Algorithm Details

Write an algorithm in the language of your choice to transform the JSON input below into the JSON output. Each child should be placed in the children array of its parent (as defined by the parent_id).

Input

{"0":
  [{"id": 10,
    "title": "House",
    "level": 0,
    "children": [],
    "parent_id": null
    }
  ],
 "1":
  [{"id": 12,
    "title": "Red Roof",
    "level": 1,
    "children": [],
    "parent_id": 10},
   {"id": 18,
    "title": "Blue Roof",
    "level": 1,
    "children": [],
    "parent_id": 10},
   {"id": 13,
    "title": "Wall",
    "level": 1,
    "children": [],
    "parent_id": 10}
  ],
 "2":
  [{"id": 17,
    "title": "Blue Window",
    "level": 2,
    "children": [],
    "parent_id": 12},
   {"id": 16,
    "title": "Door",
    "level": 2,
    "children": [],
    "parent_id": 13},
   {"id": 15,
    "title": "Red Window",
    "level": 2,
    "children": [],
    "parent_id": 12
    }
  ]
}

Output

[{"id": 10,
  "title": "House",
  "level": 0,
  "children":
   [{"id": 12,
     "title": "Red Roof",
     "level": 1,
     "children":
      [{"id": 17,
        "title": "Blue Window",
        "level": 2,
        "children": [],
        "parent_id": 12},
       {"id": 15,
        "title": "Red Window",
        "level": 2,
        "children": [],
        "parent_id": 12}],
     "parent_id": 10},
    {"id": 18,
     "title": "Blue Roof",
     "level": 1,
     "children": [],
     "parent_id": 10},
    {"id": 13,
     "title": "Wall",
     "level": 1,
     "children":
      [{"id": 16,
        "title": "Door",
        "level": 2,
        "children": [],
        "parent_id": 13}],
     "parent_id": 10}],
  "parent_id": null}]