Latest TCS Aptitude Question SOLUTION: 20.Given a collection of points P in the Plane, a 1-set is a point in P that can be seperated from the list from the line i.e the point lie each side of the line while the other l

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20.Given a collection of points P in the Plane, a 1-set is a point in P that can be seperated from the list from the line i.e the point lie each side of the line while the other lie on the othe side of the line.the no of 1-sets P is denoted by n1(P). The maximum value of n1(p) over all configarations of P of the 10 points in the P is 9,10,11,5

Solution

The meaning of this question is little complicated. In easy language the question should be:


There are some points in the plane. We have to make a separation between these points by forming a line in such a way that one point could be separate from the others. No 3 points are in a line. Maximum no of methods for plotting the line and minimum no of methods for plotting the line will be (arrangement of points is your choice)

Now Answer Is:

For Maximize: The number of methods, Points should be drawn in the circumference of the CIRCLE So answer would be the number of total point in the plane.

For minimize: The number of methods we should draw 3 points in a TRIANGLE and all other point inside this triangle in such a way that no 3 points could be in a line.

If it will be allowed to draw the points in a line then minimum possibilities will be 2 only, because if we take all points in a line then you can separate only the corner points from the others.

For example
If we have 10 points then maximum possibilities = 10
and minimum = 3

similarly for 5 points
Max = 5, Min = 3

for 19
max= 19 Min = 3


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Asked In TCS taru (12 years ago)

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Rohit kumar  (12 years ago)

answer is 10..
.for this type of questions...... in maximum value assume points to be on circle ... so the each point is non collinear and can be seprated by one line...

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