It is common in the combinatorial search community to define search spaces implicitly, that is, as a set of states and transitions between them - as opposed to explicitly, that is, as concrete sets of vertices and edges. In implicit search spaces, states can be represented as vertices and transitions as edges, however, in many cases the practical set of states may not have finite bounds and therefore the number of edges and vertices cannot always be defined with finite cardinalities (either practically or theoretically). Thus for many applications it makes more sense to define performance in terms of the branching factor $b$, as opposed to vertex and edge cardinalities.

Just adding to what @Artur said: You only need 2 points to find the slope of a straight line, even if you're given more, so that's O(1) for me...

import javax.swing.; import java.awt.; import java.awt.event.ActionEvent; import java.awt.event.ActionListener;

public class TicTacToeGUI extends JFrame { private JButton[][] buttons = new JButton[3][3]; private char currentPlayer = 'X';

public TicTacToeGUI() {
    setTitle("Tic Tac Toe");
    setSize(400, 400);
    setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    setLayout(new GridLayout(3, 3));

    initializeButtons();
}

private void initializeButtons() {
    for (int row = 0; row < 3; row++) {
        for (int col = 0; col < 3; col++) {
            buttons[row][col] = new JButton("");
            buttons[row][col].setFont(new Font("Arial", Font.PLAIN, 80));
            buttons[row][col].setFocusPainted(false);

            // Adding the action listener to each button
            buttons[row][col].addActionListener(new ButtonClickListener(row, col));
            add(buttons[row][col]);
        }
    }
}

// Inner class to handle button clicks
private class ButtonClickListener implements ActionListener {
    private int row, col;

    public ButtonClickListener(int row, int col) {
        this.row = row;
        this.col = col;
    }

    @Override
    public void actionPerformed(ActionEvent e) {
        // Check if the button is empty before marking it
        if (buttons[row][col].getText().equals("")) {
            buttons[row][col].setText(String.valueOf(currentPlayer));
            buttons[row][col].setEnabled(false);

            if (checkWinner()) {
                JOptionPane.showMessageDialog(null, "Player " + currentPlayer + " wins!");
                resetBoard();
            } else if (checkTie()) {
                JOptionPane.showMessageDialog(null, "It's a tie!");
                resetBoard();
            } else {
                // Switch players
                currentPlayer = (currentPlayer == 'X') ? 'O' : 'X';
            }
        }
    }
}

// Check for a winner
private boolean checkWinner() {
    for (int i = 0; i < 3; i++) {
        // Check rows and columns
        if ((buttons[i][0].getText().equals(String.valueOf(currentPlayer)) &&
                buttons[i][1].getText().equals(String.valueOf(currentPlayer)) &&
                buttons[i][2].getText().equals(String.valueOf(currentPlayer))) ||
                (buttons[0][i].getText().equals(String.valueOf(currentPlayer)) &&
                        buttons[1][i].getText().equals(String.valueOf(currentPlayer)) &&
                        buttons[2][i].getText().equals(String.valueOf(currentPlayer)))) {
            return true;
        }
    }
    // Check diagonals
    if ((buttons[0][0].getText().equals(String.valueOf(currentPlayer)) &&
            buttons[1][1].getText().equals(String.valueOf(currentPlayer)) &&
            buttons[2][2].getText().equals(String.valueOf(currentPlayer))) ||
            (buttons[0][2].getText().equals(String.valueOf(currentPlayer)) &&
                    buttons[1][1].getText().equals(String.valueOf(currentPlayer)) &&
                    buttons[2][0].getText().equals(String.valueOf(currentPlayer)))) {
        return true;
    }
    return false;
}

// Check for a tie
private boolean checkTie() {
    for (int row = 0; row < 3; row++) {
        for (int col = 0; col < 3; col++) {
            if (buttons[row][col].getText().equals("")) {
                return false;
            }
        }
    }
    return true;
}

// Reset the board for a new game
private void resetBoard() {
    for (int row = 0; row < 3; row++) {
        for (int col = 0; col < 3; col++) {
            buttons[row][col].setText("");
            buttons[row][col].setEnabled(true);
        }
    }
    currentPlayer ='X';

}

}