public static function compute_groups($input_data)
{
// Step 1: Set up empty groups & alternative format of input.
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
$Num_Stu = count($input_data);
//$Num_Groups = ($Num_Stu - $Num_Stu % 5) / 5; // The documented algorithm.
$Num_Groups = max(1, ($Num_Stu - $Num_Stu % 4) / 4);
// This works better.
// Explanation: Setting $Num_Groups = $Num_Stu div n always creates
// enough groups so that each group can have at least n members.
// (Because, $Num_Stu div n <= $Num_Stu / n, so $Num_Stu / $Num_Groups >= n).
// If there are less than n students in the class, then, even though
// formally there are not enough, we want to have one group anyway.
// List of groups with list of associated states.
$Groups = [];
$NeededRoles = [];
// Parallel array; roles yet to be covered.
for ($i = 1; $i <= $Num_Groups; $i++) {
$Groups[$i] = [];
$NeededRoles[$i] = array(1 => TRUE, 2 => TRUE, 3 => TRUE, 4 => TRUE);
// Bitfield for options 1, 2, 3, 4.
}
// StuCapabilities is an unchanging copy of the input, slightly different format.
// RolePools is a list of decreasing pools from which student ids are drawn.
// One "pool" per role.
$StuCapabilities = array();
foreach (array_keys($input_data) as $S_i) {
$StuCapabilities[$S_i] = [];
}
$RolePools = array(1 => [], 2 => [], 3 => [], 4 => []);
// Fill StuCapabilities and RolePools.
foreach ($input_data as $S_i => $RoleRespList_i) {
foreach ($RoleRespList_i as list($RoleNum_j, $RoleResp_j)) {
if ($RoleResp_j) {
$RolePools[$RoleNum_j][] = $S_i;
$StuCapabilities[$S_i][] = $RoleNum_j;
}
}
}
// Step 2: Distribute students with rare roles.
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
// Arbitrarily pick one of the smallest in RolePools. (Cred: Amal Murali @ StackOverflow)
$PoolSizes = array_map('count', $RolePools);
$MinPoolSize = min($PoolSizes);
$MinIndex = array_flip($PoolSizes)[$MinPoolSize];
$RarePool =& $RolePools[$MinIndex];
// Alias, so use reference op.
// Distribute the students who picked the chosen rare role.
$NumToDistribute = min($MinPoolSize, $Num_Groups);
for ($count = 1; $count <= $NumToDistribute; $count++) {
$S = SugAlg::PickOne($RarePool);
SugAlg::AddStudent($S, $Groups[$count], $StuCapabilities, $NeededRoles[$count], $RolePools);
}
// Step 3: Try to fill all roles for all groups.
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
// While there are groups that still needs roles
// (roles which have not already been exhausted)...
//REVISION-STEP: Try to use array_filter.
while ($RemGrpIds = array_keys(array_map('SugAlg::HasNeededRoles', $NeededRoles), TRUE, TRUE)) {
// For each of these groups...
foreach ($RemGrpIds as $x) {
$Groups_x =& $Groups[$x];
// Alias, so use reference op.
$NeededRoles_x =& $NeededRoles[$x];
// Alias, so use reference op.
// Pick a needed role (might be exhausted).
$R = array_search(TRUE, $NeededRoles_x);
// If there's still students for that role (not exhausted)...
if (!empty($RolePools[$R])) {
$S = SugAlg::PickOne($RolePools[$R]);
SugAlg::AddStudent($S, $Groups_x, $StuCapabilities, $NeededRoles_x, $RolePools);
} else {
$NeededRoles_x[$R] = FALSE;
}
}
}
return $Groups;
}
// ----------------------------------------------------------------------------
// Prepare input by mapping question numbers to role numbers.
// ----------------------------------------------------------------------------
// Bijective map.
$map_ques_to_role = array(15 => 1, 16 => 2, 17 => 3, 18 => 4);
// Modify $student_list, applying the map to question numbers.
foreach ($student_list as &$role_response_list) {
foreach ($role_response_list as &$ques_resp_pair) {
$question_num = $ques_resp_pair[0];
$ques_resp_pair[0] = $map_ques_to_role[$question_num];
}
}
// ----------------------------------------------------------------------------
// Invoke suggestion algorithm.
// ----------------------------------------------------------------------------
$groups = SugAlg::compute_groups($student_list);
// ----------------------------------------------------------------------------
// Add names.
// ----------------------------------------------------------------------------
$query = "SELECT student_id, name FROM student_info";
$name_responses = DB::query($query);
$names = array();
foreach ($name_responses as $name_record) {
$student_id = (int) $name_record['student_id'];
$name = $name_record['name'];
$names[$student_id] = $name;
}
// StuId -> [StuId, Name]
function add_name($stu_id)
{
global $names;
