Time Complexity of an Algorithm – Part 5

Conclusion

The time complexity of an algorithm is a measure of the time it takes to solve the problem as a function of the input size. This is an important factor to consider when designing and evaluating algorithms as it can affect the efficiency of the solution. This article discussed the most common types of time complexity and provided C++ and Python examples to illustrate each complexity.

The first complexity mentioned was O(1) or constant-time complexity. Algorithms of this type take a constant amount of time to execute, regardless of the input size. For example, accessing a specific element in an array or retrieving a value from a hash table.

The second complexity mentioned was O(log n) or logarithmic time complexity. This type of algorithm takes time to run in proportion to the logarithm of the input size. Examples are binary search and some tree-based algorithms.

The third complexity mentioned was O(n) or linear time complexity. Algorithms of this type take time to execute in proportion to the input size. Examples are sorting algorithms such as linear search and bubble sort.

The fourth complexity discussed was O(n log n) or quasi-linear time complexity. Execution of this type of algorithm takes time proportional to the input size multiplied by the logarithm of the input size. Examples are quicksort and merge-sort. The fifth complexity mentioned was O(n^2) or polynomial time complexity. Algorithms of this type take time to execute in proportion to the square of the input size. Examples are bubble sort and selection sort.

The last-mentioned complexity was O(2^n) or exponential time complexity. This type of algorithm takes time, growing exponentially with input size. Examples include exhaustive search algorithms that must consider all possible combinations of candidate inputs.

In summary, understanding the time complexity of an algorithm is important for choosing an appropriate algorithm to solve a particular problem. Each complexity has its own characteristics and well-known examples of algorithms. By analyzing the complexity of an algorithm, we can determine its efficiency and suitability for a particular use case.?

Link to Part 4: https://www.dhirubhai.net/pulse/time-complexity-algorithm-part-4-rajesh-gopalakrishnan