How to Write a Generalized String Reverse Function for All Localizations and String Types

What you're asking about is the Shortest Common Superstring problem, for which there is no algorithm that works for all cases. But it is a common problem (in compression and DNA sequencing) and several approximation algorithms are well-known.

"Greedy" algorithms are generally accepted to be the most effective (as in, they have the least-bad worst-case).

Have a read of the paper Approximation Algorithms for the Shortest Common Superstring Problem by Jonathan Turner for much more information.

The only difficulty is to find on which column a cell starts. Once you figure how to do that you can collect the cells for each column and output them as a row, exchanging colspan and rowspan. To find the starting colum you have to track what part of the table positions is used by previous cells. Each cell starts at the next available position.

I don’t know php, so I will use pseudocode.

The input is an array that gives for each row the list of variable-sized cells. The output is in the same format.

I will assume the table fills a rectangular area. If not, some padding with empty cells will be neessary in the output.

function reverse( table:array of array of cell ) 
{
  used = new array of array of boolean.
  output = new array of array of cell

  for r = 0 to table.size()-1 {
    // process row r
    c = 0;
    for each cell in table[r] {
      // skip to next position
      while used[r][c] { c++; }
      // cell starts at column c.  add it to the output
      cell2 = cell with rowspan and colspan values switched
      output[c].append(cell2)
      // mark used table positions (use 1 for missing rowspan/colspan)
      for i = 0 to cell.rowspan-1 {
        for j = 0 to cell.colspan-1 {
          used[r+i][c+j] = true;
        }
      }
    }
  }

  return output;
}

I hope you can translate it to php.