A project to build a new railroad along a county road needs to decide on the locations of the train stations to be constructed. Along the county road there are multiple towns, with their location known (assume the road to be a straight line, with mile marker 0 at the state line, with town locations marked along the way). Design an algorithm that decides at which locations to build train stations along the route with the constraints that: 1) each town must be within a distance D from a train station and 2) a minimum number of train stations are built. Example: Consider a scenario where D = 1 and towns are located at coordinates 0, 2, 3, 4, and 5. An optimal solution would be to place train stations at locations 1 and 4, which would cover all the towns. Note: to prove that your greedy strategy yields the optimal solution, you have to prove that
A project to build a new railroad along a county road needs to decide on the locations of
the train stations to be constructed. Along the county road there are multiple towns, with
their location known (assume the road to be a straight line, with mile marker 0 at the state
line, with town locations marked along the way). Design an
locations to build train stations along the route with the constraints that: 1) each town must
be within a distance D from a train station and 2) a minimum number of train stations are
built.
Example: Consider a scenario where D = 1 and towns are located at coordinates 0, 2, 3, 4,
and 5. An optimal solution would be to place train stations at locations 1 and 4, which
would cover all the towns.
Note: to prove that your greedy strategy yields the optimal solution, you have to prove that
the problem has the greedy-choice property.
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