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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 ebased 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(n1) C...
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 Spring '08
 Davulcu,H
 Computer Science, Algorithms, Data Structures

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