I have these relationships
User
 has_many :products
 has_many :stores
Product
 belongs_to :user
 belongs_to :store
 belongs_to :category
Store
 belongs_to :user
 has_many :products
Category
 acts_as_nested_set
 has_many :products
In the homepage( view file ) i have a category drop down similar to amazon's:
 <ul id="site-category-dropdown">
            <li class="has-dropdown">
                <a href="#">
                    <span class="site-category-dropdown-link-span">
                        <span class="line-1">SHOP BY</span>
                        <span class="line-2">Category</span>
                    </span>
                </a>
                <ul class="dropdown dropdown-box-shadow"> 
                    <% Category.all.each do |root_cat| %>
                        <li class="has-dropdown site-category-dropdown-element">
                            <a href="#" class="site-category-dropdown-element-link"> 
                                <span class="term"><%= root_cat.name %></span>
                            </a>
                                <ul class="dropdown">
                                    <% root_cat.children.each do |children| %>
                                        <li><%= link_to children.name, category_path(id: children.id) %></li>
                                    <% end %>
                            </ul>
                        </li>
                    <% end %>
                </ul>
            </li>
        </ul>
This looks something like the image below ( Root categories and their sub categories is shown on hover)

Now i'm on the store page, and i want to show a drop down similar to the site drop down but only for the products that are being sold by the store. 
Store products
Product 1 - (category_id: 46, store_id: 1, product_name: "Prada t-shirt")
Product 2 - (category_id: 47, store_id: 1, product_name: "Prada shoes")
Product 3 - (category_id: 47, store_id: 1, product_name: "Gucci shoes")
Product 4 - (category_id: 12, store_id: 1, product_name: "A classy Dining Table")
Product 5 - (category_id: 12, store_id: 1, product_name: "Kitchen stool")
Product 6 - (category_id: 12, store_id: 1, product_name: "Office Chair")
<br>
cateogory_id 46 is T-shirt in Fashion -> Men -> T-shirt
<br>
category_id 47 is Shoe in Fashion -> Men -> Shoe
<br>
category_id 12 is Furniture in Home -> Furniture
<br>
I'm using the awesome_nested_set gem for the categories (https://github.com/collectiveidea/awesome_nested_set)
i can map all the category_id in an array using:
category_ids = @store.products.map(&:category_id)
My question is, how can i build a drop down similar to the site drop down i showed above but only for products sold by this store. Remember the category_id for each products are the category ids for the leaf category, how do i recreate a drop down from the root categories? Using the store products I've given above, it should look something like this:
