Algorithm to convert a multi-dimensional array to a one-dimensional array

Question

It\'s easy enough to convert a 2-dimensional array to a single-dimensional array but how can I convert a multi-dimensional array of more than 2 dimensions to a one-dimension

Answer 1

You could do the following in C#.

public class ArrayIndexer
{
    private readonly int[] _bounds;
    private readonly int[] _sum;

    public ArrayIndexer(params int[] bounds)
    {
        _bounds = bounds;

        // Pre-compute bounds sums for speed.
        _sum = new int[bounds.Length - 1];
        for (int i = 1, sum = _bounds[i - 1]; i < _bounds.Length; ++i, sum *= _bounds[i - 1])
            _sum[i-1] = sum;
    }

    public T Index(T[] array, params int[] indices)
    {
        if (indices.Length != _bounds.Length)
            throw new ArgumentException("There should be as many indices as bounds", "indices");

        var index = indices[0];
        for (int i = 1, sum = _bounds[i - 1]; i < indices.Length; ++i, sum *= _bounds[i - 1])
            index += sum * indices[i];
        return array[index];
    }

    public T FastIndex(T[] array, params int[] indices)
    {
        if (indices.Length != _bounds.Length)
            throw new ArgumentException("There should be as many indices as bounds", "indices");

        var index = indices[0];
        for (int i = 1; i < indices.Length; ++i)
            index += _sum[i-1] * indices[i];
        return array[index];
    }
}

Or to transform into an n-dimensional array.

public static class ArrayExtensions
{
    public static Array CreateArray(this T[] array1d, params int[] bounds)
    {
        var arrayNd = Array.CreateInstance(typeof(T), bounds);

        var indices = new int[bounds.Length];
        for (var i = 0; i < array1d.Length; ++i)
        {
            arrayNd.SetValue(array1d[i], indices);

            for (int j = 0; j < bounds.Length; ++j)
            {
                if (++indices[j] < bounds[j])
                    break;
                indices[j] = 0;
            }
        }

        return arrayNd;
    }
}

And to test.

int[] array3d =
    new[]
    {
        0, 1, 2, 3,
        4, 5, 6, 7,
        8, 9, 10, 11,

        12, 13, 14, 15,
        16, 17, 18, 19,
        20, 21, 22, 23
    };

var copied3d = (int[, ,])array3d.CreateArray(4, 3, 2);
var indexer3d = new ArrayIndexer(4, 3, 2);

for (int i = 0; i < 4; ++i)
{
    for (int j = 0; j < 3; ++j)
    {
        for (int k = 0; k < 2; ++k)
        {
            var x = indexer3d.FastIndex(array3d, i, j, k);
            var y = copied3d[i, j, k];
            Debug.Print("Array[{0},{1},{2}] = {3} and {4} match = {5}", i, j, k, x, y, x == y);
        }
    }
}