Merge branch 'master' of github.com:sagivo/algorithms

Author: sagivo

README.md

@@ -50,6 +50,7 @@ This is my way of saying - change your interview style. There are lots of smart
 | Suggest index of a number in an array | [click](https://github.com/sagivo/algorithms/blob/master/src/sugget_index_in_array.rb) |
 | [Range minimum query sparse table algorithm](http://en.wikipedia.org/wiki/Range_minimum_query) | [click](https://github.com/sagivo/algorithms/blob/master/src/rmq.rb) |
 | [Insertion Sort](https://en.wikipedia.org/wiki/Insertion_sort) | [click](https://github.com/sagivo/algorithms/blob/master/src/insertion_sort.rb) |
+| [Tarjan's strongly connected components finder](https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm) | [click](https://github.com/sagivo/algorithms/blob/master/src/tarjan.rb) |
 
 
 # How? 

src/count_and_say.rb

@@ -2,20 +2,20 @@
 # @return {String}
 def count_and_say(n)
  return "1" unless n > 1
- a = "1"; 
+ a = "1"
  (n-1).times do
  t = ''; last = nil; count = 0
- a.chars.each_with_index do |c,i|
+ a.chars.each do |c|
  if c == last or last.nil?
- count+=1
+ count +=1
  else
- t+= (count.to_s + last); 
+ t += count.to_s + last
  count = 1 
  end
  last = c
  end
- t += (count.to_s + last) if count > 0 
- a=t
+ t += count.to_s + last if count > 0 
+ a = t
  end
  return a
 end

src/powerset.rb

@@ -1,14 +1,12 @@
 #powerset - subset of set
-def powerset arr
- a = [[]] 
- for num in arr
- size_a = a.size; j = 0;
- while j < size_a
- a << (a[j] + [num])
- j+=1
+def powerset(arr)
+ result = [[]] 
+ arr.each do |num|
+ (0...arr.size).each do |j|
+ result << result[j] + [num]
  end
  end 
- a 
+ result
 end
 
-p powerset [1,2,3] #[[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
+p powerset [1,2,3] #[[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]

src/tarjan.rb

@@ -0,0 +1,175 @@
+class Node
+ attr_accessor :name, :idx, :lowlink, :on_stack
+
+ def initialize(name)
+ @name = name
+ end
+
+ def ==(other)
+ if other.class == Node
+ other.name == self.name
+ elsif other.class == String
+ other == self.name
+ else
+ false
+ end
+ end
+
+ def to_s
+ @name
+ end
+end
+
+class Edge
+ attr_accessor :from, :to
+
+ def initialize(node_from, node_to)
+ @from, @to = node_from, node_to
+ end
+
+ def ==(other)
+ self.from == other.from && self.to == other.to
+ end
+
+ def to_s
+ "(#{from.to_s} -> #{to.to_s})"
+ end
+end
+
+class Graph
+ attr_accessor :nodes, :edges, :adjmt
+
+ def initialize(load_dict = {})
+ @nodes = []
+ @edges = []
+ @adjmt = {}
+
+ if load_dict.size > 0 && load_dict.class == Hash
+ load_dict.each do |v, edges|
+ node_from = self.add_node(v)
+ adjmt[node_from] = []
+ edges.each do |w|
+ node_to = self.add_node(w)
+ adjmt[node_from] << node_to
+ self.add_edge(v, w)
+ end
+ end
+ end
+ end
+
+ def add_node(node_name)
+ if nodes.index(node_name)
+ return nodes[nodes.index(node_name)]
+ else
+ node = Node.new(node_name)
+ nodes << node
+ return node
+ end
+ end
+
+ def add_edge(node_name_from, node_name_to)
+ node_from = nodes[nodes.index(node_name_from)]
+ node_to = nodes[nodes.index(node_name_to)]
+ edges << Edge.new(node_from, node_to)
+ end
+end
+
+class Tarjan
+ attr_accessor :graph, :idx, :stack, :sccs
+
+ def initialize(graph)
+ if graph.class == Graph
+ @graph = graph
+ elsif graph.class == Hash
+ @graph = Graph.new(graph)
+ end
+
+ if graph != nil
+ @idx = 0
+ @stack = []
+
+ # Runs Tarjan
+ # Set all node index to None
+ self.graph.nodes.each do |v|
+ v.idx = nil
+ end
+
+ @sccs = []
+ self.graph.nodes.each do |v|
+ if v.idx == nil
+ self.strongconnect(v, sccs)
+ end
+ end
+ end
+ end
+
+ def strongconnect(v, sccs)
+ # Set the depth index for v to the smallest unused index
+ v.idx = self.idx
+ v.lowlink = self.idx
+ self.idx += 1
+ stack << v
+ v.on_stack = true
+
+ if graph.adjmt[v] != nil
+ # Consider successors of v
+ graph.adjmt[v].each do |w|
+ if w.idx == nil
+ # Successor w has not yet been visited; recurse on it
+ self.strongconnect(w, sccs)
+ v.lowlink = [v.lowlink, w.lowlink].min
+ elsif w.on_stack
+ # Successor w is in stack S and hence in the current SCC
+ # If w is not on stack, then (v, w) is a cross-edge in the DFS tree and must be ignored
+ # Note: The next line may look odd - but is correct.
+ # It says w.index not w.lowlink; that is deliberate and from the original paper
+ v.lowlink = [v.lowlink, w.idx].min
+ end
+ end
+ end
+ 
+ # If v is a root node, pop the stack and generate an SCC
+ if v.lowlink == v.idx
+ # start a new strongly connected component
+ scc = []
+ while true
+ w = stack.pop()
+ w.on_stack = false
+ scc << w
+ if w == v
+ break
+ end
+ end
+ sccs << scc
+ end
+ end
+end
+
+# Graph from https://en.wikipedia.org/wiki/File:Scc.png
+example = {
+ 'A' => ['B'],
+ 'B' => ['C', 'E', 'F'],
+ 'C' => ['D', 'G'],
+ 'D' => ['C', 'H'],
+ 'E' => ['A', 'F'],
+ 'F' => ['G'],
+ 'G' => ['F'],
+ 'H' => ['D', 'G']
+}
+
+g = Tarjan.new(example)
+print g.sccs.map{|scc| scc.map{|v| v.to_s}}.to_s + "\n"
+
+# Graph from https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm#/media/File:Tarjan%27s_Algorithm_Animation.gif
+example = {
+ 'A' => ['E'],
+ 'B' => ['A'],
+ 'C' => ['B', 'D'],
+ 'D' => ['C'],
+ 'E' => ['B'],
+ 'F' => ['B', 'E', 'G'],
+ 'G' => ['F', 'C'],
+ 'H' => ['G', 'H', 'D']
+}
+g = Tarjan.new(example)
+print g.sccs.map{|scc| scc.map{|v| v.to_s}}.to_s + "\n"