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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
and2100
.
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 yeary
: Last two digits of the yearm
: 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]; }