Need help with this function, gives overlapping times and does not appropriately give times appoitnment for new patients:

function calculateAppointmentTime$($$isNewPatient, $desiredStartTime, $desiredEndTime$)\{$

$startTime $=$ strtotime$("09$:$00")$;

$endTime $=$ strtotime$("18$:$00")$;

$appointmentDuration $=30*60$;

if $($$isNewPatient $===$ "Yes"$)\{$

$appointmentDuration $=60*60$;

$\}$

$desiredStartTime $=$ empty$($$desiredStartTime$)?$ $startTime : strtotime$($date$(\text{'}$Y$-$m$-$d$\text{'}).\text{'}\text{'}.$ $desiredStartTime$)$;

$desiredEndTime $=$ empty$($$desiredEndTime$)?$ $endTime : strtotime$($date$(\text{'}$Y$-$m$-$d$\text{'}).\text{'}\text{'}.$ $desiredEndTime$)$;

if $($$desiredStartTime $<$ $startTime $||$ $desiredEndTime $>$ $endTime$)\{$

return $"*$ Constraints Violated";

$\}$

$latestEndTime $=$ $startTime;

foreach $($$$\_$SESSION$[\text{'}$patients$\text{'}]$ as $patient$)\{$

$patientEndTime $=$ strtotime$($$patient$[\text{'}$Appointment Time'$])+$ $appointmentDuration;

$latestEndTime $=$ max$($$latestEndTime, $patientEndTime$)$;

$\}$

$driveTime $=($$index $>0)?$ calculateDriveTime$($$$\_$SESSION$[\text{'}$patients$\text{'}][$$index $-1][\text{'}$Address Coordinates'$],$ $addressc$)$ : $0$;

$appointmentTime $=$ max$($$desiredStartTime, $latestEndTime$)+$ $driveTime;

while $($$appointmentTime $<$ $desiredEndTime$)\{$

$isSlotAvailable $=$ true;

foreach $($$$\_$SESSION$[\text{'}$patients$\text{'}]$ as $patient$)\{$

$patientAppointmentTime $=$ strtotime$($$patient$[\text{'}$Appointment Time'$])$;

$patientEndTime $=$ $patientAppointmentTime $+$ $appointmentDuration;

if $($

$($$appointmentTime $>=$ $patientAppointmentTime && $appointmentTime $<$ $patientEndTime$)||$

$($$appointmentTime $+$ $appointmentDuration $>$ $patientAppointmentTime && $appointmentTime $+$ $appointmentDuration $<=$ $patientEndTime$)$

$)\{$

$isSlotAvailable $=$ false;

break;

$\}$

$\}$

if $($$isSlotAvailable$)\{$

if $($$appointmentTime $+$ $appointmentDuration $<=$ $desiredEndTime$)\{$

break;

$\}$

$\}$

$appointmentTime $+=$ $appointmentDuration;

$\}$

return date$("$g:i a$",$ $appointmentTime$)$;

$\}$