Module: Graphos::Algorithm

Includes:
Containers
Defined in:
lib/graphos/algorithm/prim.rb,
lib/graphos/algorithm/dijkstra.rb

Class Method Summary collapse

Class Method Details

.dijkstra(graph, initial) ⇒ Object

Runs the dijstra algorithm on a given graph at a starting node This uses a Heap to get the lightest edge



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# File 'lib/graphos/algorithm/dijkstra.rb', line 10

def self.dijkstra graph, initial
  #OK? E o path?
  fathers = Array.new(graph.size)

  #os paf
  allPaths = Array.new(graph.size)

  #OK #dist[v] = infinito
  costs = Array.new(graph.size, Float::INFINITY)
  #dist[s] = 0
  costs[initial] = 0

  #OK
  heap = Heap.new{|x,y| (costs[x] <=> costs[y]) == -1}
  (0...graph.size).each{|i| heap.push(i)}

  update_cost = -> (idx,cost) do
    costs[idx] = cost
    heap.change_key(idx,idx)
  end


  #Para cada vértice v
  #enquanto heap (S-V) != 0
  while idx=heap.pop
    #Selecione u em V-S, tal que dist[u] é mínima
    u = graph[idx]
    distu = costs[idx]
    allPaths[idx] ||= Path.new
    #Para cada vizinho v (edge.to) de u faça
    u.edges.each do |edge|
      #Se dist[v] > dist[u] + w(u,v) então
      if costs[edge.to.index] > distu + edge.weight
        #dist[v] = dist[u] + w(u,v)
        fathers[edge.to.index] = u.index
        update_cost.call(edge.to.index, distu + edge.weight)
        #criar o Path entre root e v
        #se existe já, tem q atualizar. O novo é o do pai + ele msm
        allPaths[edge.to.index] = allPaths[u.index] + Path.new(edge)
      end
    end
  end

  allPaths
end

.prim(graph, initial) ⇒ Object

Runs the prim algorithm in order to find a MST for a given graph.



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# File 'lib/graphos/algorithm/prim.rb', line 10

def self.prim graph, initial
  fathers = Array.new(graph.size)

  costs = Array.new(graph.size, Float::INFINITY)
  costs[initial] = 0

  heap = Heap.new{|x,y| (costs[x] <=> costs[y]) == -1}
  (0..graph.size-1).each{|i| heap.push(i)}

  update_cost = -> (idx,cost) do
    costs[idx] = cost
    heap.change_key(idx,idx)
  end

  while idx=heap.pop
    node = graph[idx]
    node.edges.each do |edge|
      if costs[edge.to.index] > edge.weight
        fathers[edge.to.index] = node.index
        update_cost.call(edge.to.index, edge.weight)
      end
    end
  end

  result = Weighted::Graph.new graph.size
  fathers.each_with_index do |f,c|
    if f
      result.add_edge(f, c, costs[c])
    end
  end
  result
end