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Code Mathematics

# Find day of the week for a given date

The problem of finding the day of the week for a given date is a common task in computer programming and mathematics. The goal is to determine which day of the week (e.g. Monday, Tuesday, Wednesday, etc.) a specific date falls on, given the month, day, and year.

There are several ways to find the day of the week for a given date, including the following methods:

## Zeller's Congruence:

Zeller's congruence is a mathematical formula that can be used to calculate the day of the week for any date in the Gregorian calendar. The formula is as follows:

``````h = (q + ((13*(m+1))/5) + K + (K/4) + (J/4) - (2*J)) % 7
``````

Where:

• h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, etc.)
• q is the day of the month
• m is the month (3 = March, 4 = April, ..., 14 = February)
• K is the year of the century (i.e. year % 100)
• J is the zero-based century (i.e. year // 100)

Note that for January and February, you need to add 12 to the month and subtract 1 from the year.

## Tomohiko Sakamoto's Algorithm:

The Sakamoto's algorithm is a simpler alternative to Zeller's congruence. The algorithm is as follows:

``````t = [0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4]
y -= m < 3
dow = (y + y//4 - y//100 + y//400 + t[m-1] + d) % 7
``````

Where:

• dow is the day of the week (0 = Sunday, 1 = Monday, 2 = Tuesday, etc.)
• d is the day of the month
• m is the month (1 = January, 2 = February, ..., 12 = December)
• y is the year

Note that the algorithm assumes the Gregorian calendar, so it may not be accurate for dates before 1582.

### Program Solution

``````// C program for
// Find day of the week for a given date
#include <stdio.h>

void dayName(int year, int month, int day)
{
if (month < 1 || month > 12 || day < 1 || day > 31 || year <= 0)
{
return;
}
// Day names
const char *result[] = {
"Sunday" , "Monday" , "Tuesday" , "Wednesday" ,
"Thursday" , "Friday" , "Saturday"
};
// Month  1   2   3   4   5   6   7   8   9   10  11  12
int m[] = {
0 , 3 , 2 , 5 , 0 , 3 , 5 , 1 , 4 , 6 , 2 , 4
};
// Calculate day of week
int d = (year + year / 4 - year / 100 + year / 400 + m[month - 1] + day) % 7;
// Display given date
printf(" Y:%d  M:%d  D:%d \n", year, month, day);
// Display calculated result
printf(" Week Day : %s \n", result[d]);
}
int main(int argc, char const *argv[])
{
// Test case
dayName(2020, 11, 15);
dayName(2021, 6, 24);
return 0;
}``````

#### input

`````` Y:2020  M:11  D:15
Week Day : Sunday
Y:2021  M:6  D:24
Week Day : Thursday``````
``````/*
Java Program for
Find day of the week for a given date
*/
public class Calculation
{
public void dayName(int year, int month, int day)
{
if (month < 1 || month > 12 || day < 1 || day > 31 || year <= 0)
{
return;
}
// Day names
String[] result = {
"Sunday" , "Monday" , "Tuesday" , "Wednesday" , "Thursday" , "Friday" , "Saturday"
};
// Month
// 1   2   3   4   5   6   7   8   9   10  11  12
int[] m = {
0 , 3 , 2 , 5 , 0 , 3 , 5 , 1 , 4 , 6 , 2 , 4
};
// Calculate day of week
int d = (year + year / 4 - year / 100 + year / 400 + m[month - 1] + day) % 7;
// Display given date
System.out.println(" Y:" + year + " M:" + month + " D:" + day);
// Display calculated result
System.out.println(" Week Day : " + result[d]);
}
public static void main(String[] args)
{
// Test case
}
}``````

#### input

`````` Y:2020 M:11 D:15
Week Day : Sunday
Y:2021 M:6 D:24
Week Day : Thursday``````
``````// Include header file
#include <iostream>

using namespace std;
/*
C++ Program for
Find day of the week for a given date
*/
class Calculation
{
public: void dayName(int year, int month, int day)
{
if (month < 1 || month > 12 || day < 1 || day > 31 || year <= 0)
{
return;
}
// Day names
string result[] = {
"Sunday" , "Monday" , "Tuesday" , "Wednesday" ,
"Thursday" , "Friday" , "Saturday"
};
// Month
// 1   2   3   4   5   6   7   8   9   10  11  12
int m[] = {
0 , 3 , 2 , 5 , 0 , 3 , 5 , 1 , 4 , 6 , 2 , 4
};
// Calculate day of week
int d = (year + year / 4 - year / 100 + year / 400 + m[month - 1] + day) % 7;
// Display given date
cout << " Y:" << year << " M:" << month << " D:" << day << endl;
// Display calculated result
cout << " Week Day : " << result[d] << endl;
}
};
int main()
{
// Test case
return 0;
}``````

#### input

`````` Y:2020 M:11 D:15
Week Day : Sunday
Y:2021 M:6 D:24
Week Day : Thursday``````
``````// Include namespace system
using System;
/*
Csharp Program for
Find day of the week for a given date
*/
public class Calculation
{
public void dayName(int year, int month, int day)
{
if (month < 1 || month > 12 || day < 1 || day > 31 || year <= 0)
{
return;
}
// Day names
String[] result = {
"Sunday" , "Monday" , "Tuesday" , "Wednesday" , "Thursday" , "Friday" , "Saturday"
};
// Month
// 1   2   3   4   5   6   7   8   9   10  11  12
int[] m = {
0 , 3 , 2 , 5 , 0 , 3 , 5 , 1 , 4 , 6 , 2 , 4
};
// Calculate day of week
int d = (year + year / 4 - year / 100 + year / 400 + m[month - 1] + day) % 7;
// Display given date
Console.WriteLine(" Y:" + year + " M:" + month + " D:" + day);
// Display calculated result
Console.WriteLine(" Week Day : " + result[d]);
}
public static void Main(String[] args)
{
// Test case
}
}``````

#### input

`````` Y:2020 M:11 D:15
Week Day : Sunday
Y:2021 M:6 D:24
Week Day : Thursday``````
``````<?php
/*
Php Program for
Find day of the week for a given date
*/
class Calculation
{
public	function dayName(\$year, \$month, \$day)
{
if (\$month < 1 || \$month > 12 || \$day < 1 || \$day > 31 || \$year <= 0)
{
return;
}
// Day names
\$result = array("Sunday", "Monday", "Tuesday",
"Wednesday", "Thursday", "Friday", "Saturday");
// Month
// 1   2   3   4   5   6   7   8   9   10  11  12
\$m = array(0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4);
// Calculate day of week
\$d = (\$year + (int)(\$year / 4) - (int)(\$year / 100) +
(int)(\$year / 400) + \$m[\$month - 1] + \$day) % 7;
// Display given date
echo " Y:".\$year.
" M:".\$month.
" D:".\$day.
"\n";
// Display calculated result
echo " Week Day : ".\$result[\$d].
"\n";
}
}

function main()
{
// Test case
}
main();``````

#### input

`````` Y:2020 M:11 D:15
Week Day : Sunday
Y:2021 M:6 D:24
Week Day : Thursday``````
``````/*
Node JS Program for
Find day of the week for a given date
*/
class Calculation
{
dayName(year, month, day)
{
if (month < 1 || month > 12 || day < 1 || day > 31 || year <= 0)
{
return;
}
// Day names
var result = ["Sunday", "Monday", "Tuesday",
"Wednesday", "Thursday", "Friday", "Saturday"];
// Month
// 1   2   3   4   5   6   7   8   9   10  11  12
var m = [0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4];
// Calculate day of week
var d = (year + parseInt(year / 4) - parseInt(year / 100) +
parseInt(year / 400) + m[month - 1] + day) % 7;
// Display given date
console.log(" Y:" + year + " M:" + month + " D:" + day);
// Display calculated result
console.log(" Week Day : " + result[d]);
}
}

function main()
{
// Test case
}
main();``````

#### input

`````` Y:2020 M:11 D:15
Week Day : Sunday
Y:2021 M:6 D:24
Week Day : Thursday``````
``````#  Python 3 Program for
#  Find day of the week for a given date
class Calculation :
def dayName(self, year, month, day) :
if (month < 1 or month > 12 or day < 1 or day > 31 or year <= 0) :
return

result = ["Sunday", "Monday", "Tuesday", "Wednesday",
"Thursday", "Friday", "Saturday"]
m = [0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4]
d = (year + int(year / 4) - int(year / 100) +
int(year / 400) + m[month - 1] + day) % 7
#  Display given date
print(" Y:", year ," M:", month ," D:", day)
#  Display calculated result
print(" Week Day : ", result[d])

def main() :
#  Test case

if __name__ == "__main__": main()``````

#### input

`````` Y: 2020  M: 11  D: 15
Week Day :  Sunday
Y: 2021  M: 6  D: 24
Week Day :  Thursday``````
``````#  Ruby Program for
#  Find day of the week for a given date

class Calculation
def dayName(year, month, day)
if (month < 1 || month > 12 || day < 1 || day > 31 || year <= 0)
return
end

#  Day names
result = ["Sunday", "Monday", "Tuesday",
"Wednesday", "Thursday", "Friday", "Saturday"]
#  Month
#  1   2   3   4   5   6   7   8   9   10  11  12
m = [0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4]
#  Calculate day of week
d = (year + year / 4 - year / 100 + year / 400 +
m[month - 1] + day) % 7
#  Display given date
print(" Y:", year ," M:", month ," D:", day, "\n")
#  Display calculated result
print(" Week Day : ", result[d], "\n")
end

end

def main()
#  Test case
end

main()``````

#### input

`````` Y:2020 M:11 D:15
Week Day : Sunday
Y:2021 M:6 D:24
Week Day : Thursday
``````
``````/*
Scala Program for
Find day of the week for a given date
*/
class Calculation()
{
def dayName(year: Int, month: Int, day: Int): Unit = {
if (month < 1 || month > 12 || day < 1 || day > 31 || year <= 0)
{
return;
}
// Day names
var result: Array[String] = Array("Sunday", "Monday",
"Tuesday", "Wednesday", "Thursday", "Friday", "Saturday");
// Month
// 1   2   3   4   5   6   7   8   9   10  11  12
var m: Array[Int] = Array(0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4);
// Calculate day of week
var d: Int = (year + (year / 4).toInt - (year / 100).toInt +
(year / 400).toInt + m(month - 1) + day) % 7;
// Display given date
println(" Y:" + year + " M:" + month + " D:" + day);
// Display calculated result
println(" Week Day : " + result(d));
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: Calculation = new Calculation();
// Test case
}
}``````

#### input

`````` Y:2020 M:11 D:15
Week Day : Sunday
Y:2021 M:6 D:24
Week Day : Thursday``````
``````/*
Swift 4 Program for
Find day of the week for a given date
*/
class Calculation
{
func dayName(_ year: Int, _ month: Int, _ day: Int)
{
if (month < 1 || month > 12 || day < 1 || day > 31 || year <= 0)
{
return;
}
// Day names
let result: [String] = ["Sunday", "Monday", "Tuesday",
"Wednesday", "Thursday", "Friday", "Saturday"];
// Month
// 1   2   3   4   5   6   7   8   9   10  11  12
let m: [Int] = [0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4];
// Calculate day of week
let d: Int = (year + year / 4 - year / 100 + year / 400 +
m[month - 1] + day) % 7;
// Display given date
print(" Y:", year ," M:", month ," D:", day);
// Display calculated result
print(" Week Day : ", result[d]);
}
}
func main()
{
// Test case
}
main();``````

#### input

`````` Y: 2020  M: 11  D: 15
Week Day :  Sunday
Y: 2021  M: 6  D: 24
Week Day :  Thursday``````
``````/*
Kotlin Program for
Find day of the week for a given date
*/
class Calculation
{
fun dayName(year: Int, month: Int, day: Int): Unit
{
if (month < 1 || month > 12 || day < 1 || day > 31 || year <= 0)
{
return;
}
// Day names
val result: Array < String > = arrayOf("Sunday", "Monday", "Tuesday",
"Wednesday", "Thursday", "Friday",
"Saturday");
// Month
// 1   2   3   4   5   6   7   8   9   10  11  12
val m: Array < Int > = arrayOf(0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4);
// Calculate day of week
val d: Int = (year + year / 4 - year / 100 + year / 400 +
m[month - 1] + day) % 7;
// Display given date
println(" Y:" + year + " M:" + month + " D:" + day);
// Display calculated result
println(" Week Day : " + result[d]);
}
}
fun main(args: Array < String > ): Unit
{
// Test case
}``````

#### input

`````` Y:2020 M:11 D:15
Week Day : Sunday
Y:2021 M:6 D:24
Week Day : Thursday``````

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