O(g(n))

f(n) = O(g(n)), g(n) is an Asymptotic Upper Bound for f(n)

O(g(n)) = {f(n): there exist positive constants c and n₀ such that 0 $\leq$ f(n) $\leq$ c*g(n) for all $n \geq n_0$ }

See Figure 2.1b, page 25, for graphical depiction of O.

Examples:

• n² - 2n = O(n²)
• 200 n² - 100n = O(n²) = O(n³) = ...
• n = O(n²)
• Does f(n) = $\Theta(g(n))$ imply f(n) = O(g(n))? Yes
• Does f(n) = O(g(n)) imply f(n) = $\Theta(g(n))$? No