In a city there are n number of gas stations. A gas pipleline from government has to pass right
through (vertically only) the city. You have to create an algorithm which tells you the best place
the pipe line should pass and cost to government is minimum. Cost is always propotional to the distance
from gas station to pipeline.
Silly me, it took so much time to answer this one.
Okie i am posting my answer....
Sort the points for X axis...take a median of them. That will be the line x=c.
Lets say there are n points.
case 1: n is odd. So there will be a single point for median. say i.
Distance between a point from pipeline is abs(x1-xi).
As there are odd points so except the median, all the points will form a pair.
Between a pair of points if we move the pipeline between them, effective
distance from pipeline will remain constant.
So if median of x-axis value our pipeline is passing then effective distance
will be same till for all the pair of points on its two different sides.
P1 . P2
P1 . P2
P1 . P2
See for the above case total distance will be same pipeline passing between them
As we took median so for all the points that will make it constanst distance and minimum too.
Case 2: if n is even.
SO we can take any point in between the two median points and distance will be still same. Above appiles here again and make it minimum distance.
through (vertically only) the city. You have to create an algorithm which tells you the best place
the pipe line should pass and cost to government is minimum. Cost is always propotional to the distance
from gas station to pipeline.
Silly me, it took so much time to answer this one.
Okie i am posting my answer....
Sort the points for X axis...take a median of them. That will be the line x=c.
Lets say there are n points.
case 1: n is odd. So there will be a single point for median. say i.
Distance between a point from pipeline is abs(x1-xi).
As there are odd points so except the median, all the points will form a pair.
Between a pair of points if we move the pipeline between them, effective
distance from pipeline will remain constant.
So if median of x-axis value our pipeline is passing then effective distance
will be same till for all the pair of points on its two different sides.
P1 . P2
P1 . P2
P1 . P2
See for the above case total distance will be same pipeline passing between them
As we took median so for all the points that will make it constanst distance and minimum too.
Case 2: if n is even.
SO we can take any point in between the two median points and distance will be still same. Above appiles here again and make it minimum distance.
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