如果没有其他的话，如何将序列号从水平转换为垂直？

Question

I am working on a web-page for my company about an on-line survey page, our customer service team will simply input some check-box questions into a database. and my job is to display them on a page and gather the player's answers back to our database.

for example if I have 12 questions in the database, and I need it to be displayed in a table as:

1 5 9
2 6 10
3 7 11
4 8 12

or, if I have 13 questions, it should be displayed as
1 6 10
2 7 11
3 8 12
4 9 13
5

this can be done with some if else in PHP, but i would like to do it in mathematical ways just to enrich my knowledge.

any suggestion or hints are appreciate if I can pass the total questions(in this case 13) and vertical column counts(in this case 3) in a formula, and it simply return the orders of the numbers in this way {1, 6, 10, 2, 7, 11, 3, 8, 12, 4, 9, 13, 5}

honestly, I will not rewrite the survey page. I am just curious if this can be done with some math without if/else in the programming.

Answer 1

EDIT:

Here's my latest solution for generating the array which is even more mathematical than before:

$q = 27;//number of questions
$c = 4;//number of columns
$m =  $q%$c;//modulus
$step = floor($q/$c);
$arr = array();
for ($n=0; $n<$q; $n++){
    $arr[] = 1 + $step*($n%$c) + ($m + $n%$c - abs($m - $n%$c))/2 + floor($n/$c);
}

The output is as follows:

array(1, 8, 15, 22, 2, 9, 16, 23, 3, 10, 17, 24, 4, 11, 18, 25, 5, 12, 19, 26, 6, 13, 20, 27, 7, 14, 21);

ORIGINAL ANSWER:

$q = 13;//number of questions
$c = 3;//number of columns
$mod = array_fill(0, $c, 0);
for ($i=0; $i<($q%$c); $i++){
    $mod[$i] = 1; 
}
$step = floor($q/$c);
$arr = array();
$cum = 0;
for ($i=0; $i<$c; $i++){
    $cum += @$mod[$i-1];
    $arr[] = 1 + $step*$i + $cum;
}
$next = $arr;
for ($i=1; $i<$step; $i++){
    foreach ($next as $key => $value){
        $next[$key]++;
    }
    $arr = array_merge($arr, $next);
}
for ($i=0; $i<$c; $i++){
    $next[$i] = ($next[$i] + 1)*$mod[$i] ;
}
$arr = array_filter(array_merge($arr, $next));
var_dump($arr);

The output is:

array(1, 6, 10, 2, 7, 11, 3, 8, 12, 4, 9, 13, 5);

Here's my solution for generating a table:

$q = 27;//number of questions
$c = 4;//number of columns
$cell = '<td>i</td>';
$table = '<table>';
$mod = array_fill(0, $c, 0);
for ($i=0; $i<($q%$c); $i++){
    $mod[$i] = 1; 
}
$step = floor($q/$c);
$arr = array();
$cum = 0;
$table .= '<tr>';
for ($i=0; $i<$c; $i++){
    $cum += @$mod[$i-1];
    $num = 1 + $step*$i + $cum;
    $arr[] = $num;
    $table .= str_replace('i', $num, $cell);
}
$table .= '</tr><tr>';
$next = $arr;
for ($i=1; $i<$step; $i++){
    foreach ($next as $key => $value){
        $num = ++$next[$key];
        $table .= str_replace('i', $num, $cell);
    }
    //$arr = array_merge($arr, $next);
    $table .= '</tr><tr>';
}
$table = substr($table, 0 , -4);
for ($i=0; $i<$c; $i++){
    $next[$i] = ($next[$i] + 1)*$mod[$i] ;
}
$next = array_filter($next);
$span = $c - count($next);
$ini = '';
$fin = '';
$last = '';
foreach ($next as $key => $value){
    $ini = '<tr>';
    $last .= str_replace('i', $value, $cell);
    $fin = '<td span="'.$span.'">&nbsp;</td></tr>';
}
//$arr = array_merge($arr, $next);
$table .= $ini.$last.$fin.'</table>';
echo $table;

With 27 questions and 4 columns, the output is:

<table>
    <tr><td>1</td><td>8</td><td>15</td><td>22</td></tr>
    <tr><td>2</td><td>9</td><td>16</td><td>23</td></tr>
    <tr><td>3</td><td>10</td><td>17</td><td>24</td></tr>
    <tr><td>4</td><td>11</td><td>18</td><td>25</td></tr>
    <tr><td>5</td><td>12</td><td>19</td><td>26</td></tr>
    <tr><td>6</td><td>13</td><td>20</td><td>27</td></tr>
    <tr><td>7</td><td>14</td><td>21</td><td span="1">&nbsp;</td></tr>
</table>

You can, of course, modify the value of $cell to insert a link or whatever you want into the table cells.