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Big O Notation
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TLDR: Big O Notation is a mathematical representation used in computer science to describe the efficiency of algorithms. Introduced in the early 20th century and popularized in computational theory in the 1960s, it provides a way to measure the time complexity and space complexity of an algorithm as input size grows. Big O focuses on the upper bounds, emphasizing the worst-case scenario for performance analysis.
https://en.wikipedia.org/wiki/Big_O_notation
In algorithm analysis, Big O Notation describes how an algorithm's runtime or space requirements grow relative to input size. Common classifications include O(1) for constant time, O(n) for linear time, and O(n^2) for quadratic time. For example, accessing an element in an array has an O(1) complexity, while a nested loop iterating over the same dataset twice often has O(n^2). Understanding these classifications helps developers select the most efficient algorithm for specific tasks.
https://www.khanacademy.org/computing/computer-science/algorithms/big-o-notation/a/big-o-notation
Big O Notation abstracts away hardware and implementation details, focusing purely on how algorithms scale. This makes it a critical tool in evaluating the performance of data structures like hash tables or sorting methods such as merge sort. For instance, merge sort operates at O(n log n), making it more efficient for large datasets compared to O(n^2) algorithms like bubble sort.
https://en.wikipedia.org/wiki/Merge_sort
Mastering Big O Notation is essential for designing scalable systems and optimizing code. It provides a theoretical foundation for understanding trade-offs in algorithm design, such as balancing time and space complexity. Courses, books like The Art of Computer Programming, and tools for profiling code help developers gain deeper insights into algorithm efficiency and apply Big O Notation in practical scenarios.
https://www-cs-faculty.stanford.edu/~knuth/taocp.html
- Snippet from Wikipedia: Big O notation
Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by German mathematicians Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for Ordnung, meaning the order of approximation.
In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetical function and a better understood approximation; a famous example of such a difference is the remainder term in the prime number theorem. Big O notation is also used in many other fields to provide similar estimates.
Big O notation characterizes functions according to their growth rates: different functions with the same asymptotic growth rate may be represented using the same O notation. The letter O is used because the growth rate of a function is also referred to as the order of the function. A description of a function in terms of big O notation usually only provides an upper bound on the growth rate of the function.
Associated with big O notation are several related notations, using the symbols o, Ω, ω, and Θ, to describe other kinds of bounds on asymptotic growth rates.
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