Exploring the Tomohiko Sakamoto Algorithm for Calculating Day of the Week

Introduction to Tomohiko Sakamoto's Algorithm

Tsunehiro Tomohiko Sakamoto, a Japanese software engineer, developed an efficient algorithm for determining the day of the week for any given date. This algorithm is widely used due to its simplicity and accuracy. By using a series of mathematical operations based on the date, month, and year, one can easily find the corresponding day of the week. In this article, we will provide a detailed breakdown of the algorithm, including its steps and implementation.

Steps of the Algorithm

The Tomohiko Sakamoto Algorithm is a straightforward method to determine the day of the week for any date. Here are the key steps involved:

1. Input Date

You need three pieces of information: the year, month, and day.

2. Adjust Month and Year

If the month is January or February, treat it as the 13th or 14th month of the previous year. This adjustment is necessary because the algorithm assumes March as the first month of the year. For example, if the date is January 2023, treat it as the 13th month of 2022.

3. Calculate Variables

Let: Y the adjusted year M the adjusted month 13 for January 14 for February D the day of the month

4. Compute

K Y mod 100 (last two digits of the year) J leftlfloor frac{Y}{100} rightrfloor (the zero-based century)

5. Apply the Formula

Use the following formula to calculate the day of the week: f D leftlfloor frac{13M - 1}{5} rightrfloor K leftlfloor frac{K}{4} rightrfloor leftlfloor frac{J}{4} rightrfloor - 2J

6. Determine the Result

f mod 7 gives you a number corresponding to the day of the week where: 0 Saturday, 1 Sunday, 2 Monday, 3 Tuesday, 4 Wednesday, 5 Thursday, 6 Friday

Example Calculation

To find the day of the week for July 4, 2023:

Input Date

Year 2023 Month 7 (July) Day 4 No adjustment needed because July is not January or February.

Calculate

Y 2023 M 7 D 4 K 23 2023 mod 100 J 20 2023 divided by 100, rounded down

Apply the Formula

f 4 leftlfloor frac{137 - 1}{5} rightrfloor 23 leftlfloor frac{23}{4} rightrfloor leftlfloor frac{20}{4} rightrfloor - 2 times 20 f 4 leftlfloor frac{104}{5} rightrfloor 23 leftlfloor frac{23}{4} rightrfloor leftlfloor frac{20}{4} rightrfloor - 40 f 4 20 23 5 5 - 40 f 17

Find the Result

17 mod 7 3 This corresponds to Tuesday.

Conclusion

The Tomohiko Sakamoto Algorithm is efficient and can be easily implemented in programming languages for quick day-of-the-week calculations. It is especially useful for determining the day of the week for historical dates or scheduling tasks. This algorithm provides a reliable and accurate way to determine the day of the week, making it a valuable tool for various applications.