Question

Today we got an assignment to complete in lab (in two hours). The question was:

• You’re given an m*n matrix.
• The matrix has ‘h’ residential halls and ‘b’ main building entrances.
• The location of these ‘h’ halls and ‘b’ entrances is known (in terms of (x,y) coordinates).
• You need to lay pathways such that every residential hall has at least one way to reach one of the ‘b’ entrances.
• There can be at most ‘b’ such disconnected pathways.
• The length of the pathway must be minimum.
• You can only move up, down, left or right.
• The solution must not be a brute force attempt.

The assignment is over. But I’m still thinking how this would be solved. Is there a standard term for such problems? What should I read up?

Do people use such algorithms to laying roads in cities as well?

Answer 1

Here’s a solution I came up with. It doesn’t generate ‘b’ disconnected paths. It generates one path that goes through all residential halls and entrances.

• Calculate the distance between each pair of nodes (difference of X coordinates + difference of Y coordinates). Now you have a complete graph.
• Find the MST for this complete graph
• Each inclined edge of the MST (those that are not vertical or horizontal) can be split into two parts – the horizontal and the vertical.
• Each split can be made in two ways – either horizontal first followed by vertical or vice versa.
• Go through each such permutation and calculate the path with the least length. This is the answer.