Divide & Conquer

Solving Recurrence Relations

Solution techniques:

•

Can sometimes change

variables to make it into a

simpler recurrence

•

Make a guess then prove the

guess correct by induction

•

Build a recursion tree and

use it to determine solution

•

The Master Method

–

A “cookbook” scheme that

handles many common

recurrences


To solve T(n) = aT(n/b) + f(n)

	compare f(n) with n^log^b^a

Solution is T(n) = f(n)

	if f(n) grows more rapidly

Solution is T(n) = n^log^b^a
	if n^log^b^a grows more rapidly

Solution is T(n) = f(n) log n

	if both grow at same rate

Not an exact statement of the

	theorem (see CLR)

CS409 - Spring 2000

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