# Example: matrix = [[0,0,0,0],
# [0,0,0,0],
# [0,0,0,0]]
#
# robotPaths(matrix) = 38
#
#
# matrix = [[0,0,0],
# [0,0,0]]
#
# robotPaths(matrix) = 4



# Note: From any point, you can travel in the four cardinal directions. I decided to do backtracking approach to solve this problem.
# (north, south, east, west). A path is valid as long as it travels
# from the top left corner to the bottom right corner, does not go
# off of the matrix, and does not travel back on itself


def robot_paths(matrix):
 num_of_rows = len(matrix)
 num_of_cols = len(matrix[0])

 def traverse(row, col):
 nonlocal num_of_rows 
 nonlocal num_of_cols
 # is row and col inside the boundaries 
 if row < 0 or row >= num_of_rows or col < 0 or col >= num_of_cols:
 return 0 

 # has row, col already been visited 
 if matrix[row][col] == 1: 
 return 0 

 # is row, col the destination? 
 if row == num_of_rows - 1 and col == num_of_cols - 1:
 return 1 

 # mark coordinate as visited 
 matrix[row][col] = 1 

 # initialize sum of total unique paths to end from that coordinate
 s = traverse(row, col + 1) + traverse(row + 1, col) + traverse(row - 1, col) + traverse(row, col - 1)

 # backtrack; mark coordinate as unvisited so it can be 
 # used in another path 
 matrix[row][col] = 0 

 return s 

 return traverse(0, 0)

# Example: matrix = [[0,0,0,0],
# [0,0,0,0],
# [0,0,0,0]]
#
# robotPaths(matrix) = 38
#
#
# matrix = [[0,0,0],
# [0,0,0]]
#
# robotPaths(matrix) = 4



# Note: From any point, you can travel in the four cardinal directions. I decided to do backtracking approach to solve this problem.
# (north, south, east, west). A path is valid as long as it travels
# from the top left corner to the bottom right corner, does not go
# off of the matrix, and does not travel back on itself


def robot_paths(matrix):
 num_of_rows = len(matrix)
 num_of_cols = len(matrix[0])

 def traverse(row, col):
 nonlocal num_of_rows 
 nonlocal num_of_cols
 # is row and col inside the boundaries 
 if row < 0 or row >= num_of_rows or col < 0 or col >= num_of_cols:
 return 0 

 # has row, col already been visited 
 if matrix[row][col] == 1: 
 return 0 

 # is row, col the destination? 
 if row == num_of_rows - 1 and col == num_of_cols - 1:
 return 1 

 # mark coordinate as visited 
 matrix[row][col] = 1 

 # initialize sum of total unique paths to end from that coordinate
 s = traverse(row, col + 1) + traverse(row + 1, col) + traverse(row - 1, col) + traverse(row, col - 1)

 # backtrack; mark coordinate as unvisited so it can be 
 # used in another path 
 matrix[row][col] = 0 

 return s 

 return traverse(0, 0)

# Example: matrix = [[0,0,0,0],
# [0,0,0,0],
# [0,0,0,0]]
#
# robotPaths(matrix) = 38
#
#
# matrix = [[0,0,0],
# [0,0,0]]
#
# robotPaths(matrix) = 4



# Note: From any point, you can travel in the four cardinal directions. I decided to do backtracking approach to solve this problem.
# (north, south, east, west). A path is valid as long as it travels
# from the top left corner to the bottom right corner, does not go
# off of the matrix, and does not travel back on itself


def robot_paths(matrix):
 num_of_rows = len(matrix)
 num_of_cols = len(matrix[0])

 def traverse(row, col):
 nonlocal num_of_rows 
 nonlocal num_of_cols
 # is row and col inside the boundaries 
 if row < 0 or row >= num_of_rows or col < 0 or col >= num_of_cols:
 return 0 

 # has row, col already been visited 
 if matrix[row][col] == 1: 
 return 0 

 # is row, col the destination? 
 if row == num_of_rows - 1 and col == num_of_cols - 1:
 return 1 

 # mark coordinate as visited 
 matrix[row][col] = 1 

 # initialize sum of total unique paths to end from that coordinate
 s = traverse(row, col + 1) + traverse(row + 1, col) + traverse(row - 1, col) + traverse(row, col - 1)

 # backtrack; mark coordinate as unvisited so it can be 
 # used in another path 
 matrix[row][col] = 0 

 return s 

 return traverse(0, 0)

# Example: matrix = [[0,0,0,0],
# [0,0,0,0],
# [0,0,0,0]]
#
# robotPaths(matrix) = 38
#
#
# matrix = [[0,0,0],
# [0,0,0]]
#
# robotPaths(matrix) = 4



# Note: From any point, you can travel in the four cardinal directions. I decided to do backtracking approach to solve this problem.
# (north, south, east, west). A path is valid as long as it travels
# from the top left corner to the bottom right corner, does not go
# off of the matrix, and does not travel back on itself


def robot_paths(matrix):
 num_of_rows = len(matrix)
 num_of_cols = len(matrix[0])

 def traverse(row, col):
 nonlocal num_of_rows 
 nonlocal num_of_cols
 # is row and col inside the boundaries 
 if row < 0 or row >= num_of_rows or col < 0 or col >= num_of_cols:
 return 0 

 # has row, col already been visited 
 if matrix[row][col] == 1: 
 return 0 

 # is row, col the destination? 
 if row == num_of_rows - 1 and col == num_of_cols - 1:
 return 1 

 # mark coordinate as visited 
 matrix[row][col] = 1 

 # initialize sum of total unique paths to end from that coordinate
 s = traverse(row, col + 1) + traverse(row + 1, col) + traverse(row - 1, col) + traverse(row, col - 1)

 # backtrack; mark coordinate as unvisited so it can be 
 # used in another path 
 matrix[row][col] = 0 

 return s 

 return traverse(0, 0)

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