Find the number of week rows in a month - math

Question

Given the start day (Wednesday = 4), and the number of days in a month (31), what is an elegant way to find the number of week rows a calendar of the month would require?
For the current month (startDay = 4, daysInMonth = 31), it would be 5. But if daysInMonth = 33, it would be 6 rows.
This doesn't quite work:
int numRows = (startDay+daysInMonth)/daysInWeek;
if ((startDay+daysInMonth) % daysInWeek != 0) {
numRows++;
}

Answer 1

Just change to
int numRows = (startDay + daysInMonth - 1) / daysInWeek;
if ((startDay+daysInMonth - 1) % daysInWeek != 0) {
numRows++;
}
and you should get the correct result.
EDIT: just to slightly expand on it : you have the right idea, you just forgot to account for the fact that the offset for day 1 is 0, not 1.

Answer 2

Actually, I think your original algorithm is correct, just need to subtract 1 when doing modulo daysInWeek.
daysInWeek = 7
startDay = 3 # Zero based day of week array, 3 = Wednesday
daysInMonth = 31
numRows = (startDay+daysInMonth)/daysInWeek
if ((startDay+daysInMonth - 1) % daysInWeek != 0)
numRows += 1
end
print numRows
It shows 6 correctly. (BTW, why do you need a month with 33 days?) It should be 6 rows for a 33 day month (if there was such a thing).

Answer 3

int temp = daysInMonth;
temp = temp - (7 - startDay);
int result = ceiling(temp / 7) + 1;

Answer 4

Here is a generic way to do it in C#, which works by counting the Saturdays in a month and then adding one if there's any left over days. Since it literally reads a calendar like a human would, there's no strange calendar arithmetic needed. It's all offloaded to the C# DateTime code, we just piggyback off that.
I chose Saturday because most calendars go Sunday (far left) to Saturday (far right). You can just choose a different day if you wish to denote the end of a week.
public static int RowsForMonth(int year, int month)
{
int days = DateTime.DaysInMonth(year, month);
int rows = 0;
int i = 0;
while(i < days)
{
i++;
DateTime date = new DateTime(year, month, i);
if (date.DayOfWeek == DayOfWeek.Saturday || i == days)
rows++;
}
return rows;
}
Jan 2022 -> 6
Feb 2022 -> 5
Mar 2022 -> 5