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# Validity of a given Tic-Tac-Toe board configuration

• Difficulty Level : Hard
• Last Updated : 12 Dec, 2022

A Tic-Tac-Toe board is given after some moves are played. Find out if the given board is valid, i.e., is it possible to reach this board position after some moves or not.
Note that every arbitrary filled grid of 9 spaces isn’t valid e.g. a grid filled with 3 X and 6 O isn’t valid situation because each player needs to take alternate turns.

Input is given as a 1D array of size 9.

Examples:

```Input: board[] =  {'X', 'X', 'O',
'O', 'O', 'X',
'X', 'O', 'X'};
Output: Valid

Input: board[] =  {'O', 'X', 'X',
'O', 'X', 'X',
'O', 'O', 'X'};
Output: Invalid
(Both X and O cannot win)

Input: board[] =  {'O', 'X', ' ',
' ', ' ', ' ',
' ', ' ', ' '};
Output: Valid
(Valid board with only two moves played)```
Recommended Practice

Basically, to find the validity of an input grid, we can think of the conditions when an input grid is invalid. Let no. of “X”s be countX and no. of “O”s be countO. Since we know that the game starts with X, a given grid of Tic-Tac-Toe game would be definitely invalid if following two conditions meet

1. countX != countO AND
2. countX != countO + 1
• Since “X” is always the first move, second condition is also required.
• Now does it mean that all the remaining board positions are valid one? The answer is NO. Think of the cases when input grid is such that both X and O are making straight lines. This is also not
• valid position because the game ends when one player wins. So we need to check the following condition as well
3. If input grid shows that both the players are in winning situation, it’s an invalid position.
4. If input grid shows that the player with O has put a straight-line (i.e. is in win condition) and countX != countO, it’s an invalid position. The reason is that O plays his move only after X plays his
• move. Since X has started the game, O would win when both X and O has played equal no. of moves.
5. If input grid shows that X is in winning condition than xCount must be one greater that oCount.
• Armed with above conditions i.e. a), b), c) and d), we can now easily formulate an algorithm/program to check the validity of a given Tic-Tac-Toe board position.
```1)  countX == countO or countX == countO + 1
2)  If O is in win condition then check
a)     If X also wins, not valid
b)     If xbox != obox , not valid
3)  If X is in win condition then check if xCount is
one more than oCount or not  ```

Another way to find the validity of a given board is using ‘inverse method’ i.e. rule out all the possibilities when a given board is invalid.

## C++

 `// C++ program to check whether a given tic tac toe``// board is valid or not``#include ``using` `namespace` `std;` `// This matrix is used to find indexes to check all``// possible winning triplets in board[0..8]``int` `win[8][3] = {{0, 1, 2}, ``// Check first row.``                ``{3, 4, 5}, ``// Check second Row``                ``{6, 7, 8}, ``// Check third Row``                ``{0, 3, 6}, ``// Check first column``                ``{1, 4, 7}, ``// Check second Column``                ``{2, 5, 8}, ``// Check third Column``                ``{0, 4, 8}, ``// Check first Diagonal``                ``{2, 4, 6}}; ``// Check second Diagonal` `// Returns true if character 'c' wins. c can be either``// 'X' or 'O'``bool` `isCWin(``char` `*board, ``char` `c)``{``    ``// Check all possible winning combinations``    ``for` `(``int` `i=0; i<8; i++)``        ``if` `(board[win[i][0]] == c &&``            ``board[win[i][1]] == c &&``            ``board[win[i][2]] == c )``            ``return` `true``;``    ``return` `false``;``}` `// Returns true if given board is valid, else returns false``bool` `isValid(``char` `board[9])``{``    ``// Count number of 'X' and 'O' in the given board``    ``int` `xCount=0, oCount=0;``    ``for` `(``int` `i=0; i<9; i++)``    ``{``    ``if` `(board[i]==``'X'``) xCount++;``    ``if` `(board[i]==``'O'``) oCount++;``    ``}` `    ``// Board can be valid only if either xCount and oCount``    ``// is same or count is one more than oCount``    ``if` `(xCount==oCount || xCount==oCount+1)``    ``{``        ``// Check if 'O' is winner``        ``if` `(isCWin(board, ``'O'``))``        ``{``            ``// Check if 'X' is also winner, then``            ``// return false``            ``if` `(isCWin(board, ``'X'``))``                ``return` `false``;` `            ``// Else return true xCount and yCount are same``            ``return` `(xCount == oCount);``        ``}` `        ``// If 'X' wins, then count of X must be greater``        ``if` `(isCWin(board, ``'X'``) && xCount != oCount + 1)``        ``return` `false``;` `        ``// If 'O' is not winner, then return true``        ``return` `true``;``    ``}``    ``return` `false``;``}` `// Driver program``int` `main()``{``char` `board[] = {``'X'``, ``'X'``, ``'O'``,``                ``'O'``, ``'O'``, ``'X'``,``                ``'X'``, ``'O'``, ``'X'``};``(isValid(board))? cout << ``"Given board is valid"``:``                    ``cout << ``"Given board is not valid"``;``return` `0;``}`

## Java

 `// Java program to check whether a given tic tac toe``// board is valid or not``import` `java.io.*;``class` `GFG {` `// This matrix is used to find indexes to check all``// possible winning triplets in board[0..8]``    ``static` `int` `win[][] = {{``0``, ``1``, ``2``}, ``// Check first row.``    ``{``3``, ``4``, ``5``}, ``// Check second Row``    ``{``6``, ``7``, ``8``}, ``// Check third Row``    ``{``0``, ``3``, ``6``}, ``// Check first column``    ``{``1``, ``4``, ``7``}, ``// Check second Column``    ``{``2``, ``5``, ``8``}, ``// Check third Column``    ``{``0``, ``4``, ``8``}, ``// Check first Diagonal``    ``{``2``, ``4``, ``6``}}; ``// Check second Diagonal` `// Returns true if character 'c' wins. c can be either``// 'X' or 'O'``    ``static` `boolean` `isCWin(``char``[] board, ``char` `c) {``        ``// Check all possible winning combinations``        ``for` `(``int` `i = ``0``; i < ``8``; i++) {``            ``if` `(board[win[i][``0``]] == c``                    ``&& board[win[i][``1``]] == c``                    ``&& board[win[i][``2``]] == c) {``                ``return` `true``;``            ``}``        ``}``        ``return` `false``;``    ``}` `// Returns true if given board is valid, else returns false``    ``static` `boolean` `isValid(``char` `board[]) {``        ``// Count number of 'X' and 'O' in the given board``        ``int` `xCount = ``0``, oCount = ``0``;``        ``for` `(``int` `i = ``0``; i < ``9``; i++) {``            ``if` `(board[i] == ``'X'``) {``                ``xCount++;``            ``}``            ``if` `(board[i] == ``'O'``) {``                ``oCount++;``            ``}``        ``}` `        ``// Board can be valid only if either xCount and oCount``        ``// is same or count is one more than oCount``        ``if` `(xCount == oCount || xCount == oCount + ``1``) {``            ``// Check if 'O' is winner``            ``if` `(isCWin(board, ``'O'``)) {``                ``// Check if 'X' is also winner, then``                ``// return false``                ``if` `(isCWin(board, ``'X'``)) {``                    ``return` `false``;``                ``}` `                ``// Else return true xCount and yCount are same``                ``return` `(xCount == oCount);``            ``}` `            ``// If 'X' wins, then count of X must be greater``            ``if` `(isCWin(board, ``'X'``) && xCount != oCount + ``1``) {``                ``return` `false``;``            ``}` `            ``// If 'O' is not winner, then return true``            ``return` `true``;``        ``}``        ``return` `false``;``    ``}` `// Driver program``    ``public` `static` `void` `main(String[] args) {``        ``char` `board[] = {``'X'``, ``'X'``, ``'O'``, ``'O'``, ``'O'``, ``'X'``, ``'X'``, ``'O'``, ``'X'``};` `        ``if` `((isValid(board))) {``            ``System.out.println(``"Given board is valid"``);``        ``} ``else` `{``            ``System.out.println(``"Given board is not valid"``);``        ``}``    ``}``}``//this code contributed by PrinciRaj1992`

## Python3

 `# Python3 program to check whether a given tic tac toe``# board is valid or not` `# Returns true if char wins. Char can be either``# 'X' or 'O'``def` `win_check(arr, char):``    ``# Check all possible winning combinations``    ``matches ``=` `[[``0``, ``1``, ``2``], [``3``, ``4``, ``5``],``               ``[``6``, ``7``, ``8``], [``0``, ``3``, ``6``],``               ``[``1``, ``4``, ``7``], [``2``, ``5``, ``8``],``               ``[``0``, ``4``, ``8``], [``2``, ``4``, ``6``]]` `    ``for` `i ``in` `range``(``8``):``        ``if``(arr[matches[i][``0``]] ``=``=` `char ``and``            ``arr[matches[i][``1``]] ``=``=` `char ``and``            ``arr[matches[i][``2``]] ``=``=` `char):``            ``return` `True``    ``return` `False` `def` `is_valid(arr):``    ``# Count number of 'X' and 'O' in the given board``    ``xcount ``=` `arr.count(``'X'``)``    ``ocount ``=` `arr.count(``'O'``)``    ` `    ``# Board can be valid only if either xcount and ocount``    ``# is same or count is one more than oCount``    ``if``(xcount ``=``=` `ocount``+``1` `or` `xcount ``=``=` `ocount):``        ``# Check if O wins``        ``if` `win_check(arr, ``'O'``):``            ``# Check if X wins, At a given point only one can win,``            ``# if X also wins then return Invalid``            ``if` `win_check(arr, ``'X'``):``                ``return` `"Invalid"` `            ``# O can only win if xcount == ocount in case where whole``            ``# board has values in each position.``            ``if` `xcount ``=``=` `ocount:``                ``return` `"Valid"` `        ``# If X wins then it should be xc == oc + 1,``        ``# If not return Invalid    ``        ``if` `win_check(arr, ``'X'``) ``and` `xcount !``=` `ocount``+``1``:``            ``return` `"Invalid"``        ` `        ``# if O is not the winner return Valid``        ``if` `not` `win_check(arr, ``'O'``):``            ``return` `"valid"``        ` `    ``# If nothing above matches return invalid``    ``return` `"Invalid"`  `# Driver Code``arr ``=` `[``'X'``, ``'X'``, ``'O'``,``       ``'O'``, ``'O'``, ``'X'``,``       ``'X'``, ``'O'``, ``'X'``]``print``(``"Given board is "` `+` `is_valid(arr))`

## C#

 `// C# program to check whether a given``// tic tac toe board is valid or not``using` `System;` `class` `GFG``{` `// This matrix is used to find indexes``// to check all possible winning triplets``// in board[0..8]``public` `static` `int``[][] win = ``new` `int``[][]``{``    ``new` `int``[] {0, 1, 2},``    ``new` `int``[] {3, 4, 5},``    ``new` `int``[] {6, 7, 8},``    ``new` `int``[] {0, 3, 6},``    ``new` `int``[] {1, 4, 7},``    ``new` `int``[] {2, 5, 8},``    ``new` `int``[] {0, 4, 8},``    ``new` `int``[] {2, 4, 6}``};` `// Returns true if character 'c'``// wins. c can be either 'X' or 'O'``public` `static` `bool` `isCWin(``char``[] board,``                          ``char` `c)``{``    ``// Check all possible winning``    ``// combinations``    ``for` `(``int` `i = 0; i < 8; i++)``    ``{``        ``if` `(board[win[i][0]] == c &&``            ``board[win[i][1]] == c &&``            ``board[win[i][2]] == c)``        ``{``            ``return` `true``;``        ``}``    ``}``    ``return` `false``;``}` `// Returns true if given board``// is valid, else returns false``public` `static` `bool` `isValid(``char``[] board)``{``    ``// Count number of 'X' and``    ``// 'O' in the given board``    ``int` `xCount = 0, oCount = 0;``    ``for` `(``int` `i = 0; i < 9; i++)``    ``{``        ``if` `(board[i] == ``'X'``)``        ``{``            ``xCount++;``        ``}``        ``if` `(board[i] == ``'O'``)``        ``{``            ``oCount++;``        ``}``    ``}` `    ``// Board can be valid only if either``    ``// xCount and oCount is same or count``    ``// is one more than oCount``    ``if` `(xCount == oCount ||``        ``xCount == oCount + 1)``    ``{``        ``// Check if 'O' is winner``        ``if` `(isCWin(board, ``'O'``))``        ``{``            ``// Check if 'X' is also winner,``            ``// then return false``            ``if` `(isCWin(board, ``'X'``))``            ``{``                ``return` `false``;``            ``}` `            ``// Else return true xCount``            ``// and yCount are same``            ``return` `(xCount == oCount);``        ``}` `        ``// If 'X' wins, then count of``        ``// X must be greater``        ``if` `(isCWin(board, ``'X'``) &&``            ``xCount != oCount + 1)``        ``{``            ``return` `false``;``        ``}` `        ``// If 'O' is not winner,``        ``// then return true``        ``return` `true``;``    ``}``    ``return` `false``;``}` `// Driver Code``public` `static` `void` `Main(``string``[] args)``{``    ``char``[] board = ``new` `char``[] {``'X'``, ``'X'``, ``'O'``, ``'O'``, ``'O'``,``                                    ``'X'``, ``'X'``, ``'O'``, ``'X'``};` `    ``if` `((isValid(board)))``    ``{``        ``Console.WriteLine(``"Given board is valid"``);``    ``}``    ``else``    ``{``        ``Console.WriteLine(``"Given board is not valid"``);``    ``}``}``}` `// This code is contributed by Shrikant13`

## PHP

 ``

## Javascript

 ``

Output

`Given board is valid`

Time complexity: O(1)
Auxiliary Space: O(1), since no extra space has been taken.