I got this problem during a mock interview, and I would like to get code review for the backtracking solution. I include 7 test cases, and my solution passes 7 out of 7 test cases. See the online code compiler here

Robot Paths

Prompt: Given a matrix of zeroes, determine how many unique paths exist from the top left corner to the bottom right corner

Input: An Array of Array of Integers (matrix)

Output: Integer

Examples:

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 in bounds? 

    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 

    matrix[row][col] = 0 



    return s 



  return traverse(0, 0)







#############################################

########  DO NOT TOUCH TEST BELOW!!!  #######

#############################################



def expect(count, name, test):

    if (count == None or not isinstance(count, list) or len(count) != 2):

        count = [0, 0]

    else:

        count[1] += 1



    result = 'false'

    errMsg = None

    try:

        if test():

            result = ' true'

            count[0] += 1

    except Exception as err:

        errMsg = str(err)



    print('  ' + (str(count[1]) + ')   ') + result + ' : ' + name)

    if errMsg != None:

        print('       ' + errMsg + 'n')



def lists_equal(lst1, lst2):

    if len(lst1) != len(lst2):

        return False

    for i in range(0, len(lst1)):

        if lst1[i] != lst2[i]:

            return False

    return True



print('Robot Paths Tests')

test_count = [0, 0]





def test():

    matrix = [[0, 0, 0, 0],

              [0, 0, 0, 0],

              [0, 0, 0, 0]]

    example = robot_paths(matrix)

    return example == 38





expect(test_count, 'should work on first example input', test)





def test():

    matrix = [[0, 0, 0],

              [0, 0, 0]]

    example = robot_paths(matrix)

    return example == 4





expect(test_count, 'should work on second example input', test)





def test():

    matrix = [[0]]

    example = robot_paths(matrix)

    return example == 1





expect(test_count, 'should work on single-element input', test)





def test():

    matrix = [[0, 0, 0, 0, 0, 0]]

    example = robot_paths(matrix)

    return example == 1





expect(test_count, 'should work on single-row input', test)





def test():

    matrix = [[0],

              [0],

              [0],

              [0],

              [0]]

    example = robot_paths(matrix)

    return example == 1





expect(test_count, 'should work on a 5 x 8 matrix input', test)





def test():

    matrix = [[0, 0, 0, 0, 0, 0, 0, 0],

              [0, 0, 0, 0, 0, 0, 0, 0],

              [0, 0, 0, 0, 0, 0, 0, 0],

              [0, 0, 0, 0, 0, 0, 0, 0],

              [0, 0, 0, 0, 0, 0, 0, 0]]

    print("  Please be patient, test 6 may take longer to run")

    example = robot_paths(matrix)

    return example == 7110272





print('PASSED: ' + str(test_count[0]) + ' / ' + str(test_count[1]) + 'nn')