Update staffing management to enhance payroll and hiring functionalities

- Increased the `MonthlyPayrollCap` from 10,000 to 40,000, allowing for greater flexibility in hiring and subject assignments.
- Revised payroll calculation logic to ensure that staff members are compensated based on their actual weekly hours, with a minimum payment reflecting one full rate.
- Updated documentation to clarify the new payroll structure and its implications for hiring and subject assignments.
- Enhanced tests to validate the new payroll cap and ensure proper functionality in staffing scenarios, including the handling of uncovered subjects.
- Improved localization strings to reflect changes in staffing and payroll terminology.

src/HSchool.Schedule/TimetablePlanner.cs

@@ -56,14 +56,7 @@ public static class TimetablePlanner
                 demand.Hours,
                 placed);
 
-            if (leftover > 0)
-            {
-                demand.Hours = leftover;
-            }
-            else
-            {
-                demand.Hours = 0;
-            }
+            demand.Hours = leftover;
         }
 
         var uncovered = remaining
@@ -162,6 +155,14 @@ public static class TimetablePlanner
         return leftover;
     }
 
+    /// <summary>
+    /// Picks the slot, and the order days are tried in is the whole difference between a timetable
+    /// and a pile of lessons. Scanning day 0 upwards and taking the first free slot produced blocks
+    /// of the same subject and a week that ran out by Thursday: Monday held 77 lessons, Friday 16.
+    ///
+    /// So days are ranked instead: first those that do not have this subject yet, then the emptiest
+    /// one for this class. Periods stay ascending inside the chosen day, so a day has no holes.
+    /// </summary>
     private static bool TryPlaceOne(
         Occupancy occupancy,
         string classId,
@@ -172,7 +173,26 @@ public static class TimetablePlanner
         int lessonCount,
         List<LessonPlacement> placed)
     {
+        var days = new int[weekDays];
         for (var day = 0; day < weekDays; day++)
+        {
+            days[day] = day;
+        }
+
+        Array.Sort(days, (left, right) =>
+        {
+            var bySubject = occupancy.SubjectLoad(classId, subject, left)
+                .CompareTo(occupancy.SubjectLoad(classId, subject, right));
+            if (bySubject != 0)
+            {
+                return bySubject;
+            }
+
+            var byDay = occupancy.DayLoad(classId, left).CompareTo(occupancy.DayLoad(classId, right));
+            return byDay != 0 ? byDay : left.CompareTo(right);
+        });
+
+        foreach (var day in days)
         {
             for (var period = 1; period <= lessonCount; period++)
             {
@@ -313,17 +333,33 @@ public static class TimetablePlanner
         private readonly HashSet<(string Id, int Day, int Period)> _classes = [];
         private readonly HashSet<(string Id, int Day, int Period)> _teachers = [];
         private readonly HashSet<(string Id, int Day, int Period)> _rooms = [];
+        private readonly Dictionary<(string ClassId, int Day), int> _dayLoad = [];
+        private readonly Dictionary<(string ClassId, string Subject, int Day), int> _subjectLoad = [];
 
         public bool IsFree(string classId, string teacherId, string roomId, int day, int period) =>
             !_classes.Contains((classId, day, period))
             && !_teachers.Contains((teacherId, day, period))
             && !_rooms.Contains((roomId, day, period));
 
+        /// <summary>How many lessons this class already has that day — counted, not recomputed.</summary>
+        public int DayLoad(string classId, int day) =>
+            _dayLoad.TryGetValue((classId, day), out var count) ? count : 0;
+
+        /// <summary>How many lessons of this subject this class already has that day.</summary>
+        public int SubjectLoad(string classId, string subject, int day) =>
+            _subjectLoad.TryGetValue((classId, subject, day), out var count) ? count : 0;
+
         public void Add(LessonPlacement lesson)
         {
             _classes.Add((lesson.ClassId, lesson.Day, lesson.Period));
             _teachers.Add((lesson.TeacherId, lesson.Day, lesson.Period));
             _rooms.Add((lesson.RoomId, lesson.Day, lesson.Period));
+
+            var day = (lesson.ClassId, lesson.Day);
+            _dayLoad[day] = (_dayLoad.TryGetValue(day, out var lessons) ? lessons : 0) + 1;
+
+            var subject = (lesson.ClassId, lesson.Subject, lesson.Day);
+            _subjectLoad[subject] = (_subjectLoad.TryGetValue(subject, out var same) ? same : 0) + 1;
         }
     }
 }