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

static class Program
{
    static void Main(string[] args)
    {
        var ax = new[] { 
            new { id = 1, name = "John" },
            new { id = 2, name = "Sue" } };
        var bx = new[] { 
            new { id = 1, surname = "Doe" },
            new { id = 3, surname = "Smith" } };

        ax.FullOuterJoin(
                bx, a => a.id, b => b.id,
                (a, b, id) => new { a.name, b.surname },
                new { id = -1, name = "(no firstname)" },
                new { id = -2, surname = "(no surname)" }
            )
            .ToList().ForEach(Console.WriteLine);
    }
}

internal static class MyExtensions
{
    internal static IList<TR> FullOuterGroupJoin<TA, TB, TK, TR>(
        this IEnumerable<TA> a,
        IEnumerable<TB> b,
        Func<TA, TK> selectKeyA, 
        Func<TB, TK> selectKeyB,
        Func<IEnumerable<TA>, IEnumerable<TB>, TK, TR> projection,
        IEqualityComparer<TK> cmp = null)
    {
        cmp = cmp?? EqualityComparer<TK>.Default;
        var alookup = a.ToLookup(selectKeyA, cmp);
        var blookup = b.ToLookup(selectKeyB, cmp);

        var keys = new HashSet<TK>(alookup.Select(p => p.Key), cmp);
        keys.UnionWith(blookup.Select(p => p.Key));

        var join = from key in keys
                   let xa = alookup[key]
                   let xb = blookup[key]
                   select projection(xa, xb, key);

        return join.ToList();
    }

    internal static IList<TR> FullOuterJoin<TA, TB, TK, TR>(
        this IEnumerable<TA> a,
        IEnumerable<TB> b,
        Func<TA, TK> selectKeyA, 
        Func<TB, TK> selectKeyB,
        Func<TA, TB, TK, TR> projection,
        TA defaultA = default(TA), 
        TB defaultB = default(TB),
        IEqualityComparer<TK> cmp = null)
    {
        cmp = cmp?? EqualityComparer<TK>.Default;
        var alookup = a.ToLookup(selectKeyA, cmp);
        var blookup = b.ToLookup(selectKeyB, cmp);

        var keys = new HashSet<TK>(alookup.Select(p => p.Key), cmp);
        keys.UnionWith(blookup.Select(p => p.Key));

        var join = from key in keys
                   from xa in alookup[key].DefaultIfEmpty(defaultA)
                   from xb in blookup[key].DefaultIfEmpty(defaultB)
                   select projection(xa, xb, key);

        return join.ToList();
    }
}