Recurrence

最新推荐文章于 2021-02-05 16:37:09 发布

尧尧1988

最新推荐文章于 2021-02-05 16:37:09 发布

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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

In this method, we draw a recurrence tree and calculate the time taken by every level of tree. Finally, we sum the work done at all levels. To draw the recurrence tree, we start from the given recurrence and keep drawing till we find a pattern among levels. The pattern is typically a arithmetic or geometric series.