lec0418 - CS 173 Discrete Mathematical Structures Cinda...

This preview shows pages 1–9. Sign up to view the full content.

CS 173: Discrete Mathematical Structures Cinda Heeren [email protected] Siebel Center, rm 2213 Office Hours: BY APPOINTMENT

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Cs173 - Spring 2004 CS 173 Announcements Hwk #10 available, due 4/16, 8a Final Exam:  5/10, 7-10p, Siebel 1404
Cs173 - Spring 2004 CS 173 Divide and Conquer Recurrences General form: T(n) = aT(n/b) + f(n) What do the algorithms look like? Divide the problem into a subproblems of size n/b. Solve those subproblems (recursively). Conquer the solution in time f(n). We understand how abstract this is.  Some of  us think cs125 should be a prerequisite for  this course. The only algorithms you have as examples are  mergesort and binary search.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Cs173 - Spring 2004 CS 173 Divide and Conquer Recurrences General form: T(n) = aT(n/b) + f(n) To solve a problem of size n, we require time f(n), plus the time it takes to  solve a subproblems of size n/b. We don’t have simple recipes for solving these  in all cases, though sometimes we do… f(n) a f(n/b) a f(n/b) a f(n/b) a f(n/b) a f(n/b 2 ) a f(n/b 2 ) f(n/b 2 ) Total running time is sum of the values in the  pink rectangles.
Cs173 - Spring 2004 CS 173 Divide and Conquer Recurrences General form: T(n) = aT(n/b) + f(n) f(n) a f(n/b) a f(n/b) a f(n/b) a f(n/b) a f(n/b 2 ) a f(n/b 2 ) f(n/b 2 ) Sum over levels… How many? a) n b) b c) log b n d) no clue    ι=0 λογ β ν

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Cs173 - Spring 2004 CS 173 Divide and Conquer Recurrences General form: T(n) = aT(n/b) + f(n) f(n) a f(n/b) a f(n/b) a f(n/b) a f(n/b) a f(n/b 2 ) a f(n/b 2 ) f(n/b 2 ) How many blocks at level  i? a) a b) a i c) i∙a d) no clue    ι=0 λογ β ν    α ι φ (?)
Cs173 - Spring 2004 CS 173 Divide and Conquer Recurrences General form: T(n) = aT(n/b) + f(n) f(n) a f(n/b) a f(n/b) a f(n/b) a f(n/b) a f(n/b 2 ) a f(n/b 2 ) f(n/b 2 ) ? a) n/b i b) n log b c) i∙b d) no clue    ι=0 λογ β ν    α ι φ (?)    α ι φ ( n b i )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Cs173 - Spring 2004 CS 173 Divide and Conquer Recurrences General form: T(n) = aT(n/b) + f(n)    ι=0 λογ β ν    α ι φ ( n b i ) We no longer have recursive terms, but  we do have a sum to deal with. Consider binary search, and write a recurrence for the # of  comparisons:  T(n) = T(n/2) + 1 a = 1, b = 2, f(n) = 1.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern