Programs

Top Time Complexities that every Programmer Should Learn

Time complexity in computer science is the concept that deals with the estimation of the amount of time an algorithm or a set of codes takes for processing or running as a function of the input amount regardless of any machine it is used to run on. In a nutshell, time complexity refers to how long a program requires to process the desired input. 

The time complexity of a code or algorithm is easily achieved by “counting” the number of operations a code performs. It is the function of the input size n with the help of Big-O notation. ‘n’ denotes the input size, and O denotes the growth rate function of the worst-case scenario.

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The Big-O notation is mainly used for classifying algorithms based on running time or space (memory) as the input grows. The O function depicts the growth rate in the function of input size n. 

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Let us look into the average and worst-case time complexities of different data structures for various operations.

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The average time complexity of various data structures using different operations

Data structure Access Search Insertion Deletion
Array O(1) O(N) O(N) O(N)
Stack O(N) O(N) O(1) O(1)
Queue O(N) O(N) O(1) O(1)
Singly Linked list O(N) O(N) O(1) O(1)
Doubly Linked List O(N) O(N) O(1) O(1)
Hash Table O(1) O(1) O(1) O(1)
Binary Search Tree O(log N) O(log N) O(log N) O(log N)
AVL Tree O(log N) O(log N) O(log N) O(log N)
B Tree O(log N) O(log N) O(log N) O(log N)
Red Black Tree O(log N) O(log N) O(log N) O(log N)

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The worst-case time complexity of various data structures using different operations

Data structure Access Search Insertion Deletion
Array O(1) O(N) O(N) O(N)
Stack O(N) O(N) O(1) O(1)
Queue O(N) O(N) O(1) O(1)
Singly Linked list O(N) O(N) O(1) O(1)
Doubly Linked List O(N) O(N) O(1) O(1)
Hash Table O(N) O(N) O(N) O(N)
Binary Search Tree O(N) O(N) O(N) O(N)
AVL Tree O(log N) O(log N) O(log N) O(log N)
Binary Tree O(N) O(N) O(N) O(N)
Red Black Tree O(log N) O(log N) O(log N) O(log N)

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Types of Time Complexities Integral For Programming

Understanding time complexity is directly proportional to understanding the growth rate after an algorithm or code execution. The rate here is referred to the time required per input size. 

Here are the primarily used essential time complexities widely used by programmers:

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Constant Time Complexity; O(1)

The input size (n) does not matter when the time complexity is constant. Constant time complexity is denoted by O(1). Algorithms with Constant Time Complexity require a constant amount of time to run. It usually runs of the size of n independently and does not change its run-time against the input data, making it one of the fastest and most widely used algorithms amongst developers.

Linear Time Complexity; O(n)

You get a Linear Time Complexity when time complexity grows according to the input size. Linear time complexity is denoted by O(n). Algorithms having a linear time complexity processes the input (n) in “n” amount of operations, meaning that an algorithm takes a longer time to complete with the growth of the input.

Logarithmic Time Complexity; O(log n)

Using logarithmic time complexity to compute algorithms catalyses the process. An algorithm runs on logarithmic time if the algorithm’s execution time is proportional to the input size logarithm. Instead of increasing the performance time required in each subsequent step, the time taken is decreased at a level inversely proportional to the “n” input.

Quadratic Time Complexity; O(n²)

When algorithms with quadratic time complexity are used, the running time grows with the square of the input size. It is denoted by O(n²). In a maximum number of these scenarios, algorithms with quadratic time complexities require more time to execute and are usually avoided, especially while handling large datasets. 

Exponential Time Complexity; O(2^n)

In algorithms with exponential time complexity, the growth rate is doubled with every input (n) addition. It is denoted by O(2^n), which often iterates through all subsets of input elements.

Whenever an input unit is increased by 1, you have to double the number of operations performed and should therefore be avoided. Therefore, algorithms with exponential time complexity are only used under little information about the best possible solution and are required to try all possible permutations or combinations on the data.

Merge Sort Time Complexity

In worst, average and best cases, the Merge Sort time complexity is denoted by O(n*Log n). This time complexity always divides the array into two parts and uses linear time for merging these two halves.

Quick Sort Time Complexity

O(n*logn) denotes the quicksort time complexity and is an average-case complexity. It is used when the elements of an array are not in sequential order, i.e. neither properly descending nor ascending. 

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Conclusion

There are multiple ways to approach a coding problem. Determining the time complexities of two or more algorithms that fetch the exact solution is essential for identifying the most optimal algorithm to implement. Therefore, having in-depth knowledge of time complexity is an integral part of a software development career.  

As a budding pursuer of software development, it is essential to start at the right place, and upGrad’s Master’s course in Computer Science is a great place to help kickstart your career. With the proper guidance, and a professionally curated curriculum, achieving a successful IT career is not a problem!

How do you find time complexities?

There are different methods of finding time complexities, such as the Master’s Theorem and the Akra-Bazzi Method, used to solve time complexity recurrences of a form.

Why is finding the time complexity of an algorithm or data structure important?

Finding the time complexity of an algorithm or data structure helps to determine algorithms and quantify the amount of time taken by an algorithm to run as functions based on the length of its input.

Is the time taken by a machine to execute an algorithm considered important for evaluating the time complexity of any algorithm?

No. This is because the time complexities for algorithms are not proportional to the actual execution time in a computer. The time complexity of an algorithm is taken for the function to run.

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