19.2 Design an algorithm to figure out if someone has won in a game of tic-tac-toe.
class TicTacToe
{
enum Tic
{
X, O
}
// Given TicTacToe map, wheter t has won the game.
// Assume map is a not-null 3*3 matrix, containing no null elements.
//
// check row, check column, check corner
// This is a brute force solution.
boolean checkRow(T[][] map, int r, T t)
{
for (int i = 0 ; i < 3 ; i ++)
{
if (map[r][i] != t)
return false;
}
return true;
}
boolean checkColumn(T[][] map, int c, T t)
{
for (int i = 0 ; i < 3 ; i ++)
{
if (map[i][r] != t)
return false;
}
return true;
}
boolean checkCornerLeft(T[][] map, T t)
{
for (int i = 0 ; i < 3 ; i ++)
{
if (map[i][i] != t)
return false;
}
return true;
}
boolean checkCornerRight(T[][] map, T t)
{
for (int i = 0 ; i < 3 ; i ++)
{
if (map[2 - i][i] != t)
return false;
}
return true;
}
boolean won(T[][] map, T t)
{
// Only check first row and first column
for (int i = 0 ; i < 3 ; i ++)
{
if (checkRow(map, i, t))
return true;
if (checkColumn(map, i, t))
return true;
}
checkCornerLeft(map, t);
checkCornerRight(map, t);
return false;
}
// A second option is that.
// There is 9 positions, each position has 2 choices.
// Thus, totally there are 2^9 conditions.
// Use bit map to represents these 2^9.
// If won, mark it as 1.
// Check some one won' only needs O(1)
}
