Making a Good Guess

1.

Guess similar solutions to similar recurrences.

T(n) = 2T(n/2 + 42) + n

Guess: T(n) = O(nlgn)

2.

Narrow in on solution using loose upper and lower bounds.

$\Omega(n)$ $\longrightarrow$ $\Theta(nlgn)$ $\longleftarrow$ O(n²)

Problems: Lower-order terms may defeat mathematical induction of substitution method.