I have the following flat tree:

id    name                        parent_id    is_directory
===========================================================
50    app                         0            1
31    controllers                 50           1
11    application_controller.rb   31           0
46    models                      50           1
12    test_controller.rb          31           0
31    test.rb                     46           0

and I am trying to figure out an algorithm for getting this into the following tree structuree:

[{
  id: 50,
  name: app,
  is_directory: true
  children: [{
    id: 31,
    name: controllers,
    is_directory: true,
    children: [{
      id: 11,
      name: application_controller.rb
      is_directory: false
    },{
      id: 12,
      name: test_controller.rb,
      is_directory: false
    }],
  },{
    id: 46,
    name: models,
    is_directory: true,
    children: [{
      id: 31,
      name: test.rb,
      is_directory: false
    }]
  }]
}]

Can someone point me in the right direction? I'm looking for steps (eg. build an associative array; loop through the array looking for x; etc.).