Description
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?
Solution
设计一个tic-tac-toe游戏,初始化一个游戏,并在每次move之后判断是否有人获胜。
Use a two-dimensional array to store game status. After each move, judge is there somebody wined in this game.
Code
class TicTacToe {
int[][] board;
/** Initialize your data structure here. */
public TicTacToe(int n) {
board = new int[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) {
board[row][col] = player;
if(win(player)){
return player;
}
return 0;
}
private boolean win(int player){
for (int i = 0; i < board.length; i++){
boolean lined = true;
for (int j = 0; j < board.length; j++){
if (board[i][j] != player){
lined = false;
}
}
if(lined){
return true;
}
}
for (int i = 0; i < board.length; i++){
boolean lined = true;
for (int j = 0; j < board.length; j++){
if (board[j][i] != player){
lined = false;
}
}
if(lined){
return true;
}
}
boolean lined = true;
for (int i = 0, j = 0; i < board.length;){
if (board[i][j] != player){
lined = false;
}
i++;
j++;
}
if (lined){
return true;
}
lined = true;
for (int i = board.length - 1, j = 0; i >= 0;){
if (board[i][j] != player){
lined = false;
}
i--;
j++;
}
if (lined){
return true;
}
else{
return false;
}
}
}
/**
* Your TicTacToe object will be instantiated and called as such:
* TicTacToe obj = new TicTacToe(n);
* int param_1 = obj.move(row,col,player);
*/
Time Complexity: O(n^2)
Space Complexity: O(n^2)
Review
The point is we do not need to maintain a whole board. For each row , col and diagonal, we could assign 1 and -1 to player 1 and player 2. If a row or col is occupied with same player, that is a win. So we could optimized move to O(1) time complexity and O(n) space complexity.
class TicTacToe {
private int[] rows;
private int[] cols;
private int diagonal;
private int anti;
/** Initialize your data structure here. */
public TicTacToe(int n) {
rows = new int[n];
cols = new int[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) {
int move = player == 1 ? 1 : -1;
int size = rows.length;
rows[row] += move;
cols[col] += move;
if (row == col){
diagonal += move;
}
if ((row + col + 1) == size){
anti += move;
}
if (Math.abs(rows[row]) == size || Math.abs(cols[col]) == size || Math.abs(diagonal) == size || Math.abs(anti) == size){
return player;
}
else{
return 0;
}
}
}
/**
* Your TicTacToe object will be instantiated and called as such:
* TicTacToe obj = new TicTacToe(n);
* int param_1 = obj.move(row,col,player);
*/