What does Big-O notation describe in algorithm analysis?

What does Big-O notation describe in algorithm analysis?

• A. The exact running time for all input sizes
• B. The average-case time complexity
• C. The best-case memory usage
• D. The upper bound on growth of time or space as input size increases

Answer: (D)

Big-O notation describes how the resources an algorithm uses (time or space) grow as the input size gets larger. It provides an upper bound on this growth, focusing on the dominant term and ignoring constant factors and less significant terms. This lets you compare how scalable different algorithms are. For example, if one algorithm’s running time increases proportionally to the input size, it’s O(n); if another grows with the square of the input size, it’s O(n^2). It’s about growth behavior with large inputs and isn’t guaranteed to give exact runtimes for specific cases or sizes.

Big-O notation describes how the resources an algorithm uses (time or space) grow as the input size gets larger. It provides an upper bound on this growth, focusing on the dominant term and ignoring constant factors and less significant terms. This lets you compare how scalable different algorithms are. For example, if one algorithm’s running time increases proportionally to the input size, it’s O(n); if another grows with the square of the input size, it’s O(n^2). It’s about growth behavior with large inputs and isn’t guaranteed to give exact runtimes for specific cases or sizes.