03/10 Lecture Material

Big Oh Definition

An algorithm's time requirement f(n) is of order at most g(n) - that is, f(n) = O(g(n)) - in case a positive real number c and positive integer N exist such that f(n) <= c g(n) for all n >= N. See Figure 9-7. See Figure 9-12.

Identities

• O(k * f(n)) = O(f(n))
• O(f(n)) + O(g(n)) = O(f(n) + g(n))
• O(f(n)) * O(g(n)) = O(f(n) * g(n))

Statement Counts

Program Construct Complexities

• if statement
• loop statement