Enumerate 4x4 Tic-Tac-Toe Games
Problem Description
You are given an empty 4x4 game board. Two players, 'X' and 'O', take turns placing their marks, with 'X' always moving first.
A player achieves a win by creating three consecutive marks in any row, column, or diagonal. The game concludes immediately upon a player achieving this win condition. If the board becomes full and no player has achieved a win, the game also ends.
Your task is to write a program that uses recursion and backtracking to enumerate all valid game sequences from an empty board to any terminal state. A terminal state is defined as either:
- A win for player 'X'.
- A win for player 'O'.
- A full board with no winner.
You may choose to return either:
- The total count of such valid terminal game sequences.
- The actual terminal boards or the full move sequences themselves.
Be prepared to discuss the following aspects of your solution:
- How you represent the game board internally.
- The strategy for efficiently detecting a win condition.
- How recursion is employed to explore the game tree.
- The mechanism for backtracking and restoring the board state after each move.
- An analysis of the worst-case time complexity of your approach.
AI interview prep
Core dilemma
Managing the combinatorial explosion of game states while ensuring correct and efficient state transitions and win checks for complete enumeration.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Enumerate 4x4 Tic-Tac-Toe Games
Problem Description
You are given an empty 4x4 game board. Two players, 'X' and 'O', take turns placing their marks, with 'X' always moving first.
A player achieves a win by creating three consecutive marks in any row, column, or diagonal. The game concludes immediately upon a player achieving this win condition. If the board becomes full and no player has achieved a win, the game also ends.
Your task is to write a program that uses recursion and backtracking to enumerate all valid game sequences from an empty board to any terminal state. A terminal state is defined as either:
- A win for player 'X'.
- A win for player 'O'.
- A full board with no winner.
You may choose to return either:
- The total count of such valid terminal game sequences.
- The actual terminal boards or the full move sequences themselves.
Be prepared to discuss the following aspects of your solution:
- How you represent the game board internally.
- The strategy for efficiently detecting a win condition.
- How recursion is employed to explore the game tree.
- The mechanism for backtracking and restoring the board state after each move.
- An analysis of the worst-case time complexity of your approach.