# Immutable Keyed Set

## Description

An immutable keyed set is a readonly collection of elements without duplicates or null values having each of the elements linked to exactly one key.

### Example

This simple example of an Exact Cover solution has a constraint set $$\\{ 1,2,3,4,5,6,7 \}\$$ covered by candidates $$\\{ B,D,F \}\$$.

• $$\B: \{ 1,4 \}\$$
• $$\D: \{ 3,5,6 \}\$$
• $$\F: \{ 2,7 \}\$$

This could be presented as an immutable keyed set. What's imperative is that each of the constraints $$\X\$$ only has 1 matching candidate $$\S\$$.

### Usage

[TestMethod]
public void Usage()
{
IReadOnlyKeyedSet<char, int> set = new ImmutableKeyedSet<char, int>(Data());
var sb = new StringBuilder();

foreach (var entry in set)
{
sb.AppendLine($"{entry.Key}: {string.Join(",", entry)}"); } var rendered = sb.ToString(); // B: 1,4 // D: 3,5,6 // F: 2,7 } private static IEnumerable<KeyValuePair<char, IEnumerable<int>>> Data() { yield return new KeyValuePair<char, IEnumerable<int>>('B', new[] { 1, 4 }); yield return new KeyValuePair<char, IEnumerable<int>>('D', new[] { 3, 5, 6 }); yield return new KeyValuePair<char, IEnumerable<int>>('F', new[] { 2, 7 }); }  The purpose is to guard against an invalid set. private static IEnumerable<KeyValuePair<char, IEnumerable<int>>> Data() { yield return new KeyValuePair<char, IEnumerable<int>>('B', new[] { 1, 2, 4 }); yield return new KeyValuePair<char, IEnumerable<int>>('D', new[] { 3, 5, 6 }); yield return new KeyValuePair<char, IEnumerable<int>>('F', new[] { 2, 7 }); }  The above should throw: "Duplicate value 2 on key F and B"  ## Code Interface IReadOnlyKeyedSet<TKey, TElement> public interface IReadOnlyKeyedSet<TKey, TElement> : ILookup<TKey, TElement> { IEqualityComparer<TKey> KeyComparer { get; } IEqualityComparer<TElement> ElementComparer { get; } bool ContainsValue(TElement value); bool TryGetValues(TKey key, out IEnumerable<TElement> values); bool TryGetKey(TElement value, out TKey key); }  Implementation ImmutableKeyedSet<TKey, TElement> public class ImmutableKeyedSet<TKey, TElement> : IReadOnlyKeyedSet<TKey, TElement> { private readonly Dictionary<TKey, Bucket> buckets; private readonly Dictionary<TElement, TKey> elements; public ImmutableKeyedSet( IEnumerable<KeyValuePair<TKey, IEnumerable<TElement>>> keyedSet, IEqualityComparer<TKey> keyComparer = null, IEqualityComparer<TElement> elementComparer = null) { KeyComparer = keyComparer ?? EqualityComparer<TKey>.Default; ElementComparer = elementComparer ?? EqualityComparer<TElement>.Default; buckets = new Dictionary<TKey, Bucket>(KeyComparer); elements = new Dictionary<TElement, TKey>(ElementComparer); Set(keyedSet ?? throw new ArgumentNullException(nameof(keyedSet))); } public IEqualityComparer<TKey> KeyComparer { get; } public IEqualityComparer<TElement> ElementComparer { get; } public IEnumerable<TElement> this[TKey key] => buckets[key]; public int Count => buckets.Count; public bool Contains(TKey key) => buckets.ContainsKey(key); public bool ContainsValue(TElement value) => elements.ContainsKey(value); public IEnumerator<IGrouping<TKey, TElement>> GetEnumerator() => buckets.Values.GetEnumerator(); IEnumerator IEnumerable.GetEnumerator() => GetEnumerator(); public bool TryGetValues(TKey key, out IEnumerable<TElement> values) { var bucket = FindBucketByKey(key); values = bucket == null ? default : bucket.Values; return bucket != null; } public bool TryGetKey(TElement value, out TKey key) { var bucket = FindBucketByValue(value); key = bucket == null ? default : bucket.Key; return bucket != null; } private Bucket FindBucketByValue(TElement value) { if (elements.TryGetValue(value, out var key)) { return buckets[key]; } return null; } private Bucket FindBucketByKey(TKey key) { if (buckets.TryGetValue(key, out var bucket)) { return bucket; } return null; } private void Set(IEnumerable<KeyValuePair<TKey, IEnumerable<TElement>>> keyedSet) { foreach (var entry in keyedSet) { var key = entry.Key; if (key == null) throw new ArgumentException("Key must be set"); var bucket = FindBucketByKey(key); if (bucket != null) { throw new InvalidOperationException($"Duplicate key {key}");
}
bucket = new Bucket(key);
if (entry.Value == null) throw new ArgumentException("Value must be set");
var values = new HashSet<TElement>(entry.Value);
foreach (var value in values)
{
if (value == null) throw new ArgumentException(
"Value must not contain null");
var valueBucket = FindBucketByValue(value);
if (valueBucket != null)
{
throw new InvalidOperationException(
\$"Duplicate value {value} on key {key} and {valueBucket.Key}");
}
bucket.Values.Add(value);
}
buckets.Add(key, bucket);
foreach (var value in values)
{
elements.Add(value, key);
}
}
}

class Bucket : IGrouping<TKey, TElement>
{
public TKey Key { get; }
public IEnumerator<TElement> GetEnumerator() => Values.GetEnumerator();
IEnumerator IEnumerable.GetEnumerator() => GetEnumerator();
internal ICollection<TElement> Values { get; }

internal Bucket(TKey key)
{
Key = key;
Values = new List<TElement>();
}
}
}


## Questions

• Is this a useful type of collection?
• Is this collection implementing immutability correctly?
• What's the concrete purpose / context to use that? – πάντα ῥεῖ Sep 7 '19 at 12:25
• @πάνταῥεῖ Any situation that requires a unique set of values, where the values are linked to a key. The way I would use it today, is to store the results of an Exact Cover Problem solution, to verify the solution is a correct keyed set. – dfhwze Sep 7 '19 at 12:27
• I think the Contains method should be renamed ContainsKey since (1) it calls buckets.ContainsKey and (2) there is also a ContainsValue method so the rename adds clarity. – Rick Davin Sep 7 '19 at 14:42
• @RickDavin You are right, that would take away any ambiguity. – dfhwze Sep 7 '19 at 14:50
• @RickDavin Unfortunately, Contains is part of the ILookup interface I'm implementing. – dfhwze Sep 7 '19 at 21:08

## 1 Answer

Just a couple of thoughts

• FindBucketByKey and FindBucketByValue should be implemented as TryGetSomething because you already are doing this anyway internally and what is most important, it would save you from a ton of null-checks all over the place. Nobody likes them.
• Set should be called Initialize
• This one is funny:
• if (x == null) + throw means do not use {} whereas
• if (x != null) + throw means use {} ;-)
• You should not initialize values with = new HashSet<TElement>(entry.Value); as this could change their order. Groupings don't do this so this behavior would be unexpected. You are also not using any other features of a HashSet as I find using Distict would be more appropriate and would maintain the order of values.
• Bucket would be easier to use and implement if it was derived from List<T>.
• Use more linq. You know I like linq so I when I see how Set is implemented I feel the same way as @VisualMelon when he sees tuples :-P. This is how I imagine this method doing its main job:

var result =
from x in Data()
from y in x.Value
group x.Key by y into g
select g;


This would give you groups for each element where you later could check whether any of the groups contains more than one element. With that, you could identify all duplicates and not only the first two and of course the implementation would become much simpler too. This would also be a lot more helpful as with multiple bugs you would need to run the code multiple time to discover every one of them.

• I didn't even notice my subconscious (consistent :p) handling of parenthesis there o_O – dfhwze Sep 8 '19 at 6:51
• Do you think this class could be useful as API or is it too specific for my use case? – dfhwze Sep 8 '19 at 6:58
• @dfhwze I think this is quite useful... for example it could be used as a command identifier and the values as its aliases or tags. Or in any other use case where there is a name and some aliases/tags. I've had a lot of them recently so I think I'll borrow form it. – t3chb0t Sep 8 '19 at 7:00