Number of Sundays on the First of the Month, in the 20th Century

TL;DR + Solution

Revisiting a coding interview question that I failed, 6 months ago.

There are 171 Sundays that fall on the first of the month, in the 20th century, but that is irrelevannt.

// sundays.ts
//
// excute this with
// ts-node sundays.ts

const isLeapYear = (year: number): boolean => {
  let result = false
  if (year % 4 === 0) result = true
  if (year % 100 === 0) result = false
  if (year % 400 === 0) result = true
  return result
}

const REG_YEAR = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
const LEAP_YEAR = [31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

const getDaysInYear = (year: number): number[] =>
  isLeapYear(year) ? LEAP_YEAR : REG_YEAR

function main() {
  let sundayCounter = 0
  let currentDay = 1 + (isLeapYear(1900) ? 366 : 365)

  for (let i = 1901; i <= 2000; i++) {
    const days = getDaysInYear(i)
    days.forEach(num => {
      currentDay += num
      currentDay = currentDay % 7
      if (currentDay === 0) sundayCounter += 1
    })
  }

  console.log(sundayCounter) // logs your answer to console output
  return sundayCounter
}

main()

Personal Reflecting

About 6 months ago, I was trying to balance learning programming, an unpaid web development internship 3 days a week, and a continuous job hunt, all at once. It was hectic. Now, I’m reflecting on a coding interview question that I failed during that time.

It is totally worth noting that my interviewer was so encouraging, and the experience was overall very pleasant and educational. Had he not been so kind, I might’ve gave up on self-teaching programming, for a week or two, or indefinitely…

Thanks S.P.!

The Interview Question

Without using any date/time libraries, figure out how many Sundays fell on the first day of the month during the twentieth century: January 1, 1901 to December 31, 2000

Dec 31, 1899 was a Sunday

On years evenly divisible by 4, February has 29 days, except on a century, unless the year is divisble by 400. On all other years February has 28 days.

Struggles + Attempt

Looking back, I had no idea where to begin tackling this. I was missing a few key points in my understanding.

Modulus is my friend
How do I establish a starting point?
Expect “nested for-loops”

✖ Establishing a Starting Point

I was able to establish the helper functions that I’d need to call on each iteration, but I wasn’t able draw the line from Jan 1, 1900 to Jan 1, 1901, to establish my starting point.

If I take an array of days from Sunday…Saturday

// 0 === sunday
// 6 === saturday
const days = [0, 1, 2, 3, 4, 5, 6]

That means Monday === 1. But what I was missing was that Monday could also equal 8, 71, 106, and (n * 7) + 1. All I needed to do was add 365 to my reference point and “modulo” by 7 to get the day-of-week of my starting point.

// Sunday - Dec 31, 1899
const clue = 0

// Monday - Jan 1, 1900
const reference = 1

// 1900 is a regular year, so it has 365 days
// Tuesday - Jan 1, 1901
const currentDay = (reference + 365) % 7 // 2

✖ Visualizing the Days Per Month

This is how I visualized the days for a regular year.

let currentDay = /* some value I never resolved */
const REG_YEAR = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

But I couldn’t seem to figure out how to check if Sunday was on the first day of each. If I visualized it differently, it might’ve helped. Like:

const ALSO_REG_YEAR = [3, 0, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3]
const LEAP_YEAR = [3, 1, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3]

And “for each of these, increment your current day. If it, modulo 7 equals 0, increment your sunday counter.”

✖ I Ran Out of Time

After an hour, I think my code looked something like this, but 100x messier:

const isLeapYear = (year: number): boolean => {
  let result = false
  if (year % 4 === 0) result = true
  if (year % 100 === 0) result = false
  if (year % 400 === 0) result = true
  return result
}

const REG_YEAR = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
const LEAP_YEAR = [31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

const getDaysInYear = (year: number): number[] =>
  isLeapYear(year) ? LEAP_YEAR : REG_YEAR

function main() {
  let sundayCounter = 0

  /**
   * I never established a starting 'index' for my
   * function to base off of.
   */
  let currentDay = undefined

  for (let i = 1901; i <= 2000; i++) {
    const days = getDaysInYear(i)

    for (let j = 0; j < 12; j++) {
      /**
       * I couldn't figure out what to do with the number of days
       * in each month, and undefined starting point.
       *
       * I also couldn't figure out the logic for when I should
       * increment my sundayCounter
       */
    }
  }

  return sundayCounter
}

I gave a good effort, my interviewer commended me for explaining my processes clearly as well as getting really close to the solution, but in the end, I couldn’t solve the task, and thus, didn’t pass the cut-off point for what they were looking for in a junior engineer.

I left the interview defeated, but happy and inspired… and I immediately googled the solution.

Today, Looking Back

I tried solving this, and honestly it still gave me a tough time.

What’s the Time Complexity?

Even now, 6 months of full-time frontend engineering (psh, css, am I rite? lolz) later, I’m not confident in how the time-complexity should be notated… O(n)? There is a nested for-loop, but the inner for loop only doesn’t grow with the outer (if the outer were to grow).

Any Other Approaches?

One of my brother’s friends said,

there are only 14 different ways to have a calendar

Leap/Non-leap (2) * each day of the week falling on Jan 1 (7) = (14).

So for the sake of learning, I’ll find time to go back and make an alternate function, using this approach.

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