Validate an extended tic-tac-toe state

Q: Validate an extended tic-tac-toe state

This question evaluates the ability to validate game states by reasoning about turn counts, win detection, and termination rules, testing competencies in game-state invariants and correctness checks within the Coding & Algorithms domain.

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Question

Problem

You are given a 3×3 tic-tac-toe board state as an array of 3 strings, each of length 3. Each cell is one of:

'X' (player X)
'O' (player O)
'.' (empty)

Assume players alternate turns starting with X, and the game ends immediately when a player gets 3 in a row (row, column, or diagonal). No moves can be played after the game ends.

Task (extended vs. basic validity)

Write a function that returns the game status for the given board:

"invalid" if the board cannot occur from a valid sequence of moves.
"X_wins" if X has already won in a valid way.
"O_wins" if O has already won in a valid way.
"draw" if the board is full and there is no winner.
"X_turn" if the state is valid and it is X's turn to play next.
"O_turn" if the state is valid and it is O's turn to play next.

Input

board : string[3]

Output

One of: invalid , X_wins , O_wins , draw , X_turn , O_turn

Notes / Constraints

The input is always 3 strings of length 3.
You must enforce turn counts (X goes first, players alternate).
You must enforce the “stop playing after win” rule.
Consider tricky cases like both players appearing to win, or a win with an impossible move count.