created method to find all paths between two nodes

Author: EvandroLG

data_structure/graph/graph.lua

@@ -59,6 +59,15 @@ function Graph:add_edge(edge)
   return true
 end
 
+function Graph:remove_edge(edge)
+end
+
+function Graph:remove_vertex(vertex)
+end
+
+function Graph:destroy()
+end
+
 function Graph:find_path(start_vertex, end_vertex, path)
   path = path or {}
   table.insert(path, start_vertex)
@@ -82,4 +91,31 @@ function Graph:find_path(start_vertex, end_vertex, path)
   return nil
 end
 
+function Graph:find_all_paths(start_vertex, end_vertex, path)
+  path = path or {}
+  table.insert(path, start_vertex)
+
+  if start_vertex == end_vertex then
+    return path
+  end
+
+  if self._graph[start_vertex] == nil then
+    return {}
+  end
+
+  paths = {}
+
+  for k, vertex in pairs(self._graph[start_vertex]) do
+    if not is_in_table(path, vertex) then
+      extended_path = self:find_all_paths(vertex, end_vertex, path)
+
+      for key, value in pairs(extended_path) do
+        table.insert(paths, value)
+      end
+    end
+  end
+
+  return paths
+end
+
 return Graph

data_structure/graph/test.lua

@@ -96,7 +96,7 @@ test('find complete path between two vertices', function()
     ['b'] = {'c'}
   })
 
-  path = graph:find_path('a', 'c')
+  local path = graph:find_path('a', 'c')
 
   assert_equal(#path, 3)
   assert_equal(path[1], 'a')
@@ -110,7 +110,15 @@ test('return nil when path between two vertices does not exist', function()
     ['b'] = {'c'}
   })
 
-  path = graph:find_path('a', 'd')
+  assert_equal(graph:find_path('a', 'd'), nil)
+end)
+
+test('return all paths between two vertices', function()
+  local graph = Graph:new({
+    ['a'] = {'b', 'c'},
+    ['b'] = {'d'},
+    ['c'] = {'d'}
+  })
 
-  assert_equal(path, nil)
+  --local paths = graph:find_all_paths('a', 'd')
 end)