Find existing saddle points in any given 2-dimensional matrix

saddle.php

<?php

function find_saddle_points($arr) {
  $points = array();

  // traverse the passed matrix by row
  foreach($arr as $i => $row) {
    // get the highest value from each row
    $max = max($row);

    foreach($row as $j => $cell) {
      // for each highest value only, check whether it is the lowest value in its column
      if($cell == $max AND min_in_col($arr, $cell, $j)) {
        $points[] = array($i, $j);
      }
    }
  }

  print_r($points ? $points : 'No saddle points found.');
}


function min_in_col($arr, $val, $col) {
  foreach($arr as $row) {
    // as soon as there is at least one lower value, quit
    if($val > $row[$col]) {
      return FALSE;
    }
  }

  return TRUE;
}

tests.php

<?php

include('saddle.php');

$arr1 = array(
  array(39, 43, 49, 29, 18),
  array(30, 47, 24, 29, 15),
  array(49, 50, 39, 20, 33),
  array(18, 38, 35, 32, 35),
  array(29, 44, 18, 34, 44)
);

find_saddle_points($arr1);
// Output: Array ( [0] => Array ( [0] => 3 [1] => 1 ) )

$arr2 = array(
  array(50, 27, 36, 43, 39),
  array(36, 14, 35, 40, 19),
  array(20, 33, 48, 32, 40),
  array(41, 40, 15, 22, 19),
  array(21, 24, 24, 31, 18)
);

find_saddle_points($arr2);
// Output: No saddle points found.

$arr3 = array(
  array(39, 43, 49, 29, 18),
  array(30, 47, 24, 29, 15),
  array(49, 50, 39, 20, 33),
  array(18, 38, 35, 32, 38),
  array(29, 44, 18, 34, 44)
);

find_saddle_points($arr3);
// Output: Array ( [0] => Array ( [0] => 3 [1] => 1 ) )