MongoDB：向具有父引用的模型树结构中组织的文档添加字段

Question

我正在使用带有父引用的模型树结构，如下所示：

{
    "_id" : "YezvuyCowZdo2ZLgX",
    "title" : "Main",
    "type" : "section",
}
{
    "_id" : "eYkxs8rW3dKH5SfoE",
    "title" : "element 1",
    "order" : 1,
    "type" : "element",
    "parent" : "YezvuyCowZdo2ZLgX"
}
{
    "_id" : "siaRPzaTgDrfWZ7kn",
    "title" : "subelement 1",
    "order" : 1,
    "type" : "element",
    "parent" : "ASkJZSkPAj8mhb7An"
}
{
    "_id" : "DrfWZ7knsiaRPzaTg",
    "title" : "subelement 2",
    "order" : 2,
    "type" : "element",
    "parent" : "ASkJZSkPAj8mhb7An"
}
{
    "_id" : "XZF9hpW8ZqTnRdkEg",
    "title" : "element 2",
    "order" : 3,
    "type" : "element",
    "parent" : "YezvuyCowZdo2ZLgX"
}
{
    "_id" : "ASkJZSkPAj8mhb7An",
    "title" : "group 1",
    "type" : "group",
    "parent" : "YezvuyCowZdo2ZLgX",
    "order" : 2
}

但现在我需要的信息是＆＃39;等级＆＃39;一个元素属于。如何获得包含此信息的新字段？

eYkxs8rW3dKH5SfoE -> add field { level: 1 }
siaRPzaTgDrfWZ7kn -> add field { level: 2 }
DrfWZ7knsiaRPzaTg -> add field { level: 2 }
XZF9hpW8ZqTnRdkEg -> add field { level: 1 }
ASkJZSkPAj8mhb7An -> add field { level: 1 }

所以我想我必须为所有主要元素执行每个循环，从{ type: 'section'}开始。

Collection.find({ type: 'section'}).each(function(doc) {
    Collection.update({ parent: doc._id }, { $set: { level: 1 }});
    // go to next subelement and increase level until there is no child
});

但是如何通过树来设置所有级别？