you will build some of the foundational infrastructures of a program that implements the rules of the game Breakdown

Part 1:

For this assignment, you will build some of the foundational infrastructures of a program that implements the rules of the game Breakdown. Later in the quarter, you will write a program to interactively play the game. But before we get to that task, we need to establish what the game is: what data structures represent it, what its rules are, what constitutes a victory, etc.
You will not need to become good at playing Breakdown yourself in order to complete this project; you only need to have a complete understanding of the rules, which are specified in this document.
===> Breakdown
The breakdown was created by a computer science professor at an Illinois university who turned it into a class assignment when he couldn't get any company to license the rights to it. The game is played with pieces on a board, but, unlike many board games, the board stands up vertically. There is a grid consisting of rows and columns, the cells of which can be empty, be occupied by a black piece, or be occupied by a white piece. Pieces, known as sticks, are more than one grid cell in size. Because of gravity, sticks fall down in a column to the lowest spot they can reach. Note that they do not move laterally or rotate as they fall. Because sticks are rigid, they can have an "overhang," in which part of the stick is supported by pieces below it, but another part is hanging over empty space. (Examples below will clarify.)

Players take turns, starting with black, then white, then black, and so on. The game can be played with boards of different dimensions. We will show examples in the format that your program will display boards to screen.

  0123

0 ....

1 ....

2 ....

3 ....

4 ....

This is a board with 5 rows and 4 columns, empty at the start of the game. Empty spaces are depicted with period (.) characters.

In this particular example, we will play a game with sticks that are two grid cells long. The length of sticks is configurable from game to game, but fixed during a specific game.

Black moves first. This player drops a black stick (which will be drawn using asterisks [*]) into column 0, vertically:

  0123

0 ....

1 ....

2 ....

3 *...

4 *...

Because there were no pieces occupying column 0, the black stick immediately falls to the bottom of this column.

White moves next, and drops a stick horizontally in columns 2-3. White's sticks will be depicted using lower-case letter o (as in Oscar).

  0123

0 ....

1 ....

2 ....

3 *...

4 *.oo

White's stick similarly falls to the bottom row due to gravity.

Next, Black drops a stick horizontally in columns 0-1.
  0123

0 ....

1 ....

2 **..

3 *...

4 *.ooSince part of this stick is propped up by the stick below it, this new stick only makes it down to row 2. This is an example of the idea of an overhang: a stick dropped horizontally remains rigid, and only falls as far as the highest point where it can rest, across all of its columns. In this particular example, it may seem plausible that this could happen, as half the stick is supported. But, to be clear, even if the stick were much longer, and only one of the columns under the stick were supporting it, it would still be able to overhang. Put another way, sticks can successfully hang, even if there is "air" underneath most of their columns, so long as at least one column is supported.

Another aspect to note is that this depiction of the board does not show the outlines of the sticks; there are two Black sticks, occupying a total of four cells. But, the fact that one is a vertical stick, with a second, horizontal one resting on it, is not explicitly acknowledged, only the overall view of which cells are occupied by Black. In fact, our program will not retain this knowledge, either. It will be sufficient simply to keep track of which cells are occupied by which color. It is only while a stick is being dropped, and gravity is being simulated, that sticks must be thought of as a single rigid unit; after the stick is placed in the appropriate location, mere cell occupancy is sufficient going forward.

White moves next, and drops a piece horizontally in columns 1-2.

  0123

0 ....

1 .oo.

2 **..

3 *...

4 *.ooThis stick is also propped up by the presence of occupied Black cells below it, and has its own overhang. Note that the White stick is stable at this location; although it might be tempting to think that the Black stick below it, which is not fully supported , might break under the weight of the White stick above its unsupported part, this is not an aspect of the physics of the game. Sticks fall until any part of them lands on top of an occupied cell, then rest there.

You may be wondering what happens if you try to drop a stick in a column that is full to the top row, or to drop a stick vertically into a column that does not have enough room for the entire height of the stick. This is simply not allowed.

For each of the moves so far, players have taken turns dropping sticks. But, during a player's turn, they can, instead, perform a "breakdown" move. When they do, all sticks lose their rigidity and break down into individual squares the size of grid cells. These squares then fall within their columns if there was "air" beneath them.