Divide by 3, function in C#

Question

I have a function that returns me list of int values depends on part of values:

private List<int> GetColumn(int total, int column)
{
    List<int> retList = new List<int>();

    if (total <= 0)
    {
        return retList;
    }

    if (column < 0 || column > 2)
    {
        column = 0;
    }

    int pageSize = total / 3;

    int startIndex = column * pageSize;
    int endIndex = column * pageSize + pageSize;

    if (endIndex > total)
    {
        endIndex = total;
    }

    for (int i = startIndex; i < endIndex; i++)
    {
        retList.Add(i);
    }

    return retList;

}

but it works wrong, because for: GetColumn(17, 0)

it returns [0,1,2,3,4], but should return [0,1,2,3,4,5]
for GetColumn(17, 1) - [6,7,8,9,10,11]
for GetColumn(17, 2) - [12,13,14,15,16]

for 16 it should return: for GetColumn(16, 0) - [0,1,2,3,4,5]
for GetColumn(16, 1) - [6,7,8,9,10]
for GetColumn(16, 2) - [11,12,13,14,15]

What should I change in my function? Thanks!

Answer 1

If this is what you need (numbers increase columnwise but rows need to be filled first):

for 16:
0  6  11
1  7  12
2  8  13
3  9  14
4  10 15
5

for 17:
0  6  12
1  7  13
2  8  14
3  9  15
4  10 16
5  11

You need to define which column is getting the remainders:

int remainder = total % 3;

if remainder is 1, only first column is 6 elements. if remainder is 2, first & second columns are 6 elements. You need to calculate startIndex and endIndex according to this.

So;

int pageSize = total / 3;
int remainder = total % 3;

int startIndex = column * pageSize + min(column, remainder);
int endIndex = startIndex + pageSize + (remainder > column ? 1 : 0);

should work. I just tested it, it works for different rowsizes than 3.

Here is how I got the formulas, drawing tables is good practice for sorting out such algortihms:

r:Remainder, c:column, ps:pagesize (as calculated above)

StartingIndex:
.  |r:0 |r:1   |r:2
----------------------
c:0|0   |0     |0
----------------------
c:1|ps  |ps+1  |ps+1
----------------------
c:2|ps*2|ps*2+1|ps*2+2

You can see a pattern if you extend the table for rowsize 4:

StartingIndex:
.  |r:0 |r:1   |r:2   |r:3
------------------------------
c:0|0   |0     |0     |0
------------------------------
c:1|ps  |ps+1  |ps+1  |ps+1
------------------------------
c:2|ps*2|ps*2+1|ps*2+2|ps*2+2
------------------------------
c:3|ps*3|ps*3+1|ps*3+2|ps*3+3

the value you are adding is the minimum of the related column and remainder

Similarly for the endIndex, desired columns length can be seen when you build a table for given remainder vs column. I won't write that for now because it is taking too much time to draw the tables here and I believe you already got the idea.

Answer 2

The integer division rounds to towards zero. So 17/3 = 5 and -17/3 = -5
I think what you want is to round to the next integer like this

int pageSize = (int)Math.Ceiling(total / 3d);

Answer 3

If I understand correctly the requirement is:

If the number is 3n,   divide it in 3 groups of n,   n   and n   elements.
If the number is 3n+1, divide it in 3 groups of n+1, n   and n   elements.
If the number is 3n+2, divide it in 3 groups of n+1, n+1 and n   elements.

Best thing to do is to make that explicit in your code, and avoid any "clever" logic. The straight-forward splitting boils down to:

If the number is 3n, the divisions are:
     0 ..  n-1
     n .. 2n-1
    2n .. 3n-1
If the number is 3n+1, the divisions are:
     0 .. n
   n+1 .. 2n
  2n+1 .. 3n
If the number is 3n+2, the divisions are:
     0 .. n
   n+1 .. 2n+1
  2n+2 .. 3n+1

In c# that would be something like:

public static List<int> Divide3Columns(int total, int column)
{
  int startIndex = 0;
  int endIndex = 0;
  int pageSize = total / 3;

  if (total % 3 == 0)
  {
    startIndex = column * pageSize;
    endIndex = (column + 1) * pageSize - 1;
  }

  if (total % 3 == 1)
  {
    if (column == 0)
    {
      startIndex = 0;
      endIndex = pageSize; //pageSize + 1 elements;
    }
    else
    {
      startIndex = column * pageSize + 1;
      endIndex = (column + 1) * pageSize;
    }
  }

  if (total % 3 == 2)
  {
    if (column == 2)
    {
      startIndex = 2 * pageSize + 2;
      endIndex = 3 * pageSize + 1; //same as total - 1;
    }
    else
    {
      startIndex = column * (pageSize + 1);
      endIndex = (column + 1) * pageSize + column;
    }
  }

  List<int> result = new List<int>();
  for (int i = startIndex; i <= endIndex; i++)
  {
    result.Add(i);
  }
  return result;
}

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The answer assumes that we will always divide in 3, and only 3 columns. If the number is variable, the logic to determine the columns can be generalized.