Tiling Rectangles | Python Fiddle

class Grid:
    def __init__(self, width, height):
        self.height = height
        self.width = width
        self.grid = []
        for i in range(width):
            self.grid.append([])
            for j in range(height):
                self.grid[i].append(False)
    def totalSquares(self):
        return self.width * self.height
    def firstUnoccupiedSpace(self):
        for j in range(self.height):
            for i in range(self.width):
                if not self.occupied(i, j):
                    return (i, j)
    def occupy(self, i, j):
        if self.occupied(i,j):
            return False
        else:
            self.grid[i][j] = True
            return True
    def occupied(self, i, j):
        if i < 0 or j < 0:
            return True
        elif i >= self.width or j >= self.height:
            return True
        else:
            return self.grid[i][j]
    def clone(self):
        grid = Grid(self.width, self.height)
        for i in range(self.width):
            for j in range(self.height):
                if self.occupied(i,j):
                    grid.occupy(i,j)
        return grid
    def tile(self, tile, previousPlacements):
        if(len(previousPlacements) >= self.totalSquares() / len(tile)):
            print(drawTiling(self.width,self.height,previousPlacements))
            return [previousPlacements, ]
        tilings = []
        (i, j) = self.firstUnoccupiedSpace()
        for mirror in range(1):
            mirroredTile = tile if mirror else flipTile(tile)
            for rotation in range(4):
                rotatedTile = rotateTile(mirroredTile,rotation)
                for location in rotatedTile:
                    center = (i - location[0],j - location[1])
                    g = self.clone()
                    available = True
                    for place in rotatedTile:
                        if not g.occupy(center[0] + place[0],center[1] + place[1]):
                            available = False
                            break
                    if available:
                        tilings.extend(g.tile(tile, previousPlacements + [[(place[0] + center[0],place[1] + center[1]) for place in rotatedTile],]))
        return tilings
    def __str__(self):
        out = ""
        for j in range(self.width + 2):
            out+="-"
        out+="\n"
        for j in range(self.height):
            out+="|"
            for i in range(self.width):
                out += "x" if self.occupied(i,j) else " "
            out+="|\n"
        for j in range(self.width + 2):
            out+="-"
        return out

def rotateTile(tile, times):
    if times % 2:
        return [((-1) ** (times // 2) * j,(-1) ** (times // 2 + 1) * i) for (i,j) in tile]
    else:
        return [((-1) ** (times // 2) * i,(-1) ** (times // 2) * j) for (i,j) in tile]

def flipTile(tile):
    return [(-i,j) for (i,j) in tile]

def drawTiling(width, height, tiling):
    tileDict = {}
    for tile in range(len(tiling)):
        for location in tiling[tile]:
            tileDict[location] = tile
    output = u'\u250C'
    for i in range(width - 1):
        if tileDict[(i,0)] == tileDict[(i + 1,0)]:
            output+=u'\u2500'
        else:
            output+=u'\u252C'
    output+=u'\u2510\n'
    for j in range(height - 1):
        if tileDict[(0,j)] == tileDict[(0,j + 1)]:
            output+=u'\u2502'
        else:
            output+=u'\u251C'
        for i in range(width - 1):
            if tileDict[(i,j)] == tileDict[(i + 1,j)]:
                if tileDict[(i,j + 1)] == tileDict[(i + 1,j + 1)]:
                    if tileDict[(i,j)] == tileDict[(i,j + 1)]:
                        output +=" "
                    else:
                        output +=u'\u2500'
                else:
                    if tileDict[(i,j)] == tileDict[(i,j + 1)]:
                        output +=u'\u250C'
                    else:
                        if tileDict[(i + 1,j)] == tileDict[(i + 1,j + 1)]:
                            output+=u'\u2510'
                        else:
                            output+=u'\u252C'
            else:
                if tileDict[(i,j + 1)] == tileDict[(i + 1,j + 1)]:
                    if tileDict[(i,j)] == tileDict[(i,j + 1)]:
                        output +=u'\u2514'
                    else:
                        if tileDict[(i + 1,j)] == tileDict[(i + 1,j + 1)]:
                            output +=u'\u2518'
                        else:
                            output +=u'\u2534'
                else:
                    if tileDict[(i,j)] == tileDict[(i,j + 1)]:
                        if tileDict[(i + 1,j)] == tileDict[(i + 1,j + 1)]:
                            output +=u'\u2502'
                        else:
                            output +=u'\u251C'
                    else:
                        if tileDict[(i + 1,j)] == tileDict[(i + 1,j + 1)]:
                            output +=u'\u2524'
                        else:
                            output +=u'\u253C'

if tileDict[(width - 1,j)] == tileDict[(width - 1,j + 1)]:
            output+=u'\u2502'
        else:
            output+=u'\u2524'
        output +="\n"
    output += u'\u2514'
    for i in range(width - 1):
        if tileDict[(i,height - 1)] == tileDict[(i + 1,height - 1)]:
            output+=u'\u2500'
        else:
            output+=u'\u2534'
    output+=u'\u2518\n'
    return output

grid = Grid(9,5)
found = []
tilings = grid.tile([(0,0),(0,1),(1,0)], [])
print(len(tilings))

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