1. Three different solutions:
a.Substitution Method.
b.Recursion-Tree Method.
c.Master Method.
2.Substitution Method:Guess the form of the solution, then us mathematical induction to show that it is correct.
e.g.
3.How to make a good guess:
a. If a recurrence is similar to one seen before, then guess a similar solution.
e.g. T(n) = 3T(n/3 + 5) + n (Similar to T(n) = 3T(n/3) + n) we can guess O(n lg n).
b.Method 2: Prove loose upper and lower bounds on the recurrence and then reduce the range of uncertainty.
4.Changing Variables:use algebraic manipulation to turn an unknown recurrence into one similar to what you have seen before.
e.g.
5.Recursion-Tree Method
e.g.
6.Master Method