# Question

Design a Tic-tac-toe game that is played between two players on a n x n grid.

You may assume the following rules:

1. A move is guaranteed to be valid and is placed on an empty block.
2. Once a winning condition is reached, no more moves is allowed.
3. A player who succeeds in placing n of their marks in a horizontal, vertical, or diagonal row wins the game.

Example:

Given n = 3, assume that player 1 is "X" and player 2 is "O" in the board.

TicTacToe toe = new TicTacToe(3);

toe.move(0, 0, 1); -> Returns 0 (no one wins)
|X| | |
| | | |    // Player 1 makes a move at (0, 0).
| | | |

toe.move(0, 2, 2); -> Returns 0 (no one wins)
|X| |O|
| | | |    // Player 2 makes a move at (0, 2).
| | | |

toe.move(2, 2, 1); -> Returns 0 (no one wins)
|X| |O|
| | | |    // Player 1 makes a move at (2, 2).
| | |X|

toe.move(1, 1, 2); -> Returns 0 (no one wins)
|X| |O|
| |O| |    // Player 2 makes a move at (1, 1).
| | |X|

toe.move(2, 0, 1); -> Returns 0 (no one wins)
|X| |O|
| |O| |    // Player 1 makes a move at (2, 0).
|X| |X|

toe.move(1, 0, 2); -> Returns 0 (no one wins)
|X| |O|
|O|O| |    // Player 2 makes a move at (1, 0).
|X| |X|

toe.move(2, 1, 1); -> Returns 1 (player 1 wins)
|X| |O|
|O|O| |    // Player 1 makes a move at (2, 1).
|X|X|X|


Could you do better than $$O(n^2)$$ per move() operation?

# Solution

class TicTacToe {
class PlayerInfo {
ArrayList<Set<Integer>> cond;
boolean win;

public PlayerInfo(int n) {
cond = new ArrayList<Set<Integer>>(2 * n + 2);
for(int i = 0; i < 2 * n + 2; i++) {
}
win = false;
}

public void addMove(int row, int col) {
// row
if(cond.get(row) != null) {
if(cond.get(row).size() == n) win = true;
}
// col
if(cond.get(n + col) != null) {
if(cond.get(n + col).size() == n) win = true;
}
// top left to bottom right
if(row == col && cond.get(2 * n) != null) {
if(cond.get(2 * n).size() == n) win = true;
}
// bottom left to top right
if(row + col == n - 1 && cond.get(2 * n + 1) != null) {
if(cond.get(2 * n + 1).size() == n) win = true;
}
}

private void counterMove(int row, int col) {
if(cond.get(row) != null) {
cond.set(row, null);
}
if(cond.get(n + col) != null) {
cond.set(n + col, null);
}
if(row == col && cond.get(2 * n) != null) {
cond.set(2 * n, null);
}
if (row + col == n - 1 && cond.get(2 * n + 1) != null) {
cond.set(2 * n + 1, null);
}
}
}
PlayerInfo player1, player2;
int winner, n;

/** Initialize your data structure here. */
public TicTacToe(int n) {
this.n = n;
player1 = new PlayerInfo(n);
player2 = new PlayerInfo(n);
winner = 0;
}

/** Player {player} makes a move at ({row}, {col}).
@param row The row of the board.
@param col The column of the board.
@param player The player, can be either 1 or 2.
@return The current winning condition, can be either:
0: No one wins.
1: Player 1 wins.
2: Player 2 wins. */
public int move(int row, int col, int player) {
if(winner != 0) return winner;
if(player == 1) {
player2.counterMove(row, col);
if(player1.win) winner = 1;
} else {
player1.counterMove(row, col);
if(player2.win) winner = 2;
}
return winner;
}
}

/**
* Your TicTacToe object will be instantiated and called as such:
* TicTacToe obj = new TicTacToe(n);
* int param_1 = obj.move(row,col,player);
*/