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Suppose $n$ straight lines are drawn on a plane. When these lines are removed, the plane falls apart into several connected components called regions. $A$ region $R$ is said to be convex if it has the following property: whenever two points are in $R$, then the entire line segment joining them is in $R$. Suppose no two of the n lines are parallel. Which of the following is true?

  1. $O (n)$ regions are produced, and each region is convex.
  2. $O (n^{2})$ regions are produced but they need not all be convex.
  3. $O (n^{2})$ regions are produced, and each region is convex.
  4. $O (n \log n)$ regions are produced, but they need not all be convex.
  5. All regions are convex but there may be exponentially many of them.
in Numerical Ability by Boss (30.8k points)
edited by | 231 views

1 Answer

+1 vote
Option C must be correct.

Regions divided by n lines = 1+1+2+3+4+..........+n-1 = 1 + n(n-1)/2 = O(n^2)

option B can be easily discarded as convex segments are obvious.

Hence C is correct.
by (141 points)
edited by
how non-convex region is forming?

I think answer should be C..

sorry, my sloppy mistake.
all regions are convex.

Option C is correct.

(edited the answer)

No-convex regions are possible, isn't it?

Please correct me if i am wrong.



@Nitesh Tripathi I think region divided by n lines should be ---. n ( n + 1 ) / 2 + 1

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