What day is it again?

Recently I have been trying to up my game in programming and had started reading this book. I came across an exercise that I thought was cool—so sharing it here. The question is this, given three inputs - d (day)m, (month), and y (year), find the day of the week it falls on. And they go on to give a neat formula for the Gregorian calendar.

$$ y_0 = y - (14 - m) / 12 $$ $$ x = y_0 + y_0 / 4 - y_0 / 100 + y_0 / 400 $$ $$ m_0 = m + 12 * ((14 - m)/ 12) - 2 $$ $$ d_0 = (d + x + (31 * m_0)/12) \mod 7 $$

Well, it is pretty easy to do the calculations when you have the formula. But for me, the catch was that the formula gives an integer $\in [0-6]$ as output. My first reaction was to use conditionals. But that’s naive, and this particular section bars me from using conditionals. And it dawned on me, it is merely straightforward to use a string array of weeks and use the output given by the formula as the index for it.

So here goes my simple python implementation:

def dayOfWeek(d, m, y):
    y_0 = y - (14 - m) // 12
    x = y_0 + y_0 // 4 - y_0 // 100 + y_0 // 400
    m_0 = m + 12 * ((14 - m)// 12) - 2
    d_0 = (d + x + (31 * m_0)//12) % 7
    days = ("Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday")
    print(days[d_0])
dayOfWeek(1,3,2021)

Feel free to play with the code, it’s editable!