Decoding the Martian Calendar: A Programming Challenge

Let’s embark on a thought experiment. Imagine a calendar system designed for Mars. This Martian calendar presents some unique quirks compared to our Earth-based system, making it a fun challenge for programmers.

The Martian Week and Year:

On Mars, a year is 668 Martian days long. The week, however, is eight days long due to Mars’ two moons. This results in two “Mondays”: M1 and M2. A typical Martian week looks like this:

• Sun
• M1
• M2
• Tue
• Wed
• Thu
• Fri
• Sat

Leap Years with a Twist:

To complicate things (or simplify them, depending on your perspective), every fifth Martian year is a leap year. However, instead of adding an extra day, a leap year removes the second Monday (M2). The year length remains 668 days.

The Programming Challenge: Finding the Martian Weekday

The core of this challenge is to create an algorithm that, given a Martian year and day (in the format [year, day]), determines the corresponding Martian weekday. We know that the Martian calendar began on a Sunday (year 1, day 1).

Example Scenarios:

• Input: [1, 1] Output: "Sun"
• Input: [2, 1] Output: "Wed"
• Input: [5, 2] Output: "M1"

Breaking Down the Solution

To solve this, we need to account for the shifting weekdays caused by both regular and leap years. Here’s a step-by-step approach, illustrated with Javascript code:

1. Define Constants:

First, we define some key constants to make our code more readable and manageable:

const REGULAR_YEAR_WEEK = ["Sun", "M1", "M2", "Tue", "Wed", "Thu", "Fri", "Sat"];
const LEAP_YEAR_WEEK = ["Sun", "M1", "Tue", "Wed", "Thu", "Fri", "Sat"];

const DAYS_IN_YEAR = 668;
const REGULAR_YEAR_OFFSET = DAYS_IN_YEAR % REGULAR_YEAR_WEEK.length; // 668 % 8 = 4
const LEAP_YEAR_OFFSET = DAYS_IN_YEAR % LEAP_YEAR_WEEK.length; // 668 % 7 = 3

• REGULAR_YEAR_WEEK and LEAP_YEAR_WEEK: Arrays representing the weekdays in regular and leap years, respectively.
• DAYS_IN_YEAR: The constant number of days in a Martian year.
• REGULAR_YEAR_OFFSET and LEAP_YEAR_OFFSET: These represent how many days the weekday shifts forward each year. For example, a REGULAR_YEAR_OFFSET of 4 means that if a year starts on Sunday, the next year will start on Wednesday (shifted forward by 4 days).

2. Helper Functions:

Next, we create helper functions to determine leap years and retrieve the appropriate week array:

function isLeapYear(year) {
    return year % 5 === 0;
}

function getWeekForYear(year) {
    return isLeapYear(year) ? LEAP_YEAR_WEEK : REGULAR_YEAR_WEEK;
}

function getYearlyOffset(year) {
    return isLeapYear(year) ? LEAP_YEAR_OFFSET : REGULAR_YEAR_OFFSET;
}

• isLeapYear(year): A simple function to check if a year is a leap year.
• getWeekForYear(year): Returns the appropriate week array based on the year.
• getYearlyOffset(year): Returns how much the week shifts.

3. The Main Function: getMartianWeekday

This function takes the year and day as input and calculates the weekday:

function getMartianWeekday([targetYear, targetDay]) {
    // Edge case: Year 1 (Direct lookup)
    if (targetYear === 1) {
        return REGULAR_YEAR_WEEK[(targetDay - 1) % REGULAR_YEAR_WEEK.length];
    }

    let currentWeekdayIndex = 0; // Starts at 'Sun'

    // Step 1: Advance through past years
    for (let y = 1; y < targetYear; y++) {
        currentWeekdayIndex = (currentWeekdayIndex + getYearlyOffset(y)) % getWeekForYear(y).length;
    }

    // Step 2: Calculate weekday for the target year
    const currentWeek = getWeekForYear(targetYear);
    currentWeekdayIndex = (currentWeekdayIndex + (targetDay - 1)) % currentWeek.length;

    return currentWeek[currentWeekdayIndex];
}

• Edge Case (Year 1): If the target year is 1, we can directly calculate the weekday using the REGULAR_YEAR_WEEK array and the modulo operator (%).
• Initialization: We start with currentWeekdayIndex = 0, representing Sunday.
• Step 1 (Advance Through Past Years): We loop through all the years before the target year. In each iteration, we update currentWeekdayIndex by adding the appropriate yearly offset and taking the modulo of the week length. This effectively “shifts” the weekday forward based on the previous years.
• Step 2 (Calculate Weekday for Target Year): We get the correct week array (currentWeek) for the target year. Then, we add the targetDay - 1 (since days are 1-indexed) to the currentWeekdayIndex and take the modulo of the week length. This gives us the final index of the weekday within the currentWeek array.
• Return Result: Finally, we return the weekday string from the currentWeek array.

Testing the Solution:

// Test Cases
console.log(getMartianWeekday([1, 1]) === "Sun");
console.log(getMartianWeekday([2, 1]) === "Wed");
console.log(getMartianWeekday([5, 2]) === "M1");

The results are:

true
true
true

Key Takeaways:

This problem, while seemingly complex, highlights several important programming principles:

• Attention to Detail: Understanding the specific rules of the Martian calendar (leap year behavior, starting day) is crucial.
• Modular Design: Breaking the problem down into smaller, manageable functions (like isLeapYear and getWeekForYear) improves code readability and maintainability.
• Using Modulo Arithmetic: The modulo operator (%) is essential for handling the cyclical nature of weekdays.
• Iterative Approach: The solution involves iterating through past years to correctly calculate the weekday shift.

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