Day 5: Binary Boarding

Functions:

apply(first, last, directive)	Apply the directive given the range as [first, last] (inclusive).
determine_row(identifier)	Compute the row of the seat identified by the identifier.
determine_column(identifier)	Compute the column of the seat identified by the identifier.
determine_row_and_column(identifier)	Compute the (row, column) of the seat identified by the identifier.
determine_id(row, column)	Compute the identifier of the seat given its row and column.

apply(first: int, last: int, directive: str) → Tuple[int, int]

Apply the directive given the range as [first, last] (inclusive).

Returns

new first, new last

Requires

• re.match(r"^[FBLR]Z", directive)

• first >= 0

• last >= 1

• first % 2 == 0

• last % 2 == 1

• first < last

• (last - first + 1) % 2 == 0

  (Range always divisible by 2)

Ensures

• result[0] != result[1] ⇒ result[1] % 2 == 1

  (next last always not divisible by 2 unless the last step)

• result[0] != result[1] ⇒ result[0] % 2 == 0

  (next first always divisible by 2 unless the last step)

• first <= result[0] <= result[1] <= last

• not (directive in "BR")
  or (first < result[0] and result[1] == last)
  

  (Only first increases on B/R.)

• not (directive in "FL")
  or (result[0] == first and result[1] < last)
  

  (Only last decreases on F/L.)

determine_row(identifier: str) → int

Compute the row of the seat identified by the identifier.

Requires

• re.match(r"^[FB]{7}Z", identifier)

Ensures

• 0 <= result <= 127

determine_column(identifier: str) → int

Compute the column of the seat identified by the identifier.

Requires

• re.match(r"^[LR]{3}Z", identifier)

Ensures

• 0 <= result <= 127

determine_row_and_column(identifier: str) → Tuple[int, int]

Compute the (row, column) of the seat identified by the identifier.

Requires

• re.match(r"^[FB]{7}[LR]{3}Z", identifier)

Ensures

• 0 <= result[1] <= 8

• 0 <= result[0] <= 127

determine_id(row: int, column: int) → int

Compute the identifier of the seat given its row and column.

Requires

• 0 <= column <= 8

• 0 <= row <= 127

Ensures

• result <= 127 * 8 + 8

  (The highest seat ID)