Generate random "pattern-lock" sequence of digits

Today my friend raised a challenge that I still can't solve: "Generate a random digit sequence in PHP"

The digits are arranged as dial-pad/pattern-lock that consist 1-9 keys in 3 rows and 3 columns:

 ---------------------------
|                           |
|     1       2      3      |
|                           |
|     4       5      6      |
|                           |
|     7       8      9      |
|                           |
 ---------------------------

Now, given a length, we have to generate a random, non-repeating sequence of digits of the provided length, using these criteria:

A generated sequence should follow a specific direction/pattern going only via neighboring digits (possibly diagonally), for example (length:8), 12569874:
```
 1 🡪 2
      🡫
 4    5 🡪 6
 🡩        🡫
 7 🡨 8 🡨 9 
```
Digits from the first row should never be followed by a digit from the third row, and vice-versa. The same goes for columns. For example a 1 cannot be followed by a 8, and a 6 cannot be followed by a 4.
can guess more criteria can easily from android pattern-lock system

Here are some example generated sequences for length 9: 12369874/5, 142536987, etc, and for length = 6: 987532, etc

I tried to do this with rand():

  $chars = "123456789";
  $length = 9;
  $clen   = strlen( $chars )-1;
  $id  = '';

  for ($i = 0; $i < $length; $i++) {
      $id .= $chars[mt_rand(0,$clen)];
  }
  return ($id);

but, still no luck...

How can I solve this question?

Solution

has some limitations but that's for you to work out. I only deal with headaches when I get paid :).

<pre>
<?php

// Keypad
$grid = [
    ['1', '2', '3'],
    ['4', '5', '6'],
    ['7', '8', '9'],
];

// Sequence Target Length
$target_length = 5;

// Place to store the Keypad sequence
$points = [];

// Starting Point
$x = rand(0, 2);
$y = rand(0, 2);

// Run through the process until we have the sequence at the desired length
while (count($points) < $target_length):

    // Check if the grid keypad entry has been used
    if ($grid[$x][$y]):
        // Hasn't been used, so stire it
        $points[] = $grid[$x][$y]; 
        // Mark it used 
        $grid[$x][$y] = NULL;
    endif;

    // Sanity Check, imagine if you will,.... target length of 9, and you hit 6 5 2 1,  You'll vault off into the twilight zone without this
    if ((!$grid[$x + 1][$y]) && (!$grid[$x][$y + 1]) && (!$grid[$x - 1][$y]) && (!$grid[$x][$y - 1])):
        // We have no where to go
        break;
    endif;

    // Start looking for possible values 
    do {
        $test_x = $x;
        $test_y = $y;
        $dir = rand(0, 3);

        switch ($dir):
            case (0):
                $test_y--; // Up
                break;
            case (1):
                $test_x++; // Right
                break;
            case (2):
                $test_y++; // Down
                break;
            case (3):
                $test_x--; // Left
                break;
        endswitch;
        // Optional Gibberish 
        echo "Moving from {$x}, {$y} to {$test_x}, {$test_y} --> " . (($grid[$test_x][$test_y] === NULL) ? 'FAILED' : 'OK!') . '<br>';

        // Keep going until we find a valid direction
    } while ($grid[$test_x][$test_y] === NULL);

    // assign the new coords
    $x = $test_x;
    $y = $test_y;

    // repeat
endwhile;

// report
echo implode('-', $points) . "\n";

?>
</pre>