GrößerOhNotation

GrößerOhNotation, commonly referred to as Big O notation, is a mathematical notation used in computer science to describe the performance or complexity of an algorithm. Specifically, it characterizes functions according to their growth rates. When an algorithm is described as having a Big O complexity of O(f(n)), it means that as the input size 'n' grows, the algorithm's execution time or space requirements will grow no faster than a constant multiple of f(n).

The purpose of Big O notation is to provide an upper bound on the growth rate of an algorithm's resource usage, focusing on the worst-case scenario. It abstracts away constant factors and lower-order terms, allowing for a clear comparison of algorithms independent of specific hardware or implementation details. For example, an algorithm with O(n) complexity is considered more efficient for large inputs than one with O(n^2) complexity.

Common Big O complexities include O(1) (constant time), O(log n) (logarithmic time), O(n) (linear time), O(n log n) (linearithmic time), and O(n^2) (quadratic time). Understanding Big O notation is crucial for analyzing the scalability and efficiency of algorithms, enabling developers to choose the most appropriate solutions for a given problem.