Complexity Of Time And Space Javascript

Michael Zippo 04.11.2021

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Note : If you haven’t read our article on temporal complexity , we recommend that you start there. Part 2 of this series assumes you know several possible Big O values.

In our first article on Big O scoring and temporal complexity , we are talking about the time it takes for the algorithm to complete as its input increases. This is important when interacting with very large datasets. A large dataset combined with a fair amount of time complexity leads to more efficient algorithms. However, there is another aspect of Big O notation that must be taken into consideration: The complexity of the space.

What is the space complexity

Time complexity and space complexity ? are similar with respect to the amount of input to an algorithm. When time complexity is related to quantity operations that an algorithm must perform to complete, spatial complexity is related to the total amount of space needed to complete the algorithm. Spatial complexity is expressed in terms of Big O notation.

Spatial complexity includes the amount of space needed for input and the auxiliary space needed in the algorithm for execution . Auxiliary space is the extra space used to store temporary or variable data structures used to solve the algorithm. Just like in time complexity, the Big O of an algorithm considers the worst case, or the asymptotic upper bound.

Calculating the space needed to run an algorithm

When calculating the spatial complexity of an algorithm, look at two things: the size of the input and the space auxiliary required to perform the function. In most cases, we are not reducing the size to the number of bytes of the entry - we are just looking at how much memory the entry or auxiliary space should use.

The input to an algorithm is what is passed to the function when it is invoked. Typically, this will be some sort of primitive value: string, number, or object. The exact size of each may differ depending on the language, but we can usually figure out how much space is needed.

Simple input and output example

( Note : We are using Java here, so you can easily distinguish between different data types, but it can work for just about any language. )

Take the above function. The purpose of this function is to take one input - in this case two int (short for integers) and return an output, also an int.

In our post, we have two variables - int a and int b. Our return value - an int - also takes up space. Since our integers are evaluated only once, here we consider spatial complexity as O (1) - constant time.

Example with more complex entries

This function takes an array as input. The array, not knowing the length, has indices. The two variables of the first two lines of the function are O (1) because they are evaluated only once. The sum is an integer, it is also O (1). The large O for spatial complexity is O (n) to dictate the space for the array.

Conclusion

The most efficient algorithm is the one that requires the least time and memory. It will be almost impossible, if not impossible, to write an algorithm that satisfies both conditions. In the end, you have to sacrifice one for the other. The question becomes, what sacrifice ?

The answer is: it depends. It all depends on the requirements of the project or the algorithm you are working on. If you only have minimal memory, you have to sacrifice time complexity to use minimal space and vice versa.

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We hope this article has helped you to resolve the problem. Apart from Complexity Of Time And Space Javascript, check other array Python module-related topics.

Want to excel in Python? See our review of the best Python online courses 2023. If you are interested in Data Science, check also how to learn programming in R.

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Carlo Sikorski

Munchen | 2023-02-02

I was preparing for my coding interview, thanks for clarifying this - Complexity Of Time And Space Javascript in Python is not the simplest one. Will use it in my bachelor thesis

Jan OConnell

California | 2023-02-02

Simply put and clear. Thank you for sharing. Complexity Of Time And Space Javascript and other issues with types Python module was always my weak point 😁. I am just not quite sure it is the best method

Carlo Emmerson

San Francisco | 2023-02-02

Maybe there are another answers? What Complexity Of Time And Space Javascript exactly means?. Will use it in my bachelor thesis