348. Design Tic-Tac-Toe

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 trade extra space such that move() operation can be done in O(1)?
只有两个player

如果一个player想要赢，那么整行或者整列或者整个对角线都得是他的点。怎么O(1) move 实现这个呢？
就是说每次move的时候就要O(1) check 是否win。

You need two arrays: int rows[n], int cols[n], plus two variables: diagonal, anti_diagonal.

player1 positive score
player2 negative score
每个cell 存score 只有score == n的时候才win

 public class TicTacToe {  
   int[] rows;  
   int[] cols;  
   int diagonal;  
   int anti_diagonal;  
   int n;  
   /** Initialize your data structure here. */  
   public TicTacToe(int n) {  
     //if move to ith row, if ith row already has some thing, fail  
     rows = new int[n];  
     cols = new int[n];  
     diagonal = 0;  
     anti_diagonal = 0;  
     this.n = n;  
   }  
   /** 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) {  
     //player1 positive score  
     //player2 negative score  
     int score = player == 1 ? 1:-1;  
     rows[row]+=score;  
     cols[col]+=score;  
     if(row == col)  
       diagonal+=score;  
     if(row+col == n-1)  
       anti_diagonal += score;  
     if(rows[row] == n || cols[col] == n ||diagonal==n||anti_diagonal==n) return 1;   
     if(rows[row] == -n || cols[col] == -n ||diagonal==-n||anti_diagonal==-n) return 2;  
     return 0;  
   }  
 }