Manipulate the array based on start_time and end_time in PHP - php

Question

i want output based on start_time and end_time.
Suppose there is parent array which has start_time and end_time has 6am and 8am. give it parent element 0.
3rd array has start_time and end_time has 6am and 6:30am this time falls between 1st arrays start_time and end_time so give it parent 1.
2nd array has start_time and end_time has 6am and 6:15am this time falls between 2nd array start_time and end_time so give it parent 2.
Note: there can be a lot of arrays and there is 24 hours time so anyone can be parent of anyother array. you can see in the example.
input array:
Array
(
[0] => Array
(
[id] => 1
[start_time] => 6am
[end_time] => 8am
)
[1] => Array
(
[id] => 2
[start_time] => 6am
[end_time] => 6:15am
)
[2] => Array
(
[id] => 3
[start_time] => 6am
[end_time] => 6:30am
)
)
Expected output:
Array
(
[0] => Array
(
[id] => 1
[start_time] => 6am
[end_time] => 8am
[parent] => 0
)
[1] => Array
(
[id] => 2
[start_time] => 6am
[end_time] => 6:15am
[parent] => 2 //increment this value of 3rd array parent by +1 because this time falls under 3rd array
)
[2] => Array
(
[id] => 3
[start_time] => 6am
[end_time] => 6:30am
[parent] => 1 //increment this value of 1st array parent by +1 because this time falls under 1st array
)
)
My code:
$count = count($input);
$output = array();
for ($i=0; $i < $count; $i++) {
$output[$i] = $input[$i];
$output[$i]['parent'] = $i;
for ($j=0; $j < $count; $j++) {
if ($i !== $j) {
if (checkOverlap($input[$i]['start_time'], $input[$i]['end_time'], $input[$j]['start_time'], $input[$j]['end_time'])) {
$output[$i]['parent'] = $j;
break;
}
}
}
}
function checkOverlap($start1, $end1, $start2, $end2) {
$start1 = strtotime($start1);
$end1 = strtotime($end1);
$start2 = strtotime($start2);
$end2 = strtotime($end2);
if ($start1 < $start2) {
if ($end1 > $start2 && $end1 < $end2) {
return true;
}
} else {
if ($start1 > $start2 && $start1 < $end2) {
return true;
}
}
return false;
}
I'm getting this output now which is wrong.
Array
(
[0] => Array
(
[id] => 1
[start_time] => 6am
[end_time] => 8am
[parent] => 0
)
[1] => Array
(
[id] => 2
[start_time] => 6am
[end_time] => 6:15am
[parent] => 1
)
[2] => Array
(
[id] => 3
[start_time] => 6am
[end_time] => 6:30am
[parent] => 2
)
)
it would very help for me if you can solve this.
see this event picture