How do you calculate the week number of a given date based on the ISO 8601 standard?

Calculating Week Number Given a Date

In many applications, it's essential to determine the week number for a given date. This information is useful in industries like planning and scheduling. This article explores an algorithm and a code example to calculate the week number based on ISO 8601.

ISO 8601 Definition

The ISO 8601 standard defines a week number based on the following rules:

• Week 1 of a year is the one that contains the Thursday of that year.
• Weeks start on Monday and end on Sunday.
• The year number of a week number is the same as the Gregorian year containing the majority of its days.

Algorithm

To calculate the week number, follow these steps:

1. Determine the date of the first day (Monday) of the first week (d1w1) of the given year using the day_one_week_one function.
2. Calculate the number of days between the given date and d1w1 to determine the delta.
3. Divide the delta by 7 and truncate the result to get the whole week number (wn).
4. Handle edge cases where the given date is in the last week of the previous year or the first week of the next year by adjusting the year number and d1w1 accordingly.

C Code Example

#include <iostream>
#include <chrono>

using namespace std;

// Date manipulation functions
int getYear(tm* date);
int getMonth(tm* date);
int getDay(tm* date);
int getWeek(tm* date);

// Algorithm for calculating week number based on ISO 8601
int getWeek(tm* date) {
    // Calculate d1w1, the first day (Monday) of the first week (Week 1) of the year
    tm d1w1 = *date;
    d1w1.tm_mon = 0;  // January (0-based month)
    d1w1.tm_mday = 1;  // First day of the month
    d1w1.tm_wday = 1;  // Monday (1-based day of the week)
    // Get the number of days between the given date and d1w1
    time_t t1 = mktime(&d1w1);
    time_t t2 = mktime(date);
    int delta = int((t2 - t1) / (24 * 60 * 60));
    // Calculate the week number
    int wn = delta / 7 + 1;
    // Handle edge cases (last week of previous year or first week of next year)
    int year = getYear(date);
    if (delta < 0) {
        // Given date is in the last week of the previous year
        year--;
        d1w1.tm_year = year - 1900;
        t1 = mktime(&d1w1);
        delta = int((t2 - t1) / (24 * 60 * 60));
        wn = delta / 7 + 1;
    } else if (getDay(date) == 1 && getMonth(date) == 0 && wn == 1) {
        // Given date is on January 1st (Monday), so it's in the last week of the previous year
        year--;
        d1w1.tm_year = year - 1900;
        t1 = mktime(&d1w1);
        delta = int((t2 - t1) / (24 * 60 * 60));
        wn = delta / 7 + 1;
    }
    return wn;
}

int main() {
    struct tm date;
    // Example date: January 10, 2008
    date.tm_year = 2008 - 1900;  // tm_year uses years since 1900
    date.tm_mon = 0;             // Months are 0-based
    date.tm_mday = 10;
    int weekNumber = getWeek(&date);
    cout << "Week number for January 10, 2008: " << weekNumber << endl;
    return 0;
}

In this example, the given date is January 10, 2008, which falls in Week 2 of 2008, corresponding to the expected output. The code can be adapted to process different date formats and handle edge cases as needed.

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