# 1185. Day of the Week

## Description

Given a date, return the corresponding day of the week for that date.

The input is given as three integers representing the day, month and year respectively.

Return the answer as one of the following values {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"}.

Example 1:

Input: day = 31, month = 8, year = 2019
Output: "Saturday"


Example 2:

Input: day = 18, month = 7, year = 1999
Output: "Sunday"


Example 3:

Input: day = 15, month = 8, year = 1993
Output: "Sunday"


Constraints:

• The given dates are valid dates between the years 1971 and 2100.

## Solutions

Solution 1: Zeller’s Congruence

We can use Zeller’s Congruence to calculate the day of the week. Zeller’s Congruence is as follows:

$w = (\left \lfloor \frac{c}{4} \right \rfloor - 2c + y + \left \lfloor \frac{y}{4} \right \rfloor + \left \lfloor \frac{13(m+1)}{5} \right \rfloor + d - 1) \bmod 7$

Where:

• w: Day of the week (starting from Sunday)
• c: First two digits of the year
• y: Last two digits of the year
• m: Month (the range of m is from 3 to 14, that is, in Zeller’s Congruence, January and February of a certain year are considered as the 13th and 14th month of the previous year. For example, January 1, 2003 is considered as the 1st day of the 13th month of 2002)
• d: Day
• ⌊⌋: Floor function (round down)
• mod: Modulo operation

The time complexity is $O(1)$, and the space complexity is $O(1)$.

• import java.util.Calendar;

class Solution {
private static final String[] WEEK
= {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"};

public static String dayOfTheWeek(int day, int month, int year) {
Calendar calendar = Calendar.getInstance();
calendar.set(year, month - 1, day);
return WEEK[calendar.get(Calendar.DAY_OF_WEEK) - 1];
}
}

• class Solution {
public:
string dayOfTheWeek(int d, int m, int y) {
if (m < 3) {
m += 12;
y -= 1;
}
int c = y / 100;
y %= 100;
int w = (c / 4 - 2 * c + y + y / 4 + 13 * (m + 1) / 5 + d - 1) % 7;
vector<string> weeks = {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"};
return weeks[(w + 7) % 7];
}
};

• class Solution:
def dayOfTheWeek(self, day: int, month: int, year: int) -> str:
return datetime.date(year, month, day).strftime('%A')


• func dayOfTheWeek(d int, m int, y int) string {
if m < 3 {
m += 12
y -= 1
}
c := y / 100
y %= 100
w := (c/4 - 2*c + y + y/4 + 13*(m+1)/5 + d - 1) % 7
weeks := []string{"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"}
return weeks[(w+7)%7]
}

• function dayOfTheWeek(d: number, m: number, y: number): string {
if (m < 3) {
m += 12;
y -= 1;
}
const c: number = (y / 100) | 0;
y %= 100;
const w = (((c / 4) | 0) - 2 * c + y + ((y / 4) | 0) + (((13 * (m + 1)) / 5) | 0) + d - 1) % 7;
const weeks: string[] = [
'Sunday',
'Monday',
'Tuesday',
'Wednesday',
'Thursday',
'Friday',
'Saturday',
];
return weeks[(w + 7) % 7];
}