Learning goals

By the end of this assignment, you should be able to:

Introduction: the Blocky game

Blocky is a game with simple moves on a simple structure, but like a Rubik’s Cube, it is quite challenging to play. The game is played on a randomly-generated game board made of squares of four different colours, such as this:

Blocky game

Each player has their own goal that they are working towards, such as creating the largest connected “blob” of blue. After each move, the player sees their score, determined by how well they have achieved their goal. The game continues for a certain number of turns, and the player with the highest score at the end is the winner.

Now let’s look in more detail at the rules of the game and the different ways it can be configured for play.

The Blocky board

We call the game board a ‘block’. It is best defined recursively. A block is either:

The largest block of all, containing the whole structure, is called the top-level block. We say that the top-level block is at level 0. If the top-level block is subdivided, we say that its four sub-blocks are at level 1. More generally, if a block at level k is subdivided, its four sub-blocks are at level k+1.

A Blocky board has a maximum allowed depth, which is the number of levels down it can go. A board with maximum allowed depth 0 would not be fun to play on – it couldn’t be subdivided beyond the top level, meaning that it would be of one solid colour. This board was generated with maximum depth 5:

Blocky game

For scoring, the units of measure are squares the size of the blocks at the maximum allowed depth. We will call these blocks unit cells.

Choosing a block and levels

The moves that can be made are things like rotating a block. What makes moves interesting is that they can be applied to any block at any level. For example, if the user selects the entire top-level block for this board:

Blocky game

and chooses to rotate it counter-clockwise, the resulting board is this:

Blocky game

But if instead, on the original board, they rotated the block at level 1 (one level down from the top-level block) in the upper left-hand corner, the resulting board is this:

Blocky game

And if instead they were to rotate the block a further level down, still sticking in the upper-left corner, they would get this:

Blocky game

Of course there are many other blocks within the board at various levels that the player could have chosen.


These are the moves that are allowed on a Blocky board:

Goals and scoring

At the beginning of the game, each player is assigned a randomly-generated goal. There are two types of goal:

Notice that both goals are relative to a particular colour. We will call that the target colour for the goal.


The game can be played solitaire (with a single player) or with two or more players. There is no defined limit on the number of players, although the game would not likely be fun to play with a very large number of players.

There are three kinds of player:

Configurations of the game

A Blocky game can be configured in several ways:

Setup and starter code

Please download the following starter code files and save these into your assignments/a2 folder.

Task 1: Understand the Block data structure

Surprise, surprise: we will use a tree to represent the nested structure of a block. Our trees will have some very strong restrictions on their structure and contents, however. For example, a node cannot have 3 children. This is because a block is either solid-coloured or subdivided; if it is solid-coloured, it is represented by a node with no children, and if it is subdivided, it is subdivided into exactly four sublocks. Representation invariants document this rule and several other critically important facts.

  1. Open, and read through the class docstring carefully. A Block has quite a few attributes to understand, and the Representation Invariants are critical.
  2. Draw the Block data structure corresponding to the game board below, assuming the maximum depth was 2 (and notice that it was indeed reached). You can just write a letter for each colour value. Assume that the size of the top-level block is 750.
    Blocky game
    Did you draw 9 nodes? Do the attribute values of each node satisfy the representation invariants? NB: If you come to office hours, we will ask to see your drawing before answering questions!

Task 2: Initialize Blocks and draw them

With a good understanding of the data structure, you are ready to start implementing class Block.

  1. Write method __init__.
  2. To make any interesting Blocks using this rudimentary initializer would be incredibly tedious. And for the game, we want to be able to generate random boards. This is what function random_init is for. Implement this function, which you will find at the top level of the module, outside any class. It is outside the Block class because it doesn’t need to refer to self.

    Here is the strategy to use in random_init: If a Block is not yet at its maximum depth, it can be subdivided; this function must decide whether or not to actually do so. To decide:

    • Use function random.random to generate a random number in the interval [0, 1).
    • Subdivide if the random number is less than math.exp(-0.25 * level), where level is the level of the Block within the tree.
    • If a Block is not going to be subdivided, use a random integer to pick a colour for it from the list of colours in renderer.COLOUR_LIST.

    Notice that the randomly-generated Block may not reach its maximum allowed depth. It all depends on what random numbers are generated.

    Function random_init is responsible for giving appropriate values to the attributes of all Blocks within the Block it generates except attributes position and size. In the next step, you will write a method that a client can use to set these attributes.

    Implementation note: function random_init can do its work almost entirely through calls to the initializer for Block.

  3. Define method update_block_locations, which updates the values for attributes position and size throughout a Block, ensuring that they are consistent with the representation invariants for the class. Notice that the position and size of a Block are determined by the position and size of its parent Block.
  4. To make a Block drawable, we must be able to provide a list of rectangles to the renderer. Write method rectangles_to_draw. (This may remind you of the tiling task in a recent lab.)

We can’t mutate a Block yet, but we will have enough to go through the steps of a game once we define at least one kind of Player and Goal, and get the Game class ready.

Check your work: We will provide a function called print_block the will print the contents of a Block in text form. Use this to confirm that your __init__ and random_init work correctly. We will provide some pytest code for testing your method get_draw_rectangles You will be able to test get_selected_block once the game is running.

Task 3: Complete basic goal classes

We need to have some basic ability to set goals and compute a player’s score with respect to their goal.

  1. Open and get familiar with the interface for the abstract class Goal. It has some basic infrastructure for storing information that any goal must have. It also defines an abstract methods score and description that any child class must implement.
  2. Define both of the specific goal classes: BlobGoal and PerimeterGoal. (We have started BlobGoal for you.) For now, have all goals report the same value for score no matter what the state of the board is. How about 148? :-) Ignore the method _undiscovered_blob_size; you will implement and use it when you implement scoring for real.

Check your work: With the game running after Task 4, you will be able to see that the pieces of code connect together.

Task 4: Complete class Game

Now we have enough pieces to assemble a rudimentary game!

  1. Open and review the docstring for class Game. Make sure that you understand all its attributes.
  2. This class has only two methods, and we’ve implemented method run_game for you. Implement the initializer. It must do the following:

    • Create a Renderer for this game.
    • Generate a random goal type, for all players to share.
    • Generate a random board with the given maximum depth.
    • Generate the right number of human players, random players, and smart players (with the given difficulty levels), in that order. Give the players consecutive player numbers, starting at 0. Assign each of them a random target colour and display their goal to them.
    • Before returning, draw the board.
  3. We have written an abstract Player class and a HumanPlayer subclass for you. In order for the user to play the game, they must be able to select a block for action (such as for rotating) by hovering over the board to a desired location, and using the up and down arrows to choose a level. In, method get_selected_block takes those user inputs and finds the corresponding Block within the tree. Implement that method.

Check your work: You should be able to run a game with only human players. Try running method two_player_game – you can uncomment out the call to it in the main block of module game. To select a block for action, put the cursor anywhere inside it and use the up and down arrow keys to select the desired level. The area at the bottom of the game board tells you how to select an action.

So far, no real moves are happening and the score never changes, but you should see the board, see play pass back and forth between players (as indicated by the red “PLAYER n” label just below the board), and the game should end when the desired number of moves has been reached.

Task 5: Make Blocks mutable

Let’s make the game real by allowing players to make moves on the board.

  1. Review the representation invariants for class Block. They are critical to the correct functioning of the program, and it is the responsibility of all methods in the class to maintain their truth.
  2. Define methods swap, rotate and smash. Ensure that each of them calls update_block_locations before returning.
  3. Double check that each of your mutating methods maintains the representation invariants of class Block.

Check your work: Now when you play the game, you should see the board changing. You may find it easiest to use function solitaire_game to try out the various moves.

Task 6: Implement scoring for perimeter goals

Now let’s get scoring working.

The unit we use when scoring against a goal is a unit cell. The size of a unit cell depends on the maximum depth in the Block. For example, with maximum depth of 4, we might get this board:

Blocky game

If you count down through the levels, you’ll see that the smallest blocks are at level 4. Those blocks are unit cells. It would be possible to generate that same board even if maximum depth were 5. In that case, the unit cells would be one size smaller, even though no Block has been divided to that level.

Notice that the perimeter may include unit cells of the target colour as well as larger blocks of that colour. For a larger block, only the unit-cell-sized portions on the perimeter count. For example, suppose maximum depth were 3, the target colour were red, and the board were in this state:

Blocky game

Only the red blocks on the edge would contribute, and the score would be 4: one for each of the two unit cells on the right edge, and two for the unit cells inside the larger red block that are actually on the edge. (Notice that the larger red block isn’t divided into four unit cells, but we still score as if it were.)

Remember that corner cells count twice towards the score. So if the player rotated the lower right block to put the big red block on the corner:

Blocky game

the score would rise to 6.

Now that we understand these details of scoring for a perimeter goal, we can implement it.

  1. It is very difficult to compute a score for a perimeter goal or a blob goal by walking through the tree structure. (Think about that!) The goals are much more easily assessed by walking through a two-dimensional representation of the game board. Your next task is to provide that possibility: In module block, define method flatten.
  2. Now re-implement the score method in class PerimeterGoal to truly calculate the score. Begin by flattening the board to make your job easier!

Check your work: Now when you play the game, if a player has a perimeter goal, you should see the score changing. Check to confirm that it is changing correctly.

Task 7: Implement scoring for blob goals

Scoring with a blob goal involves flattening the tree, iterating through the cells in the flattened tree, and finding out, for each cell, what size of blob it is part of (if it is part of a blob of the target colour). The score is the biggest of these.

But how do we find out the size of the blob that a cell is part of? (Sounds like a helper method, eh?) We’ll start from the given cell and

A potential problem with this is that when we ask a neighbour for their blob size, they will count us in that blob size, and this cell will end up being double counted (or worse). To avoid such issues, we will keep track of which cells have already been “visited” by the algorithm. To do this, make another nested list structure that is exactly parallel to the flattened tree. In each cell, store:

Your task is to implement this algorithm.

  1. Open and read the docstring for helper method _undiscovered_blob_size.
  2. Draw a 4-by-4 grid with a small blob on it, and a parallel 4-by-4 grid full of -1 values. Pick a cell that is in your blob, and suppose we call _undiscovered_blob_size. Trace what the method should do. Remember not to unwind the recursion! Just assume that when you ask a neighbour to report its answer, it will do it correctly (and will update the visited structure correctly).
  3. Implement _undiscovered_blob_size.
  4. Now replace your placeholder implementation of BlobGoal.score with a real one. Use _undiscovered_blob_size as a helper method.

Although we only have two types of goal, you can see that to add a whole new kind of goal, such as stringing a colour along a diagonal, one would only have to define a new child class of Goal, implement the score method for that goal, and then update the code that configures the game to include the new goal as a possibility.

Check your work: Now when you play the game, a player’s score should update after each move, regardless of what type of goal the player has.

Task 8: Add random and smart players

  1. Inside, Implement class RandomPlayer. Method make_move should do the following:

    • Randomly choose a block.
    • Highlight the chosen block and draw the board.
    • Call pygame.time.wait(TIME_DELAY) to introduce a delay so that the user can see what is happening.
    • Randomly choose one of the 5 possible types of action and do it on the chosen block.
    • Un-highlight the chosen block and draw the board again.

  2. Implement class SmartPlayer. A SmartPlayer has a “difficulty” level, which indicates how difficult it is to play against it. The difficulty level is an integer >= 0, and dictates how many possible moves it compares when choosing a move to make. For example, if difficulty is 0, it compares 5 possible moves. See the table below for the meaning of the other difficulty levels.

    Difficulty Moves to compare
    0 5
    1 10
    2 25
    3 50
    4 100
    5 150
    >5 150

    When generating these random moves to compare, don’t forget that a SmartPlayer isn’t allowed to do smashes.

    In order to assess each of the possible moves and pick the best one, the SmartPlayer must actually apply the move, score it, and then undo the move. None of this moving and undoing shows on the screen because we won’t ask the renderer to draw the board while this is happening.

    Method make_move should do the following:

    • Assess the right number of possible moves and pick the best one among them.
    • Highlight the block involved in the chosen move, and draw the board.
    • Call pygame.time.wait(TIME_DELAY) to introduce a delay so that the user can see what is happening.
    • Do the chosen move.
    • Un-highlight the block involved in the chosen move, and draw the board again.

Check your work: Now you can run games with all types of players.


Take some time to polish up. This step will improve your mark, but it also feels so good. Here are some things you can do: