Mapping a flat list to a hierarchical list with parent IDs C#

Question

I have a flat list of categories as shown in the following classes

public class FlatCategoryList
{
    public List<FlatCategory> Categories { get; set; }
}
public class FlatCategory
{
    public string ID { get; set; }
    public string Name { get; set; }
    public string ParentID { get; set; }
}

I'm trying to map my flat list of categories to a heirarical structure such as shown below:

public class HieraricalCategoryList
{
    public List<Category> Categories { get; set; }
}
public class Category
{
    public string ID { get; set; }
    public string Name { get; set; }
    public string ParentID { get; set; }

    public List<Category> ChildCategories { get; set; }
}

My question is, what is the best way to achieve this, given the fact that there could be an infinite number child tiers?

public HieraricalCategoryList MapCategories(FlatCategoryList flatCategoryList)
{
    var hieraricalCategoryList = new HieraricalCategoryList();

    //Do something here to map the flat category list to the hierarichal one...

    return hieraricalCategoryList;
}

Answer 1

public HieraricalCategoryList MapCategories(FlatCategoryList flatCategoryList)
{
    var categories = (from fc in flatCategoryList.Categories
                      select new Category() {
                          ID = fc.ID,
                          Name = fc.Name,
                          ParentID = fc.ParentID
                      }).ToList();

    var lookup = categories.ToLookup(c => c.ParentID);

    foreach(var c in categories)
    {
        // you can skip the check if you want an empty list instead of null
        // when there is no children
        if(lookup.Contains(c.ID))
            c.ChildCategories = lookup[c.ID].ToList();
    }

    return new HieraricalCategoryList() { Categories = categories };
}