CSE 310-Lectures

# CSE 310-Lectures - C M L Click to edit Master subtitle...

This preview shows pages 1–8. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: C M L Click to edit Master subtitle style 10/22/10 C M L CSE 310 Algor ithms and Data Aviral Shrivastava Assistant Professor Computer Science and Engineering Arizona State University C M L 10/22/10 C M L H ow do we know • Consider a circle with n points on it. If I draw n chords in the circle, what is the maximum number of regions that will be created in the circle? C M L 10/22/10 C M L Conjectur e-based hit- Make a conjecture Try the conjecture on some examples Conjecture Works? NO YE S Think up a reasoning for the conjecture C M L 10/22/10 C M L Conjectur e • 0 chords & 1 region • 1 chord b 2 regions • 2 chords & 4 regions • 3 chords & 7 regions • 4 chords _ 11 regions +1 +2 +3 +4 r (n+1) = r (n) + n+1 C M L 10/22/10 C M L Reasoning • Suppose the number of regions is given by r(n) when there are n lines drawn in the circle. – Now draw one more line cutting all the other n lines. – There are n points on the additional line, and so this line must traverse n+1 of the available r(n) regions, dividing each into two parts. – It therefore adds n+1 more regions to those present. Thus r(n+1) = r(n) + n+1 C M L 10/22/10 C M L H ow do we know • Consider a circle with n points on it. How many regions will the circle be divided into if each pair of points is connected with a chord? 2 points 2 regions 3 points 4 regions 4 points 8 regions 5 points 16 regions C M L 10/22/10 C M L # of Regions if each pair of points • 1 point & 1 region • 2 points ¡ 2 regions • 3 points ¡ 4 regions • 4 points ¡ 8 regions r(n) = 2(n-1) C...
View Full Document

{[ snackBarMessage ]}

### Page1 / 21

CSE 310-Lectures - C M L Click to edit Master subtitle...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online