gistfile1.php

<?php
// My original function
function max_length($array) {
    $max = 0;
    foreach($array as $child) {
        if(count($child) > $max) {
            $max = count($child);
        }
    }
    return $max;
}
// From Stack Overflow
function max_length_so1($input_arr) {
    $counts = array_map('count', $input_arr);
    $key = array_flip($counts)[max($counts)];
    return count($input_arr[$key]);
}

function max_length_so2($input_arr) {
    $count = array_map('count', $input_arr);
    $min = array_keys($count , max($count))[0];
    return count($input_arr[$min]);
}
 
$dataset = [
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,30), 'a'),
    array_fill(0, mt_rand(2,30), 'b'),
    array_fill(0, mt_rand(2,30), 'c'),
    array_fill(0, mt_rand(2,30), 'd'),
    array_fill(0, mt_rand(2,30), 'e'),
    array_fill(0, mt_rand(1,50), 'f'),
    array_fill(0, mt_rand(2,30), 'g'),
    array_fill(0, mt_rand(2,30), 'h'),
    ['i'],
    array_fill(0, mt_rand(30,55), 'j'),
    array_fill(0, mt_rand(1,80), 'k'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),
    array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x'),  array_fill(0, mt_rand(2,20), 'x')
];
 
$start = microtime(1);
for($i = 0; $i < 100000; ++$i) {
    $x = max_length($dataset);
}
$end = microtime(1);
echo "Naive solution:\n";
echo "Result {$x} calculated in " . ( $end - $start) . " seconds.\n";
 
$start = microtime(1);
for($i = 0; $i < 100000; ++$i) {
    $x = max_length_so1($dataset);
}
$end = microtime(1);
echo "Stack Overflow 1:\n";
echo "Result {$x} calculated in " . ( $end - $start) . " seconds.\n";

$start = microtime(1);
for($i = 0; $i < 100000; ++$i) {
    $x = max_length_so2($dataset);
}
$end = microtime(1);
echo "Stack Overflow 2:\n";
echo "Result {$x} calculated in " . ( $end - $start) . " seconds.\n";

/*
$ php array.php 
Naive solution:
Result 43 calculated in 9.6717028617859 seconds.
Stack Overflow 1:
Result 43 calculated in 15.327514886856 seconds.
Stack Overflow 2:
Result 43 calculated in 14.802617788315 seconds.
*/

Changing N to 250000:

Naive solution:
Result 47 calculated in 12.74768781662 seconds.
Stack Overflow 1:
Result 47 calculated in 21.176842927933 seconds.
Stack Overflow 2:
Result 47 calculated in 18.850181102753 seconds.

So it appears that your second solution is better than your first, but the naive approach still wins the race.