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Big-O notation is a mathematical notation used to describe the upper limit of the time complexity or space complexity of an algorithm. It characterizes functions according to their growth rates: different functions with the same 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.
Big-O notation is crucial in computer science because it provides a high-level understanding of how the runtime or space requirements of an algorithm scale with the size of the input. It allows developers and computer scientists to predict the efficiency of algorithms and compare them in terms of their computational complexity without getting bogged down in the details of the implementation.
To express the efficiency of an algorithm, Big-O notation uses various symbols like:
– O(1): Constant time complexity, indicating that the execution time or space is fixed and does not change with the size of the input data.
– O(log n): Logarithmic time complexity, indicating that the execution time or space grows logarithmically as the input size increases.
– O(n): Linear time complexity, indicating that the execution time or space grows linearly with the input size.
– O(n log n): Log-linear time complexity, often seen in efficient sorting algorithms.
– O(n^2), O(n^3), …: Polynomial time complexity, indicating that the execution time or space grows with the square, cube, etc., of the input size. These are typically seen in more