Reachable Noughts and Crosses Position

Medium

A 3×3 noughts and crosses board is given as a list of three strings rows. Each character is 'X', 'O' or a space ' ' for an empty cell. The rules: - players take turns placing their own mark in an empty cell; - the 'X' player always moves first, the 'O' player second; - the game ends as soon as three identical marks fill a row, a column or a diagonal, or when no empty cells remain. No moves are made after that. Return True if this position can come up in a fair game played by these rules, and False otherwise.

Example 1

rows=['XX ', 'OO ', '   '] → True

X has made two moves and O has made two, so it is X's turn. This position can happen.

Example 2

rows=['OOO', 'XX ', 'XX '] → False

O completed a row, yet X has more marks: once O won, X could not have moved again.

Example 3

rows=['  X', '   ', '  X'] → False

Two X marks and no O marks: players alternate, so this cannot happen.

Constraints

len(rows) == 3
len(rows[i]) == 3
rows[i][j] is 'X', 'O' or ' '

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Topics

Array Matrix

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Input

rows=['XX ', 'OO ', '   ']

Expected

True

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