what is order of complexity in Big O notation?

Question

Question

Hi I am trying to understand what order of complexity in terms of Big O notation is. I have read many articles and am yet to find anything

Answer 1

Others have explained big O notation well here. I would like to point out that sometimes too much emphasis is given to big O notation.

Consider matrix multplication the naïve algorithm has O(n^3). Using the Strassen algoirthm it can be done as O(n^2.807). Now there are even algorithms that get O(n^2.3727).

One might be tempted to choose the algorithm with the lowest big O but it turns for all pratical purposes that the naïvely O(n^3) method wins out. This is because the constant for the dominating term is much larger for the other methods.

Therefore just looking at the dominating term in the complexity can be misleading. Sometimes one has to consider all terms.