crt.js

// @ts-check

const schedule = [
  13,
  'x',
  'x',
  41,
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  997,
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  23,
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  19,
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  29,
  'x',
  619,
  'x',
  'x',
  'x',
  'x',
  'x',
  37,
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  'x',
  17,
]

const buses = schedule.map((a) => (typeof a !== 'number' ? 0 : a))

/** @returns {[number, number]} */
function divmod(x, y) {
  var div = Math.trunc(x / y)
  var rem = x % y
  return [div, rem]
}

function extended_gcd(a, b) {
  let [last_remainder, remainder] = [Math.abs(a), Math.abs(b)]
  let [x, last_x, y, last_y] = [0, 1, 1, 0]
  let quotient
  while (remainder != 0) {
    ;[last_remainder, [quotient, remainder]] = [
      remainder,
      divmod(last_remainder, remainder),
    ]
    ;[x, last_x] = [last_x - quotient * x, x]
    ;[y, last_y] = [last_y - quotient * y, y]
  }
  return [last_remainder, last_x * (a < 0 ? -1 : 1)]
}

function invmod(e, et) {
  const [g, x] = extended_gcd(e, et)
  if (g != 1) {
    throw 'Multiplicative inverse modulo does not exist!'
  }
  return x % et
}

function chinese_remainder(mods, remainders) {
  const max = mods.reduce((a, b) => a * b) // product of all moduli
  const series = remainders
    .map((r, index) => [r, mods[index]])
    .map((r, m) => (r * max * invmod(max / m, m)) / m)
  return series.reduce((a, b) => a + b) % max
}

const ba = buses.filter((a) => a !== 0)

console.log(
  chinese_remainder(
    ba.map((b) => b[0]),
    ba.map((a, b) => a - b)
  )
)