n cities [1, 2, 3, .... n] and
k available pumps. These pumps can be installed in
k cities. The cities are all in a straight line.
How do I need to install these so that the average distance between the cities and the nearest pumps is minimized?
What I am thinking is that dividing is this:
Suppose there are 6 cities
[C1, C2, C3, C4, C5, C6] and 3 pumps
[P1, P2, P3].
I divide the array of cities equally ->
[C1, C2] , [C2, C3] .. and then each block gets one pump.
Then again break that
[C1,C2] and let
C2 have the pump. Same way
So basically recursively calling and assigning the city a pump. Is this the right way to approach this problem?