Combining two items (recipe-like) - actionscript-3

Question

I'd like a user to be able to combine two items and if compatible will yield a new item. In this example, the item IDs will be saved as Strings.
I was wondering what the most efficient way to do this would be, while making sure that swapped order will always yield the same result, so the user could input the order:
item X + item Y = item Z
item Y + item X = item Z
I've tried using Dictionaries and Objects, but I just haven't been able to get anything to work. I've also tried some various libraries that include HashMap/HashSet but nothing is working. here's some pseduo-code:
itemRecipe1:HashSet = new HashSet();
itemRecipe1.add("2");//Add item with ID of 2
itemRecipe1.add("3");//Add item with ID of 3
inputRecipe:HashSet = new HashSet();
inputRecipe.add("3");//Add item with ID of 3 (swapped)
inputRecipe.add("2");//Add item with ID of 2 (swapped)
recipeList:HashMap = new HashMap();
receipeList.put(itemRecipe1, "11");//Recipe has been added, the result of the recipe should be item 11
//This should output as TRUE since the composition of itemRecipe1 and inputRecipe are the same, despite a different input order.
trace(receipeList.containsKey(inputRecipe));
If anyone has a solution for this issue, please elt me know as I am willing to implement any design I can get working. I just don't see how a Dictionary could work as the key order matters.

Answer 1

So you're trying to associate two or more objects with each other. The first thing you need is some primitive data you can use to represent each item uniquely, typically an ID. This should give you something like the following to begin with:
class Item {
public var _id:int;
public function Item(id:int) {
_id = id;
}
public function get id():int { return _id; }
}
Now you need some piece of data that establishes a relationship between multiple Items using this ID. That could be as simple as the following, with a little extra functionality thrown in to see if an input list of these IDs matches the relationship:
class ItemRelationship {
private var _items:Vector.<Item>;
public function ItemRelationship(items:Vector.<Item>) {
_items = items;
}
public function matches(ids:Vector.<int>):Boolean {
if (_items.length !== ids.length) {
return false;
}
for each (var item:Item in _items) {
var found:Boolean = false;
for each (var id:int in ids) {
if (item.id === id) {
found = true;
break;
}
}
if (!found) return false;
}
return true;
}
public function get items():Vector.<Item> { return _items; }
}
This lets us do something like this, assuming we have a bunch of items (item1, item2, ...) with IDs.
var rel:ItemRelationship = new ItemRelationship(new <Item>[item1, item2]);
And then:
trace(rel.matches(new <int>[1,2])); // true
trace(rel.matches(new <int>[2,1])); // true
trace(rel.matches(new <int>[3,4])); // false
Now all we need is something that stores all of these relationships and lets us fetch one based on a list of input IDs:
class RelationshipCollection {
private var _relationships:Vector.<ItemRelationship>;
public function RelationshipCollection(relationships:Vector.<ItemRelationship>) {
_relationships = relationships;
}
public function find(ids:Vector.<int>):ItemRelationship {
for each(var relationship:ItemRelationship in _relationships) {
if (relationship.matches(ids)) return relationship;
}
return null;
}
}
Put a load of relationships in there:
var collection:RelationshipCollection = new RelationshipCollection(new <ItemRelationship>[
new ItemRelationship(new <Item>[item1, item4]),
new ItemRelationship(new <Item>[item2, item3])
]);
And give it a whirl:
trace(collection.find(new <int>[1, 3])); // null (no match)
trace(collection.find(new <int>[1, 4])); // works
trace(collection.find(new <int>[3, 2])); // works
trace(collection.find(new <int>[2, 3])); // works
Of course for the sake of readability you can rename each class to something more appropriate for its application e.g. Item => Potion, ItemRelationship => Recipe, RelationshipCollection => RecipeBook.

Answer 2

so the user could input the order
The first step is to limit the possible input. If you allow any type of input, you have to parse that input and things get complicated very quickly.
Create an input method that only allows the user to put two items together, say for example via drag and drop of the items to only 2 slots.
I just don't see how a Dictionary could work as the key order matters.
The important part is to design the keys well.
As #George Profenza pointed out in the comments, you could change your IDs to a different format. Instead of having 1, 2, 3, ... n you could use 1, 2, 4, ... 2^n. The advantage is that you can combine any two IDs uniquely via bitwise or operator (|). In the following example, two such IDs are combined (binary notation):
00001
| 10000
--------
10001
As you can see, each ID occupies a separate position in binary: the 1st position and the 5th. Combining both via or operator means that now both 1st and 5th position are 1. The order doesn't matter. If you use such IDs in the form of powers of 2 you can combine them regardless of the order to form pairs, which can then be used as keys to a dictionary.
Another solution is to simply sort the pair of IDs.
The combination 3-2 becomes 2-3 and the combination 2-3 stays 2-3. Both 2-3 and 3-2 lead to the same result.
You can then build your data structure accordingly, that is: the outer data structure is for the lower ID number and the nested, inner one is for the bigger ID number. Here's some pseudo code with generic objects:
var map:Object = {};
map["2"] = {"3":"combination 2-3"};
To access that, you'd do something like:
trace(map[Math.min(ID1, ID2)][Math.max(ID1, ID2)])
There's also the brute force way of doing it by storing both possible combinations in the data structure. The code for that could roughly look like that:
var map:Object = {};
map["2"] = {"3":"combination 2-3"};
map["3"] = {"2":"combination 2-3"};
Now both
trace(map[ID1][ID2]);
and
trace(map[ID2][ID1]);
Should yield the same result.