Pseudo-code for shelf-stacking

Question

Suppose I have some serially numbered items that are 1-n units wide, that need to be displayed in rows. Each row is m units wide. I need some pseudo-code that will output the rows, for me, so that the m-width limit is kept. This is not a knapsack problem, as the items must remain in serial number order - empty spaces at the end of rows are fine.

I've been chasing my tail over this, partly because I need it in both PHP and jQuery/javascript, hence the request for pseudo-code....

Answer 1

while (!items.isEmpty()) {
  rowRemain = m;
  rowContents = [];
  while (!items.isEmpty() && rowRemain > items[0].width) {
    i = items.shift();
    rowRemain -= i.width
    rowContents.push(i);
  }
  rows.push(rowContents);
}

Running time is Θ(number of items)

Answer 2

Modulus is your friend. I would do something like:

$items = array(/* Your list of stuff */);
$count = 0;
$maxUnitsPerRow = 4; // Your "m" above

while ($item = $items[$count]) {
 if ($count % $maxUnitsPerRow == 0) {
    $row = new row();
 }
$row->addItemToRow($item);
$count++;
}

Answer 3

For what it's worth, I think I have what I was looking for, for PHP - but not sure if there is a simpler way...

<?php
// working with just a simple array of widths...
$items     = array(1,1,1,2,1,1,2,1);
$row_width = 0;
$max_width = 2;

echo "Begin\n"; // begin first row
foreach($items as $item=>$item_width) {
  // can we add item_width to row without going over?
  $row_width += $item_width;
  if($row_width < $max_width) {
    echo "$item_width ";
  } else if($row_width == $max_width) {
    echo "$item_width";
    echo "\nEnd\nBegin\n"; // end last row, begin new row
    $row_width = 0;
  } else if($row_width == 2* $max_width) {
    echo "\nEnd\nBegin\n"; // end last row, begin new row
    echo "$item_width";
    echo "\nEnd\n"; // end new row
    $row_width = 0;
    if($item < count($items)) echo "Begin\n"; // new row
  } else if($row_width > $max_width) {
    echo "\nEnd\nBegin\n"; // end last row, begin new row
    echo "$item_width";
    $row_width = $item_width;
  }
}
echo "\nEnd\n"; // end last row

?>

Answer 4

Here is an alternative php code ...

function arrayMaxWidthString($items, $maxWidth) {
    $out = array();
    if (empty($items)) {
     return $out;
    }

    $row = $maxWidth;
    $i = 0;

    $item = array_shift($items);
    $row -= strlen($item);
    $out[0] = $item;

    foreach ($items as $item) {
     $l = strlen($item);
     $tmp = ($l + 1);
     if ($row >= $tmp) {
      $row -= $tmp;
      $out[$i] = (($row !== $maxWidth) ? $out[$i] . ' ' : '') . $item;
     } elseif ($row === $maxWidth) {
      $out[$i] = $item;
      ++$i;
     } else {
      ++$i;
      $row = $maxWidth - $l;
      $out[$i] = $item;
     }
    }
    return $out;
}