How to perform merge sort using LINQ?

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There is no such method in LINQ. And I don’t think it’s possible to combine the existing methods to do exactly what you want (if it was, it would be overly complicated).

But implementing such method yourself isn’t that hard:

static IEnumerable<T> Merge<T>(this IEnumerable<T> first,
                               IEnumerable<T> second,
                               Func<T, T, bool> predicate)
{
    // validation ommited

    using (var firstEnumerator = first.GetEnumerator())
    using (var secondEnumerator = second.GetEnumerator())
    {
        bool firstCond = firstEnumerator.MoveNext();
        bool secondCond = secondEnumerator.MoveNext();

        while (firstCond && secondCond)
        {
            if (predicate(firstEnumerator.Current,  secondEnumerator.Current))
            {
                yield return firstEnumerator.Current;
                firstCond = firstEnumerator.MoveNext();
            }
            else
            {
                yield return secondEnumerator.Current;
                secondCond = secondEnumerator.MoveNext();
            }
        }

        while (firstCond)
        {
            yield return firstEnumerator.Current;
            firstCond = firstEnumerator.MoveNext();
        }

        while (secondCond)
        {
            yield return secondEnumerator.Current;
            secondCond = secondEnumerator.MoveNext();
        }
    }
}

And you could use it like this:

lst1.Merge(lst2, (i, j) => i < j)

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