A Tic-Tac-Toe board is given as a string array board. Return True if and only if it is possible to reach this board position during the course of a valid tic-tac-toe game.

The board is a 3 x 3 array, and consists of characters " ", "X", and "O".  The " " character represents an empty square.

Here are the rules of Tic-Tac-Toe:


       Players take turns placing characters into empty squares (" ").
       The first player always places "X" characters, while the second player always places "O" characters.
       "X" and "O" characters are always placed into empty squares, never filled ones.
       The game ends when there are 3 of the same (non-empty) character filling any row, column, or diagonal.
       The game also ends if all squares are non-empty.
       No more moves can be played if the game is over.



Example 1:
Input: board = ["O  ", "   ", "   "]
Output: false
Explanation: The first player always plays "X".

Example 2:
Input: board = ["XOX", " X ", "   "]
Output: false
Explanation: Players take turns making moves.

Example 3:
Input: board = ["XXX", "   ", "OOO"]
Output: false

Example 4:
Input: board = ["XOX", "O O", "XOX"]
Output: true


Note:


       board is a length-3 array of strings, where each string board[i] has length 3.
       Each board[i][j] is a character in the set {" ", "X", "O"}.

Difficulty: interview

Starter code:

class Solution:
    def validTicTacToe(self, board: List[str]) -> bool:
        

Solutions:
class Solution:
     def swimInWater(self, grid):
         """
         :type grid: List[List[int]]
         :rtype: int
         """
         N = len(grid)
         if N == 1:
             return 0
         
         eleD = {}
         for i in range(N):
             for j in range(N):
                 eleD[grid[i][j]] = (i,j)
 
 
         C = [[0 for _ in range(N)] for _ in range(N)]
         stack = set()
         nextstack = set()
         nextstack.add((0,0))
         for t in range(grid[0][0],N*N):
             if eleD[t] not in nextstack:
                 continue
             stack.add(eleD[t])
             nextstack.remove(eleD[t])
             while stack:
                 (x,y) = stack.pop()
                 if x == N-1 and y == N-1:
                     return t
                 C[x][y] = 1
                 if x > 0:
                     P = (x-1,y)
                     if C[P[0]][P[1]] == 0:
                         if grid[P[0]][P[1]] <= t:
                             stack.add(P)
                         else:
                             nextstack.add(P)
                 if y > 0:
                     P = (x,y-1)
                     if C[P[0]][P[1]] == 0:
                         if grid[P[0]][P[1]] <= t:
                             stack.add(P)
                         else:
                             nextstack.add(P)
                 if x < N-1:
                     P = (x+1,y)
                     if C[P[0]][P[1]] == 0:
                         if grid[P[0]][P[1]] <= t:
                             stack.add(P)
                         else:
                             nextstack.add(P)
                 if y < N-1:
                     P = (x,y+1)
                     if C[P[0]][P[1]] == 0:
                         if grid[P[0]][P[1]] <= t:
                             stack.add(P)
                         else:
                             nextstack.add(P)
             print(t)
                 
                 
 
         # eleD = {}
         # for i in range(N):
         #     for j in range(N):
         #         eleD[grid[i][j]] = (i,j)
         # res = grid
         # for t in range(N*N):
         #     (x,y) = eleD[t]
         #     if x > 0:
         #         if res[x-1][y] <= t:
         #             temp = res[x-1][y]
         #             for i in range(N):
         #                 for j in range(N):
         #                     if res[i][j] == temp:
         #                         res[i][j] = t
         #     if y > 0:
         #         if res[x][y - 1] <= t:
         #             temp = res[x][y - 1]
         #             for i in range(N):
         #                 for j in range(N):
         #                     if res[i][j] == temp:
         #                         res[i][j] = t
         #     if x < N - 1:
         #         if res[x + 1][y] <= t:
         #             temp = res[x + 1][y]
         #             for i in range(N):
         #                 for j in range(N):
         #                     if res[i][j] == temp:
         #                         res[i][j] = t
         #     if y < N - 1:
         #         if res[x][y + 1] <= t:
         #             temp = res[x][y + 1]
         #             for i in range(N):
         #                 for j in range(N):
         #                     if res[i][j] == temp:
         #                         res[i][j] = t
         #     #print(t,res)
         #     if res[0][0] == res[N-1][N-1]:
         #         return t


class Solution:
     def swimInWater(self, grid):
         """
         :type grid: List[List[int]]
         :rtype: int
         """
         n = len(grid)
         flag = []
         for i in range(n):
             flag.append([0] * n)
         flag[0][0] = 1
         pos = [0] * (n * n)
         for i in range(n):
             for j in range(n):
                 pos[grid[i][j]] = (i, j)
 
                 
         def search(x, y, n, grid, flag, k):
             if x < 0 or x >= n or y < 0 or y >= n or flag[x][y] == 2:
                 return
             if grid[x][y] > k:
                 flag[x][y] = 1
             else:
                 flag[x][y] = 2
                 search(x - 1, y, n, grid, flag, k)
                 search(x + 1, y, n, grid, flag, k)
                 search(x, y - 1, n, grid, flag, k)
                 search(x, y + 1, n, grid, flag, k)
         for k in range(n * n):
             x, y = pos[k]
             if flag[x][y] == 1:
                 search(x, y, n, grid, flag, k)
             if flag[n - 1][n - 1] == 2:
                 return k


class Solution:
     def swimInWater(self, grid):
         """
         :type grid: List[List[int]]
         :rtype: int
         """
         n = len(grid)
         pq = [(grid[0][0], 0, 0)]
         seen = set([(0, 0)])
         res = 0
         while True:
             val, y, x = heapq.heappop(pq)
             res = max(res, val)
             if y == x == n - 1:
                 return res
             for i, j in [(y + 1, x), (y - 1, x), (y, x + 1), (y, x - 1)]:
                 if 0 <= i < n and 0 <= j < n and (i, j) not in seen:
                     seen.add((i, j))
                     heapq.heappush(pq, (grid[i][j], i, j))
         return 0


import heapq
 
 class Solution:
     def swimInWater(self, grid):
         """
         :type grid: List[List[int]]
         :rtype: int
         """
         q = [(grid[0][0], (0, 0))]
         n = len(grid)
         grid[0][0] = -1
         
         dirs = [(0, 1), (0, -1), (1, 0), (-1, 0)]
         
         while q:
             val = heapq.heappop(q)
             i = val[1][0]
             j = val[1][1]
             
             if i == j == n - 1:
                 return val[0]
             
             for d in dirs:
                 x = i + d[0]
                 y = j + d[1]
                 
                 if 0 <= x < n and 0 <= y < n and grid[x][y] != -1:
                     heapq.heappush(q, (max(grid[x][y], val[0]), (x, y)))
                     grid[x][y] = -1
         
         return -1
         
         
                     
                     
                     
         

import heapq
 class Solution:
     def swimInWater(self, grid):
         """
         :type grid: List[List[int]]
         :rtype: int
         """
         
         def neighbors(n, x, y):
             neighbors = []
             if 0 <= x+1 < n and 0 <= y < n: neighbors.append((x+1, y))
             if 0 <= x-1 < n and 0 <= y < n: neighbors.append((x-1, y))
             if 0 <= x < n and 0 <= y+1 < n: neighbors.append((x, y+1))
             if 0 <= x < n and 0 <= y-1 < n: neighbors.append((x, y-1))
             return neighbors
                 
             
         
         n = len(grid)
         
         poss = set((0,0))
         pq = [(grid[0][0],0,0)]
         maxx = 0
         while pq:
             elem, x, y = heapq.heappop(pq)
             maxx = max(maxx, elem)
             for newx, newy in neighbors(n, x, y):
                 if newx == n-1 and newy == n-1:
                     return max(maxx, grid[n-1][n-1])
                 if (newx, newy) not in poss:
                     poss.add((newx, newy))
                     # neighborval = grid[newx][newy]
                     # if neighborval <= elem:
                     heapq.heappush(pq, (grid[newx][newy], newx, newy))
             # print(pq)
         return maxx
                     
             
             
         

class Solution:
     def swimInWater(self, grid):
         """
         :type grid: List[List[int]]
         :rtype: int
         """
         N, pq, seen, res = len(grid), [(grid[0][0], 0, 0)], set([(0, 0)]), 0
         while True:
             T, x, y = heapq.heappop(pq)
             res = max(res, T)
             if x == y == N - 1:
                 return res
             for i, j in [(x + 1, y), (x, y + 1), (x - 1, y), (x, y - 1)]:
                 if 0 <= i < N and 0 <= j < N and (i, j) not in seen:
                     seen.add((i, j))
                     heapq.heappush(pq, (grid[i][j], i, j))

class Solution:
     def swimInWater(self, grid):
         """
         :type grid: List[List[int]]
         :rtype: int
         """
         m, n = len(grid), len(grid[0])
         seen = set()
         seen.add((0, 0))
         heap = [(grid[0][0], 0, 0)]
         ans = 0
         while heap:
             h, i, j = heapq.heappop(heap)
             ans = max(ans, h)
             if i == m-1 and j == n-1:
                 return ans
             for a, b in [[i-1, j], [i+1, j], [i, j-1], [i, j+1]]:
                 if 0 <= a < m and 0 <= b < n and (a, b) not in seen:
                     heapq.heappush(heap, (grid[a][b], a, b))
                     seen.add((a, b))