Finding the optimum column and row size for a table with n elements and a given range for its proportion

Question

I am looking for an optimum way to create a table from n elements so that ideally there are no empty cells, but at the same time the proportion of the table dimensions columns /

Answer 1

Here is some pseudocode for how I've implemented something similarly:

int rowCount;
int colCount;

double tempSQR = SquareRoot(cellCount);
int maxRowCount = RoundAwayFromZero(tempSQR);

if(tempSQR == maxRowCount)
{
   rowCount = maxRowCount;
   colCount = rowCount;
}
else if(cellCount is Even)
{
   rowCount = Min(cellCount/2, maxRowCount);
   colCount = RoundAwayFromZero(cellCount/rowCount);
}
else if(cellCount> 1)
{
   rowCount = Min((cellCount+ 1)/2, maxRowCount);
   colCount = RoundAwayFromZero((cellCount+ 1)/rowCount);
}

if(rowCount * colCount < cellCount)
    rowCount++;

Answer 2

Instead of doing a prime factorization of n, start from the square root and find the next larger (or smaller -- makes no difference) factor. That pair of factors will the closest to the square root, and therefore the closest to a proportion of 1:1.