Align multiple sorted lists

Question

If I have, for example the following List<int>s

{ 1, 2, 3, 4 } //list1
{ 2, 3, 5, 6 } //list2
...
{ 3, 4, 5 }    //listN

What is the best way to retrieve the following corresponding List<int?>s?

{    1, 2,    3,    4,    null, null } //list1
{ null, 2,    3,    null, 5,    6    } //list2
...
{ null, null, 3,    4,    5,    null } //listN

Answer 1

I'm posting the solution we discussed in chat. I had an unoptimized version using Linq for all things loopy/filtering:

• http://ideone.com/H4gCoE (live demo)

However, I suspect it won't be too performant because of all the enumerator classes created, and the collections being instantiated/modified along the way.

So I took the time to optimize it into handwritten loops with an administration to keep track of active iterators instead of modifying the iters collection. Here it is:

See http://ideone.com/FuZIDy for full live demo.

Note I assume the lists are pre-ordered by DefaultComparer<T>, since I use Linq'sMin() extension method without a custom comparer

public static IEnumerable<IEnumerable<T>> AlignSequences<T>(this IEnumerable<IEnumerable<T>> sequences)
{
    var iters = sequences
        .Select((s, index) => new { active=true, index, enumerator = s.GetEnumerator() })
        .ToArray();

    var isActive = iters.Select(it => it.enumerator.MoveNext()).ToArray();
    var numactive = isActive.Count(flag => flag);

    try
    {
        while (numactive > 0)
        {
            T min = iters
                .Where(it => isActive[it.index])
                .Min(it => it.enumerator.Current);

            var row = new T[iters.Count()];

            for (int j = 0; j < isActive.Length; j++)
            {
                if (!isActive[j] || !Equals(iters[j].enumerator.Current, min)) 
                    continue;

                row[j] = min;
                if (!iters[j].enumerator.MoveNext())
                {
                    isActive[j] = false;
                    numactive -= 1;
                }
            }
            yield return row;
        }
    }
    finally
    {
        foreach (var iter in iters) iter.enumerator.Dispose();
    }
}

Use it like this:

public static void Main(string[] args)
{
    var list1 = new int?[] { 1, 2, 3, 4, 5 };
    var list2 = new int?[] { 3, 4, 5, 6, 7 };
    var list3 = new int?[] { 6, 9, 9 };

    var lockstep = AlignSequences(new[] { list1, list2, list3 });

    foreach (var step in lockstep)
        Console.WriteLine(string.Join("\t", step.Select(i => i.HasValue ? i.Value.ToString() : "null").ToArray()));
}

It prints (for demo purposes I print the results sideways):

1       null    null
2       null    null
3       3       null
4       4       null
5       5       null
null    6       6
null    7       null
null    null    9
null    null    9

Note: You might like to change the interface to accept arbitrary number of lists, instead of a single sequence of sequences:

public static IEnumerable<IEnumerable<T>> AlignSequences<T>(params IEnumerable<T>[] sequences)

That way you could just call

var lockstep = AlignSequences(list1, list2, list3);

Answer 2

Here's another approach using List.BinarySearch.

sample data:

var list1 = new List<int>() { 1, 2, 3, 4 };
var list2 = new List<int>() { 2, 3, 5, 6, 7, 8 }; 
var list3 = new List<int>() { 3, 4, 5 };
var all   = new List<List<int>>() { list1, list2, list3 };

calculate min/max and all nullable-lists:

int min = all.Min(l => l.Min());
int max = all.Max(l => l.Max());
// start from smallest number and end with highest, fill all between
int count = max - min + 1;  

List<int?> l1Result = new List<int?>(count);
List<int?> l2Result = new List<int?>(count);
List<int?> l3Result = new List<int?>(count);

foreach (int val in Enumerable.Range(min, count))
{
    if (list1.BinarySearch(val) >= 0)
        l1Result.Add(val);
    else
        l1Result.Add(new Nullable<int>());

    if (list2.BinarySearch(val) >= 0)
        l2Result.Add(val);
    else
        l2Result.Add(new Nullable<int>());

    if (list3.BinarySearch(val) >= 0)
        l3Result.Add(val);
    else
        l3Result.Add(new Nullable<int>());
}

output:

Console.WriteLine(string.Join(",", l1Result.Select(i => !i.HasValue ? "NULL" : i.Value.ToString())));
Console.WriteLine(string.Join(",", l2Result.Select(i => !i.HasValue ? "NULL" : i.Value.ToString())));
Console.WriteLine(string.Join(",", l3Result.Select(i => !i.HasValue ? "NULL" : i.Value.ToString())));

1,      2,      3,      4,      NULL,   NULL,   NULL,   NULL
NULL,   2,      3,      NULL,   5,      6,      7,      8
NULL,   NULL,   3,      4,      5,      NULL,   NULL,   NULL

DEMO