CS3510 Course Project Solution

Designing Efficient Minesweeper Algorithms
0 Clarifications and Revisions
Optimization goal and evaluation metric
Your goal should be to minimize the number of tiles opened until all bombs are discovered.
This should also be the evaluation metric for comparing the performance of your two algorithms: how many tiles does the algorithm need to mine before identifying all bomb squares?
Non-deterministic States
- You should not assume that any 0 tiles will be automatically opened for you. Given that you try to minimize the number of opened tiles, there is no point in mining a tile if you are certain that it is a 0 tile.
Starting Square
Trivial Algorithms
Generally, any algorithm that does not make use of the information provided by numbered tile squares is trivial. A couple of examples of trivial algorithms include:
- Mining tiles randomly.
- Not trying to minimize the number of mined tiles.
Differentiating Your Two Algorithms
The two algorithms should be different enough so that they produce clearly different results in terms of running time and/or number of mined tiles (performance).
1 Problem Description
Minesweeper is a puzzle game with a simple set of rules. The single player is presented with an n-by-m rectangular grid of covered squares that he or she can choose to reveal. Within each square can be either a dangerous landmine, a helpful number, or nothing at all. The player’s job is to uncover all safe squares and leave all landmines untouched.

Figure 1.1: Numbers, flags, and undeterminable squares.
A landmine, once uncovered, will end the game for the player. In almost all implementations of Minesweeper, the player can set an unvalidated flag on the square to indicate its danger. These flags are for the player to use to mark dangerous squares.
Nothing at all is equivalent to having ‘0’ in a tile; there are no nearby landmines in the eight surrounding tiles.
Solving a Minesweeper puzzle is a co-NP-complete problem — that is, a solution to a Minesweeper board configuration is the complement of a related problem.
2 Project Requirements
2.1 Algorithm Implementation Details
Your algorithms will take as input a file representing Minesweeper board description. As output, the algorithms should return the presumed locations of all landmines on the on board. A board description is a json file in the following format:
{
dim: “<int height>,<int width>”
bombs: “<int num_bombs>”,
safe: “<int x>,<int y>”,
board:
} “<string<0-9>height * width board_state>”
- height and width are integers representing the height and width of the board.
bombs is an integer representing the number of bombs on the board.
- safe is a pair of integers separated by a semicolon. It represents the x and y coordinate of a zero square. This will allow you to discover an “island” of non-mines that will inform your algorithm’s start.
- board is a height * width length string of values 0 - 9 (the number of adjacent bombs -- 9 represents a bomb in that location). The row, col coordinate board value is represented by the row * width + col position value in the string. Note the origin (0, 0) is in the top left of the board.
Your two algorithms and other code can be implemented in any language you are comfortable with. Python is recommended. If you choose an “exotic” language (ie not Python, Java, JavaScript, C/C++), you should notify arnoldwang@gatech.edu before proceeding to make sure that we will be able to run your program. Programs should be annotated so as to be understandable. Statistics to be mentioned in your report (explained in detail later) should be printed for each problem instance.
2.2 Example Board Configuration
Consider the following board:

A potential JSON representation:

2.3 Project Report
Within your project report, you will explain your two algorithms (and show their correctness, if they can provably find the right solution). Your group will also analyze and compare results for the two algorithms. One metric you should assess is the runtime complexity of your algorithm. Another metric is the number of squares you have “probed” in order to deduce the location of all bombs. This metric cannot be lower than the “bomb-density” — the number of bombs over the number of tiles.
You should include plots comparing your two algorithms in terms of: 1) the runtime and 2) the “fraction of squares revealed” metric. These plots should visualize how performance changes as grid size increases and as bomb density increases. (Bomb density being the ratio of the number of bombs over grid size.)
A minimal checklist of items to include in your project report:
❏ Algorithm A
❏ Description
❏ Justification of correctness
❏ Asymptotic, worst-case runtime analysis
❏ Algorithm B
❏ Description
❏ Justification of correctness
❏ Asymptotic, worst-case runtime analysis
❏ Experimental plots with two curves (one curve for each algorithm)
❏ Runtime vs grid area (from 100 to 1000 squares in steps of 100)
❏ Runtime vs bomb density (from 2% to 20% in steps of 2%)
❏ Performance (“fraction of squares revealed”) vs grid area
❏ Performance (“fraction of squares revealed”) vs bomb density
3 Grading
Grading will be based primarily on completion of the previous tasks (rather than algorithm performance or runtime). To recap, assignment tasks include two instances of algorithm design and a complete project report.
We reserve the right to give partial credit in cases where one or both algorithms are trivial (e.g., random guessing).
4 Submission Procedure
You will need to submit a single ZIP/tar archive for the entire project. The archive should include code, your project report as a PDF file, and a README plain-text (.txt) file.
The README file must contain:
● Names and descriptions of all files submitted
● Instructions for compiling and running your programs (if applicable)
● Any known bugs or limitations of your program that we should know about
You should name the submitted file based on the names of the group members. For example, if the team consists of Alpha Beta, Gamma Delta, and Epsilon Zeta, the filename should be: AlphaBeta-GammaDelta-EpsilonZeta.zip
AlphaBeta-GammaDelta-EpsilonZeta.zip | -- minesweeper-3510/
| -- minesweeper-3510.py
| -- <supporting_file.py> | -- ...
| -- README.txt
| -- algorithm.pdf
Only one member of each group needs to submit the actual code and documentation. The other group members can submit a simple text file in which they mention their partner’s name that has submitted the actual assignment and the corresponding filename.
5 Resources
➔ You can play Minesweeper at https://minesweeperonline.com/.
➔ A couple of papers to fuel your design process:
◆ David Becerra – Algorithmic Approaches to Playing Minesweeper ◆ Jan Cicvárek – Algorithms for Minesweeper Game Grid Generation ◆ Don’t forget to cite your sources if you decide to borrow an idea.