Question

When expressing an algorithm's time complexity in big O notation, which of the following statements is correct?

a) Lower order terms should be dropped.
b) Higher order terms should be dropped.
c) Both lower and higher order terms should be kept.
d) The constant factor should be emphasized.

Answer 1

In big O notation, the correct option is to drop lower order terms, keep the higher order term, and ignore constant factors. This simplifies the expression to only reflect the dominant factors influencing the algorithm's running time as input size grows.

Step-by-step explanation:

When expressing an algorithm's time complexity in big O notation, the correct approach is to drop the lower order terms and ignore constant factors. For example, if an algorithm has a time complexity of O(3n² + n + 100), in big O notation, this would be simplified to O(n²). The higher order term, n², represents the dominant factor that most influences the growth rate of the running time as the size of the input increases, which is why it is retained while the linear term and the constant are omitted. The inclusion of lower order terms and constants offers little value in comparing the efficiency of algorithms, as they do not significantly affect the computational complexity for large input sizes.