Time complexity is a measure of the amount of time needed to execute an algorithm. It is a function of the algorithm’s input size and the type of computing system used. The time complexity of an algorithm determines how long it will take to execute it.
The higher the time complexity, the longer it will take for that algorithm to finish running. Algorithms with high time complexities are generally preferred over those with low time complexities if there are other considerations, such as accuracy or space complexity. In time complexity, there are two types of searches.
A binary search is a method of searching for an item in a list, array, or table by making comparisons to the central element of the data set. The time complexity of binary search is O(log n), with n being the number of elements in a data set. It takes less time to find an element in an extensive data set than in a small one.
Linear search is an algorithm that sequentially checks every element of the list. It can be used to find a given item in a list or to find the position of an item in a sorted list. The time complexity used for linear search is O(n). For example, it will take ten steps to complete a linear search if you work with ten things.
Let’s dive deep into learning the importance and application of time complexity.
How Time Complexity Is Used in Algorithms
Algorithmic complexity is an essential aspect of time complexity. It is the step or operation that a computer must go through to complete a process. You might not realize it, but many AI-driven tasks rely on time complexity. Algorithms are so ubiquitous in our lives that it’s nearly impossible to avoid them. From the GPS on your phone to the algorithm behind Facebook’s News Feed, we rely more on algorithms than ever before.
Algorithmic Complexity vs. Actual Computational Times
A computer algorithm is a list of instructions for solving a problem, which can be written as a series of steps to be followed to reach an answer. Algorithms are usually described by the number of steps required, and these steps can vary significantly in length, complexity, and dimensionality.
Algorithms come in two types: deterministic and non-deterministic. While deterministic algorithms yield the same kind of output, non-deterministic algorithms generate different outputs for all inputs. Deterministic algorithms guarantee a correct answer based on the input provided. Non-deterministic algorithms need not always have the same result for any given input, meaning that they may not provide an answer guaranteed to be correct based on the feedback provided.
The algorithmic complexity is the asymptotic upper bound for the number of operations needed to compute a solution for a given problem. The computational time for an algorithm is the time spent executing it on a given input. In general, algorithms with low algorithmic complexities have high computational times and vice versa.
Understanding Merge Sort Time Complexity
Merge Sort Algorithm is one of computer science’s most common sorting algorithms. A comparison sort algorithm divides the input list into smaller sublists, recursively sorting each sublist and then merging them to produce a sorted list.
Merge Sort time complexity uses the divide-and-conquer strategy. It can be used on any input data size but only works well with manageable data sets because it requires time proportional to the list size to complete. It has O(n log(n)) time complexity, meaning it takes linear time on lists of any size.
Merge Sort can be summarized as follows:
- Divide the array into two halves by picking the middle element as the pivot index
- Sort each half of the array in descending order
- Exchange elements to make their respective arrays identical if there is more than one element
- Recursively call merge sort on each of these sorted arrays until they are both sorted
How To Use the Laws of Time Complexity for Better Decision-making
The time complexity can be used to decide between different algorithms with different running times. The one with lower time complexity will outperform the other in most cases. The space complexity can also choose whether algorithms have additional space requirements.
Two key concepts of time complexity should be considered when making a decision. These include:
1) the expected running time for a program, which is the average amount of time it will take to execute that program on all possible inputs, and
2) the space complexity, which is the amount of memory needed to store all information needed to run a program.
How To Calculate Time Complexity
The time complexity of a function is the amount of work it needs to do about the size of its input. The time complexity is calculated by using Big-O notation. This notation describes the complexity of a function as a mathematical expression involving one or more variables.
The letter “O” represents the term “order” and comes after a variable in the expression that represents how many times the variable appears in an equation. For example, if we want to calculate how much work a function does concerning its input size, we would use this formula: ƒ(x)=O(x).
Types of Time Complexity
Constant Time Complexity – O(1)
In constant time complexity, the algorithm will take the same amount of time to run regardless of how large the input size is. It is an essential property because as long as you have enough memory, you should be able to process any input size reasonably.
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Logarithmic Time Complexity – O(log n)
The logarithmic time complexity is O(log n). Although the algorithm description seems lengthy, it is simple. One more operation is required to process every item added to the list. It is made more difficult to understand by the notation used.
Linear Time Complexity – O(n)
Linear time complexity measures an algorithm’s efficiency. One can calculate it by dividing the number of operations by the number of input items. The time complexity for an algorithm is linear if it takes a constant amount of time to process each input item. As the size of the input increases, so does the processing time.
O(n log n) Time Complexity
An algorithm with O(n log n) time complexity is an algorithm with a running time proportional to the logarithm’s input size. An algorithm with O(n) time complexity ensures the running time is proportional to the input size and will take more time as we increase the input size. An algorithm’s time complexity is measured by calculating how long it takes for the program to finish its work. The lower, the better.
Quadratic Time Complexity – O(n2)
The quadratic time complexity is also known as O(n2). In this type, the problem’s solving time will be proportional to the number of inputs’ squares. It can happen for two reasons –either because it takes more steps to find each input or because it takes more steps to process each input. This type of complexity applies to any algorithm where there is a constant difference in computation power between each step, which implies that any algorithm with quadratic time complexity will be inefficient when there are many inputs.
The Importance of Choosing Appropriate Algorithms for Your Purpose
In computer science, many algorithms are used for different purposes. The choice of algorithm you make depends on the problem and the resources you have available. Different algorithms have different time complexities; some are used for various issues. Some algorithms are more efficient than others, but they may not be appropriate for your particular task.
We should be mindful when choosing a suitable algorithm for our purpose. If we choose the correct algorithm, it might lead to a good result. One of the most popular algorithms is the k-means clustering algorithm. It is an unsupervised Machine Learning algorithm that groups data points into clusters.
Many factors go into choosing the suitable algorithm. The first factor is the time complexity of the algorithm. If your algorithm needs to be fast, you should choose a faster one. The second factor is the accuracy of the algorithm. If you need your algorithm to be as accurate as possible, you should choose a more complex and slower-running one.
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The third factor is how much data you have available. Many algorithms can work for your purposes if you have a lot of data. Still, if there is little data available, it’s essential to find an appropriate algorithm that can effectively use the little data there is.
Time complexity is an important part of Machine Learning. Algorithms have been a part of our lives for years now. From how we search for things on Google to how we shop online, algorithms are used in many ways. The growth rate of computational costs has been going strong for a while.
The computational costs of machine learning algorithms have increased exponentially in the past few years. One of the reasons for the increased costs is the exponential growth in data. To keep up with these costs, companies must find better ways to train their models and more efficient methods to use their computational power. To learn more about how this works, you can opt for upGrad’s Master of Science in Machine Learning and Artificial Intelligence offered by IIIT-Bangalore and LJMU.