexity for searching any specific node:

Average Complexity: O(log N)

Worst Complexity: O(N)

The time complexity for inserting any specific node:

Average Complexity: O(log N)

Worst Complexity: O(N)

The time complexity for deleting any specific node:

Average Complexity: O(log N)

Worst Complexity: O(N)

Space Complexity

For all the operations, no extra space is required, thus the space complexity will be O(1).

The first word of ‘Binary Search Trees’, namely ‘Binary’, tells us that every node in the tree can have at most two children, the left child, and the right child. The data of the right child and the left child must be greater and smaller than the data of the parent node, respectively.

Lets us see an example of a binary search tree.

For a binary search tree consisting of N nodes:

Time Complexity

The time complexity for accessing any specific node:

Average Complexity: O(log N)

Worst Complexity: O(N)

The time complexity for searching any specific node:

Average Complexity: O(log N)

Worst Complexity: O(N)

The time complexity for inserting any specific node:

Average Complexity: O(log N)

Worst Complexity: O(N)

The time complexity for deleting any specific node:

Average Complexity: O(log N)

Worst Complexity: O(N)

Space Complexity

For all the operations, no extra space is required, thus the space complexity will be O(1).

What is a Data structure? A data structure is a way of storing data and organizing it, so that it is easier to use the information stored efficiently, change, add more of it or delete any. In different programs, we use different data structures based on the requirements of the operations further.

What are non-linear data structures? Linear Data Structures are those data structures in which data is stored sequentially, and each element is connected to the previous or next element so that they can be accessed in a single run. Some examples of linear data structures are arrays, stacks, queues, etc.

Among linear and non-linear data structures, which one is more memory efficient? Non-linear data structures are more memory efficient than linear data structures but this efficiency increases the complexity of non-linear data structures.

What is time complexity? Time complexity can be understood as a concept that constitutes the quantification of time taken by an algorithm or code snippet to execute. The time complexity is also a measure of the efficiency, such that the lesser the time is taken by the algorithm, the more its efficiency will be.

What is space complexity? Space Complexity can be understood as the amount of memory space occupied by a code snippet or algorithm. It is one of the two measures of the efficiency of an algorithm. The lesser the space it takes, the more efficient it is.

Key Takeaways

In the above article, we learned about the time and space complexity of Non-Linear Data Structures, which is a very important concept required in the preparation for all the DSA based interviews.