Woodstock Blog

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[Google] Winner of Tic-tac-toe



How would you determine if someone has won a game of tic-tac-toe on a board of any size?

(This is also on CC150v4 19.2 and CC150v4 17.2)


First, confirm that when the number of pieces in a line equals to the dimension of the board, one person wins. Eg. for 10 * 10 board, 10 pieces need to be in 1 line.

We can determine if someone has won during a game in real time, as in checking after every move.

Create an array of size 2n+2 at the beginning of the game and fill it with zeros. Each spot in the array will be a sum of X’s or O’s horizontally (the first n places in the array), vertically (the second n places in the array) and diagonally (the last 2 places). Then with every move, you add 1 to the 2 places (or 3 if on a diagnol) of the array if X, and subtract 1 if its an O. After adding you check and see if the value of the array is equal to n or -n, if it is, n mean X has won and -n means O has won.

This is uses O(2n+2) space, but it’s the best solution I can find online. I wrote code posted below.


written by me

enum Piece {
    Empty, Red, Blue

public static Piece hasWon3(Piece[][] board) {

    int N = board.length;

    // O(2n+2) space to store count info
    int[] rowCnt = new int[N];
    int[] colCnt = new int[N];
    int[] digCnt = new int[2];

    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {

            int pieceValue = 0;
            if (board[i][j] == Piece.Blue) {
                pieceValue = 1;
            } else if (board[i][j] == Piece.Red) {
                pieceValue = -1;

            // if empty, pieceValue is 0
            // if blue, add 1 in count
            // if red, subtract 1 in count
            rowCnt[i] += pieceValue;
            if (checkFinish(rowCnt[i], N) != null) {
                return checkFinish(rowCnt[i], N);

            // after adding the count, check if the game finishes
            colCnt[j] += pieceValue;
            if (checkFinish(colCnt[j], N) != null) {
                return checkFinish(colCnt[j], N);

            if (i == j) {
                digCnt[0] += pieceValue;
                if (checkFinish(digCnt[0], N) != null) {
                    return checkFinish(digCnt[0], N);
            } else if (i + j == N) {
                digCnt[1] += pieceValue;
                if (checkFinish(digCnt[1], N) != null) {
                    return checkFinish(digCnt[1], N);
    // game not finished, continue
    return Piece.Empty;

private static Piece checkFinish(int count, int N) {
    if (count == N)
        return Piece.Blue;
    else if (count == -1 * N)
        return Piece.Red;
        return null;