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Design Tic-Tac-Toe 解答
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:
- A move is guaranteed to be valid and is placed on an empty block.
- Once a winning condition is reached, no more moves is allowed.
- 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|
Follow up:
Could you do better than O(n2) per move()
operation?
Hint:
- Could you trade extra space such that
move()
operation can be done in O(1)? - You need two arrays: int rows[n], int cols[n], plus two variables: diagonal, anti_diagonal.
Answer
对于move操作,简单粗暴的方法是遍历整个二维数组,对每一行每一列以及对角线检查。时间,空间复杂度均为O(n^2)
我们可以单独考虑行,列,对角。
对于一行row[i],如果这一行中有棋手1下过,则+1。如果有棋手2下过,则-1。所以如果这一行全为棋手1下的,row[i]=n。棋手1获胜。
Similar case for col and diagonal, anti diagonal。
Time complexity O(1) Space complexity O(n)
1 public class TicTacToe { 2 3 private int[] row; 4 private int[] col; 5 private int diagonal; 6 private int anti_diagonal; 7 private int size; 8 /** Initialize your data structure here. */ 9 public TicTacToe(int n) { 10 size = n; 11 row = new int[n]; 12 col = new int[n]; 13 Arrays.fill(row, 0); 14 Arrays.fill(col, 0); 15 diagonal = 0; 16 anti_diagonal = 0; 17 } 18 19 /** Player {player} makes a move at ({row}, {col}). 20 @param row The row of the board. 21 @param col The column of the board. 22 @param player The player, can be either 1 or 2. 23 @return The current winning condition, can be either: 24 0: No one wins. 25 1: Player 1 wins. 26 2: Player 2 wins. */ 27 public int move(int row, int col, int player) { 28 int change = player == 1 ? 1 : -1; 29 this.row[row] += change; 30 this.col[col] += change; 31 if (row == col) { 32 diagonal += change; 33 } 34 if (row == (size - col - 1)) { 35 anti_diagonal += change; 36 } 37 if (this.row[row] == size || this.col[col] == size || diagonal == size || anti_diagonal == size) { 38 return 1; 39 } 40 if (this.row[row] == -size || this.col[col] == -size || diagonal == -size || anti_diagonal == -size) { 41 return 2; 42 } 43 return 0; 44 } 45 } 46 47 /** 48 * Your TicTacToe object will be instantiated and called as such: 49 * TicTacToe obj = new TicTacToe(n); 50 * int param_1 = obj.move(row,col,player); 51 */
Design Tic-Tac-Toe 解答
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