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.
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