How to find connected components in an array

Question

I'm attempting an algorithm problem in hackerrank, Roads and Libraries . The idea behind the problem is to use DFS to find connected components (CC) using an array.

Here is the test case:

queries = [
  {
    n_cities_roads: [9,2],
    c_lib_road: [91, 84],
    matrix: [
      [8, 2], [2, 9]
    ]
  },
  {
    n_cities_roads: [5,9],
    c_lib_road: [92, 23],
    matrix: [
      [2,1], [5, 3], [5,1], 
      [3,4], [3,1],  [5, 4], 
      [4,1], [5,2],  [4,2]
    ]
  },
  {
    n_cities_roads: [8,3],
    c_lib_road: [10, 55],
    matrix: [
      [6,4], [3,2], [7,1]
    ]
  },
  {
    n_cities_roads: [1, 0],
    c_lib_road: [5, 3],
    matrix: []
  },

  {
    n_cities_roads: [2, 0],
    c_lib_road: [102, 1],
    matrix: []
  }
]

queries.each do |query|
  (n_city, n_road), (c_lib, c_road) = [*query[:n_cities_roads]], [*query[:c_lib_road]]
  roads_and_libraries n_city, c_lib, c_road, query[:matrix]
end

The output should be:

805
184
80
5
204

My current solution below can get CC for some cases, but not for all.

def dfs(i, visited, matrix)
  visited[i] = true
  unless matrix[i].nil?
    matrix[i].each do |j|
      unless visited[j]
        dfs j, visited, matrix
      end
    end
  end
end

def roads_and_libraries(no_cities, c_lib, c_road, cities)
  return c_lib * no_cities if c_lib <= c_road
  visited, count = Array.new(no_cities, false), 0

  (0..no_cities).each do |i|
    unless visited[i]
      count += 1
      dfs i, visited, cities
    end
  end
  p (c_road * (no_cities - count)) + (c_lib * count)
end

The output of the test with my code above is:

805
184
7
305

I'm struggling to understand how to use DFS correctly to find connected components. Not sure where I'm going wrong.

Answer 1

Just print this line:

p roads_and_libraries n_city, c_lib, c_road, query[:matrix]

Not this

p (c_road * (no_cities - count)) + (c_lib * count)

Because there is a return in the method:

return c_lib * no_cities if c_lib <= c_road

I don't know the algorithm, but it seems that the matrix can not be empty [] , at least it has to be [[1,1]] to get the required output:

roads_and_libraries 1, 5, 3, [[1,1]] #=> 5
roads_and_libraries 2, 102, 1, [[1,1]] #=> 204

So, to deal with empty matrix, one way is to just add this as first line in dfs method:

matrix = [[1,1]] if matrix.empty?