# Find the first day of a given year from a base year having first day as Monday

Given two integers** Y** and** B** representing two years, the task is to find the day of the week in which 1^{st} January of the year **Y** lies assuming that 1^{st} January of the year **B** was a Monday.

**Examples:**

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Input:

Y = 2020

B = 1900Output:

WednesdayExplanation:

01/01/2020 was a Wednesday considering that 01/01/1900 was a Monday

Input:

Y = 2020

B = 1905Output:

ThursdayExplanation:

01/01/2020 was a Wednesday assuming that 01/01/1905 was a Monday

**Approach:** Follow the steps below to solve the problem:

- Total years lying between
**base year (B)**and the**year (Y)**is equal to**(Y – 1) – B**. - Total number of leap years lying in between = Total years / 4
- Total number of non-leap years in between =
**Total Years – Leap Years**. - Total Days =
**Total Leap Years * 366 + Non-Leap Years * 365 + 1**. - Therefore, the day of the 1
^{st}January of**Y**is**Total Days % 7**.

Below is the implementation of the above approach:

## C++14

`// C++ Implementation of` `// the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the day of` `// 1st January of Y year` `void` `findDay(` `int` `Y, ` `int` `B)` `{` ` ` `int` `lyear, rest, totaldays, day;` ` ` `// Count years between` ` ` `// years Y and B` ` ` `Y = (Y - 1) - B;` ` ` `// Count leap years` ` ` `lyear = Y / 4;` ` ` `// Non leap years` ` ` `rest = Y - lyear;` ` ` `// Total number of days in the years` ` ` `// lying between the years Y and B` ` ` `totaldays = (rest * 365)` ` ` `+ (lyear * 366) + 1;` ` ` `// Actual day` ` ` `day = (totaldays % 7);` ` ` `if` `(day == 0)` ` ` `printf` `(` `"Monday"` `);` ` ` `else` `if` `(day == 1)` ` ` `printf` `(` `"Tuesday"` `);` ` ` `else` `if` `(day == 2)` ` ` `printf` `(` `"Wednesday"` `);` ` ` `else` `if` `(day == 3)` ` ` `printf` `(` `"Thursday"` `);` ` ` `else` `if` `(day == 4)` ` ` `printf` `(` `"Friday"` `);` ` ` `else` `if` `(day == 5)` ` ` `printf` `(` `"Saturday"` `);` ` ` `else` `if` `(day == 6)` ` ` `printf` `(` `"Sunday"` `);` ` ` `else` ` ` `printf` `(` `"INPUT YEAR IS WRONG!"` `);` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `Y = 2020, B = 1900;` ` ` `findDay(Y, B);` ` ` `return` `0;` `}` |

## Java

`// Java program to implement` `// the above approach` `import` `java.util.*;` `class` `GFG` `{` ` ` `// Function to find the day of` ` ` `// 1st January of Y year` ` ` `static` `void` `findDay(` `int` `Y, ` `int` `B)` ` ` `{` ` ` `int` `lyear, rest, totaldays, day;` ` ` `// Count years between` ` ` `// years Y and B` ` ` `Y = (Y - ` `1` `) - B;` ` ` `// Count leap years` ` ` `lyear = Y / ` `4` `;` ` ` `// Non leap years` ` ` `rest = Y - lyear;` ` ` `// Total number of days in the years` ` ` `// lying between the years Y and B` ` ` `totaldays = (rest * ` `365` `)` ` ` `+ (lyear * ` `366` `) + ` `1` `;` ` ` `// Actual day` ` ` `day = (totaldays % ` `7` `);` ` ` `if` `(day == ` `0` `)` ` ` `System.out.println(` `"Monday"` `);` ` ` `else` `if` `(day == ` `1` `)` ` ` `System.out.println(` `"Tuesday"` `);` ` ` `else` `if` `(day == ` `2` `)` ` ` `System.out.println(` `"Wednesday"` `);` ` ` `else` `if` `(day == ` `3` `)` ` ` `System.out.println(` `"Thursday"` `);` ` ` `else` `if` `(day == ` `4` `)` ` ` `System.out.println(` `"Friday"` `);` ` ` `else` `if` `(day == ` `5` `)` ` ` `System.out.println(` `"Saturday"` `);` ` ` `else` `if` `(day == ` `6` `)` ` ` `System.out.println(` `"Sunday"` `);` ` ` `else` ` ` `System.out.println(` `"INPUT YEAR IS WRONG!"` `);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `Y = ` `2020` `, B = ` `1900` `;` ` ` `findDay(Y, B);` ` ` `}` `}` `// This code is contributed by code_hunt.` |

## Python3

`# Python program to implement` `# the above approach` `# Function to find the day of` `# 1st January of Y year` `def` `findDay(Y, B):` ` ` `lyear, rest, totaldays, day ` `=` `0` `, ` `0` `, ` `0` `, ` `0` `;` ` ` `# Count years between` ` ` `# years Y and B` ` ` `Y ` `=` `(Y ` `-` `1` `) ` `-` `B;` ` ` `# Count leap years` ` ` `lyear ` `=` `Y ` `/` `/` `4` `;` ` ` `# Non leap years` ` ` `rest ` `=` `Y ` `-` `lyear;` ` ` `# Total number of days in the years` ` ` `# lying between the years Y and B` ` ` `totaldays ` `=` `(rest ` `*` `365` `) ` `+` `(lyear ` `*` `366` `) ` `+` `1` `;` ` ` `# Actual day` ` ` `day ` `=` `(totaldays ` `%` `7` `);` ` ` `if` `(day ` `=` `=` `0` `):` ` ` `print` `(` `"Monday"` `);` ` ` `elif` `(day ` `=` `=` `1` `):` ` ` `print` `(` `"Tuesday"` `);` ` ` `elif` `(day ` `=` `=` `2` `):` ` ` `print` `(` `"Wednesday"` `);` ` ` `elif` `(day ` `=` `=` `3` `):` ` ` `print` `(` `"Thursday"` `);` ` ` `elif` `(day ` `=` `=` `4` `):` ` ` `print` `(` `"Friday"` `);` ` ` `elif` `(day ` `=` `=` `5` `):` ` ` `print` `(` `"Saturday"` `);` ` ` `elif` `(day ` `=` `=` `6` `):` ` ` `print` `(` `"Sunday"` `);` ` ` `else` `:` ` ` `print` `(` `"INPUT YEAR IS WRONG!"` `);` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `Y ` `=` `2020` `; B ` `=` `1900` `;` ` ` `findDay(Y, B);` `# This code is contributed by 29AjayKumar` |

## C#

`// C# program to implement` `// the above approach` `using` `System;` `class` `GFG` `{` ` ` `// Function to find the day of` ` ` `// 1st January of Y year` ` ` `static` `void` `findDay(` `int` `Y, ` `int` `B)` ` ` `{` ` ` `int` `lyear, rest, totaldays, day;` ` ` `// Count years between` ` ` `// years Y and B` ` ` `Y = (Y - 1) - B;` ` ` `// Count leap years` ` ` `lyear = Y / 4;` ` ` `// Non leap years` ` ` `rest = Y - lyear;` ` ` `// Total number of days in the years` ` ` `// lying between the years Y and B` ` ` `totaldays = (rest * 365)` ` ` `+ (lyear * 366) + 1;` ` ` `// Actual day` ` ` `day = (totaldays % 7);` ` ` `if` `(day == 0)` ` ` `Console.WriteLine(` `"Monday"` `);` ` ` `else` `if` `(day == 1)` ` ` `Console.WriteLine(` `"Tuesday"` `);` ` ` `else` `if` `(day == 2)` ` ` `Console.WriteLine(` `"Wednesday"` `);` ` ` `else` `if` `(day == 3)` ` ` `Console.WriteLine(` `"Thursday"` `);` ` ` `else` `if` `(day == 4)` ` ` `Console.WriteLine(` `"Friday"` `);` ` ` `else` `if` `(day == 5)` ` ` `Console.WriteLine(` `"Saturday"` `);` ` ` `else` `if` `(day == 6)` ` ` `Console.WriteLine(` `"Sunday"` `);` ` ` `else` ` ` `Console.WriteLine(` `"INPUT YEAR IS WRONG!"` `);` ` ` `}` `// Driver code` `static` `void` `Main()` `{` ` ` `int` `Y = 2020, B = 1900;` ` ` `findDay(Y, B);` `}` `}` `// This code is contribute by susmitakundugoaldanga` |

## Javascript

`<script>` `// Javascript program of the above approach` ` ` `// Function to find the day of` ` ` `// 1st January of Y year` ` ` `function` `findDay(Y, B)` ` ` `{` ` ` `let lyear, rest, totaldays, day;` ` ` ` ` `// Count years between` ` ` `// years Y and B` ` ` `Y = (Y - 1) - B;` ` ` ` ` `// Count leap years` ` ` `lyear = Math.floor(Y / 4);` ` ` ` ` `// Non leap years` ` ` `rest = Y - lyear;` ` ` ` ` `// Total number of days in the years` ` ` `// lying between the years Y and B` ` ` `totaldays = (rest * 365)` ` ` `+ (lyear * 366) + 1;` ` ` ` ` `// Actual day` ` ` `day = (totaldays % 7);` ` ` ` ` `if` `(day == 0)` ` ` `document.write(` `"Monday"` `);` ` ` ` ` `else` `if` `(day == 1)` ` ` `document.write(` `"Tuesday"` `);` ` ` ` ` `else` `if` `(day == 2)` ` ` `document.write(` `"Wednesday"` `);` ` ` ` ` `else` `if` `(day == 3)` ` ` `document.write(` `"Thursday"` `);` ` ` ` ` `else` `if` `(day == 4)` ` ` `document.write(` `"Friday"` `);` ` ` ` ` `else` `if` `(day == 5)` ` ` `document.write(` `"Saturday"` `);` ` ` ` ` `else` `if` `(day == 6)` ` ` `document.write(` `"Sunday"` `);` ` ` ` ` `else` ` ` `document.write(` `"INPUT YEAR IS WRONG!"` `);` ` ` `}` ` ` `// Driver Code` ` ` ` ` `// Given array` ` ` `let Y = 2020, B = 1900;` ` ` `findDay(Y, B);` ` ` `</script>` |

**Output:**

Wednesday

**Time Complexity: **O(1)**Auxiliary Space:** O(1)