Description
2) Introduction
Now that you’ve mastered 2D mines, it’s time for a small field trip. 🙂 There’s just a small twist. Planet Htrae is
not very different from Earth, except that space in the Yklim way, Htrae’s star cluster, doesn’t have three
dimensions — at least, not always: it fluctuates between 2 and, on the worst days, 60. In fact, it’s not
uncommon for an Htraean to wake up flat, for example, and finish the day in 7 dimensions — only to find
themselves living in three or four dimensions on the next morning. It takes a bit of time to get used to, of
course.
In any case, Htraeans are pretty particular about playing Mines. Kids on Htrae always play on regular, 2D
boards, but champions like to play on higher-dimensional boards, usually on as many dimensions as the
surrounding space. Your code will have to support that flexibility, of course. Here’s the weather advisory for the
week of the tournament:
…VERY DIMENSIONAL IN SOUTHWEST OHADI ON YADIRF…
.AN EXITING LOW PRESSURE SYSTEM WILL INCREASE NORTHWEST DIMENSIONAL
FLUX IN AND SOUTH OF THE EKANS RIVER BASIN ON YADIRF. ESIOB IS NOW
INCLUDED IN THE ADVISORY BUT THE STRONGEST FLUX WILL BE SOUTH AND
EAST OF MOUNTAIN EMOH TOWARD THE CIMAG VALLEY.
ZDI014>030-231330-016-
UPPER ERUSAERT VALLEY-SOUTHWEST HYPERLANDS-WESTERN CIMAG VALLEY-
1022 MP TDM UHT PES 22 6102
…DIMENSION ADVISORY REMAINS IN EFFECT FROM 10 MA TO 9 MP ON
YADIRF…
* DIMENSIONAL FLUX…30 TO 35 DIMENSIONS WITH GUSTS TO 45.
* IMPACTS…CROSSFLUXES WILL MAKE FOR DIFFICULT TRAVELLING
CONDITIONS ON LOW-DIMENSIONAL ROADS.
Since most of the difficulty of this lab lies in implementing recursive functions, please do not use standard
library modules that use recursion behind the scenes, such as itertools .
3) Rules
HyperMines is the Htraean twist on Mines. Unlike Mines, HyperMines is played on a board with an arbitrary
number of dimensions. Everything works just the same as in Mines, except for the fact that each cell has up to
3 − 1 neighbors, instead of 8.
As usual, you only need to edit lab.py to complete this assignment. You will need to correctly implement
nd_new_game(dims, bombs) , nd_dig(game, coords) , nd_render(game, xray) to earn full credit for this lab.
As always, please write documentation and doctests for all new functions.
If you’re starting with a copy of your 2D Mines code, you can delete the testing functions you added for Part 3:
Bug hunt. They aren’t needed for this lab.
One of the implementation challenges in HyperMines is arbitrary-depth iteration. We include a few hints
(https://6009.csail.mit.edu/fall17/labs/lab4/hints) that you may find useful as you think about which recursive
helper functions would be helpful in dealing with N-dimensional arrays represented as nested lists.
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4) How to test your code
We provide three scripts to test and enjoy your code:
python3 simpletests.py is an interactive script that will let you select which doctests to run.
python3 server.py lets you play HyperMines in your browser!
(https://6009.csail.mit.edu/fall17/labs/lab4#catsoop_footnote_1) The server uses your code to compute
consecutive game states.
python3 test.py runs all the tests used for grading, as well as any additional test cases you put in
test.py
5) Implementation
5.1) Game state
As before, the state of an ongoing HyperMines game is represented as a dictionary with four fields:
“dimensions” , the board’s dimensions (an arbitrary list of positive numbers in HyperMines)
“board” , an N-dimensional array (implemented using nested lists) of integers and strings. In
HyperMines, game[“board”][x_0][…][x_k] is “.” if the square with coordinate (x ,…, x ) contains
a bomb.
“mask” , an N-dimensional array (implemeted using nested lists) of Booleans. In HyperMines,
game[“mask”][x_0][…][x_k] indicates whether the contents of square (x ,…, x ) are visible to the
player.
“state” , a string containing the state of the game: “ongoing” if the game is in progress, “victory” if
the game has been won, and “defeat” if the game has been lost. The state of a new game is always
“ongoing” .
For example, the following is a valid HyperMines game state:
gameN = {‘dimensions’: [4, 3, 2],
‘board’: [[[1, 1], [‘.’, 2], [2, 2]],
[[1, 1], [2, 2], [‘.’, 2]],
[[1, 1], [2, 2], [1, 1]],
[[1, ‘.’], [1, 1], [0, 0]]],
‘mask’: [[[True, False], [False, False], [False, False]],
[[False, False], [True, False], [False, False]],
[[False, False], [True, True], [True, True]],
[[False, False], [True, True], [True, True]]],
‘state’: ‘ongoing’}
You may find the dump(game) function (included in lab.py ) useful to print game states.
5.2) Game logic
Your task is to implement three functions: nd_new_game(dims, bombs) , nd_dig(game, coords) , and
nd_render(game, xray) . These functions behave just like their 2D counterparts, and each of them is
documented in detail in lab.py .
HINT: the test cases we will use to check your code in this lab are pretty complex, and so they are difficult to
reason about. You will want to create some test cases of your own in test.py , to handle more straightforward
cases that are easier to reason about. Try making a few small 1-, 2-, and 3-dimensional test cases. As always,
you should be prepared to discuss any test cases you create during your checkoff.
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5.3) An example game
This section runs through an example game in 3D, showing which functions are called and what they should
return in each case. To help understand what happens, calls to dump(game) are inserted after each statemodifying step.
>>> from lab import *
>>> game = nd_new_game([3,3,2],[[1,2,0]])
>>> dump(game)
dimensions: (3, 3, 2)
board: [[0, 0], [1, 1], [1, 1]]
[[0, 0], [1, 1], [‘.’, 1]]
[[0, 0], [1, 1], [1, 1]]
mask: [[False, False], [False, False], [False, False]]
[[False, False], [False, False], [False, False]]
[[False, False], [False, False], [False, False]]
state: ongoing
The player tries digging at [2,1,0] , which reveals 1 tile.
>>> nd_dig(game, [2,1,0])
1
>>> dump(game)
dimensions: (3, 3, 2)
board: [[0, 0], [1, 1], [1, 1]]
[[0, 0], [1, 1], [‘.’, 1]]
[[0, 0], [1, 1], [1, 1]]
mask: [[False, False], [False, False], [False, False]]
[[False, False], [False, False], [False, False]]
[[False, False], [True, False], [False, False]]
state: ongoing
… then at [0,0,0] which reveals 11 new tiles:
>>> nd_dig(game, [0,0,0])
11
>>> dump(game)
dimensions: (3, 3, 2)
board: [[0, 0], [1, 1], [1, 1]]
[[0, 0], [1, 1], [‘.’, 1]]
[[0, 0], [1, 1], [1, 1]]
mask: [[True, True], [True, True], [False, False]]
[[True, True], [True, True], [False, False]]
[[True, True], [True, True], [False, False]]
state: ongoing
Emboldened by this success, the player then makes a fatal mistake and digs at [1,2,0] , revealing a bomb:
>>> nd_dig(game, [1,2,0])
1
>>> dump(game)
dimensions: (3, 3, 2)
board: [[0, 0], [1, 1], [1, 1]]
[[0, 0], [1, 1], [‘.’, 1]]
[[0, 0], [1, 1], [1, 1]]
mask: [[True, True], [True, True], [False, False]]
[[True, True], [True, True], [True, False]]
[[True, True], [True, True], [False, False]]
state: defeat
5.4) Check Yourself
To get a feel for working with an abitrary number of dimensions, answer the following few questions about
determining cells’ neighbors:
In a one-dimensional game with dimensions of [10] , what are the neighbors of the coordinates [5] ? Enter a
Python list of coordinates below:
In a two-dimensional game with dimensions of [10, 20] , what are the neighbors of the coordinates [5,
13] ? Enter a Python list of coordinates below:
In a three-dimensional game with dimensions of [10, 20, 3] , what are the neighbors of the coordinates [5,
13, 0] ? Enter a Python list of coordinates below:
Take a careful look at your results for these questions. How do the results from one question help you solve
the next?
6) Code Submission
Select File No file selected
7) Checkoff
Once you are finished with the code, please come to a tutorial, lab session, or office hour and add yourself to
the queue asking for a checkoff. You must be ready to discuss your code and test cases in detail before
asking for a checkoff.
You should be prepared to demonstrate your code (which should be well-commented, should avoid repetition,
and should make good use of helper functions). In particular, be prepared to discuss:
Your implementation of nd_new_game , including any helper functions.
Your implementation of nd_dig , including any helper functions.
Your implementation of nd_render , including any helper functions.
Any new test cases you added to test.py .
7.1) Grade
You have not yet received this checkoff. When you have completed this checkoff, you will see a grade here.
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/ /\__/\
\__=( o_O )=
(__________)
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(Download Source Code (https://6009.csail.mit.edu/cs_util/source.zip?course=fall17))
Footnotes
Our visualizer only works in 2D. Above that, things get hard to visualize (though there is a reasonably nice UI
here (http://gravitation3d.com/xezlec/) for playing actual HyperMines). (click to return to text)
(https://6009.csail.mit.edu/fall17/labs/lab4#catsoop_footnote_ref_1)
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