从索引组合计算索引

Question

I have a 2D list that might look something like this:

List<List<object>> myCategories;

Now each inner list is a list of options in a category. It's a jagged collection, so there might be 2 options in the first list and 4 in the second.

Now I'm transforming that into rows for each combination of categories so, in my example, I'd expect to end up with 2 * 4 = 8 rows in total. Which would be arranged like so:

Row | Cat 0    | Cat 1
 0  | Item 0_0 | Item 1_0
 1  | Item 0_0 | Item 1_1
 2  | Item 0_0 | Item 1_2
 3  | Item 0_0 | Item 1_3
 4  | Item 0_1 | Item 1_0
 5  | Item 0_1 | Item 1_1
 6  | Item 0_1 | Item 1_2
 7  | Item 0_1 | Item 1_3

Now what I'm struggling with is, given an array of indexes into each category, say [1,2] , the row I need would be 6 because that's where I have item 1 from category 0 and item 2 from category 1 .

I had something like this (where idx is a List<int> with my indexes):

var rowIdx = idx.Select((v, i) => new { v, i }).Aggregate(0, (c, n) =>
{
    c += n.v * Math.Max(1, myCategories.Skip(n.i + 1).Sum(a => a.Count));
    return c;
});

Which works great with 1 or 2 categories, but falls apart once you hit three categories. For example, if you have 4 , 1 and 1 as the Count of each category, and you are looking for the row corresponding to item 1 in category 0 (and obviously 0 and 0 in the other two, because there is only one choice), you end up with an index of 2 instead of 1 .

Here's a fiddle :

var categories = new List<List<object>>()
{
    new List<object>(){ null, null },
    new List<object>(){ null, null, null, null }
};

var idx = new List<int>() { 1, 2 };

var rowIdx = CalcIndex(categories,idx);

Console.WriteLine(rowIdx);      // outputs 6 as expected

categories = new List<List<object>>()
{
    new List<object>() { null, null, null, null },
    new List<object>() { null },
    new List<object>() { null }
};

idx = new List<int>() { 2, 0, 0 };

rowIdx = CalcIndex(categories,idx);

Console.WriteLine(rowIdx);      // should give 2, but gives 4 instead.

public static int CalcIndex(List<List<object>> categories, List<int> idx) 
{
    return idx.Select((v, i) => new { v, i }).Aggregate(0, (c, n) =>
    {
        c += n.v * Math.Max(1, categories.Skip(n.i + 1).Sum(a => a.Count));
        return c;
    });
}

Answer 1

As long as you know the lower (usually 0) and upper (usually n-1) bounds of each index range, you can call the correct "row" for an almost infinite amount of inidices:

sample: 4D list with sizes 2, 4, 6, 8.
GetRow (1,2,3,4) -> 1×4×6×8 + 2×6×8 + 3×8 + 4 (row numbering starting at 0)