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Combine Elements in a List based on Type and Summate their Values, LINQ

Given this structure..

I basically want to be able to take a list of items with multiple types, and create a new list that condenses down the sum of the values of each like-type. However the names of the types are dynamic (they may or may not have a specific order, and there is no finite list of them)

 using System.Linq;
using System.Collections.Generic;

class Item
{
    public ItemType Type;
    public int Value;

    public int Add(Item item)
    {
        return this.Value + item.Value;
    }
}

class ItemType
{
    public string Name;
}

class Test
{
    public static void Main()
    {
        List<ItemType> types = new List<ItemType>();
        types.Add(new ItemType { Name = "Type1" });
        types.Add(new ItemType { Name = "Type2" });
        types.Add(new ItemType { Name = "Type3" });

        List<Item> items = new List<Item>();

        for (int i = 0; i < 10; i++)
        {
            items.Add(new Item
            {
                Type = types.Single(t => t.Name == "Type1"),
                Value = 1
            });
        }

        for (int i = 0; i < 10; i++)
        {
            items.Add(new Item
            {
                Type = types.Single(t => t.Name == "Type2"),
                Value = 1
            });
        }

        for (int i = 0; i < 10; i++)
        {
            items.Add(new Item
            {
                Type = types.Single(t => t.Name == "Type3"),
                Value = 1
            });
        }

        List<Item> combined = new List<Item>();

        // create a list with 3 items, one of each 'type', with the sum of the total values of that type.
        // types included are not always known at runtime.
    }
}

Something like this should work. Warning: I didn't compile this.

items.GroupBy(i => i.Name)
   .Select(g => new Item { Type= g.First().Name, Value = g.Sum(i => i.Value)})
   .ToList()

It seems to me like you are trying to get a list of Types along with their count (since Value will always be 1 in your example). Below is some code that should do this:

from i in items
group i by i.Type into t
select new { t.Key, TypeCount = t.Count() }

This would return 3 objects (displayed in table form below):

Type      TypeCount
--------  ---------
Type1     10
Type2     10
Type3     10

If value is always going to be one then I believe it's the same as just getting the count.

List<Item> combined = items.GroupBy(i => i.Type).Select(g => new Item { Type = g.Key, Value = g.Sum(i => i.Value) }).ToList();
var itemsByType = items.ToLookup(i => i.Type);
var sums = from g in itemsByType
           select new Item {
               Type = g.Key,
               Value = g.Sum(i => i.Value)
           };
var sumList = sums.ToList();

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