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<h1 class="post-title">Minesweeper Bomb Generation And Tile Revealing</h1>
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<time datetime="20-09-12" class="post-date">Saturday, September 12 2020</time>
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</header>
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<hr>
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<p>When I was creating a little Minesweeper game, I got confused at some points.
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My bomb generation didn’t look quite right, and I for sure didn’t quite get the whole cascading tile reveal thing.
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With a bit of internet research, I found what I was looking for.
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I’ll explain it all in one place for my own research purposes.</p>
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<h2 id="bomb-generation">Bomb Generation</h2>
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<p>When I started this project I attempted to use a random bomb generator.
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By this I mean on each square, before it gets generated, give it a one in 15 change of being a bomb.
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Personally, I’m not sure why this never looked right.
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Something about the layout of the bombs did not mimic the classic Minesweeper game.</p>
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<p>After looking at some open source Minesweeper examples, I started to get the idea.
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I wrote some mathematical statements describing the generation of bombs and how to get their x,y position from an appropriate number.
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For those non-mathy people, don’t leave just yet;
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there will be code equivalents to the math.</p>
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<p>W and H are the width and height of the board respectively.</p>
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<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn mathvariant="italic">0</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mtext>W</mtext><mo>×</mo><mtext>H</mtext></mrow><annotation encoding="application/x-tex">
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\it 0 \leq r \leq \text W \times \text H
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</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8193em;vertical-align:-0.13597em;"></span><span class="mord"><span class="mord mathit">0</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathit">r</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord text"><span class="mord">W</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">H</span></span></span></span></span></span></span>
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<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>=</mo><mi>r</mi><mtext> </mtext><mo lspace="0.22em" rspace="0.22em"><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi></mrow></mo><mtext> </mtext><mtext>W</mtext></mrow><annotation encoding="application/x-tex">
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\it x = r \bmod \text W
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</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord"><span class="mord mathit">x</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathit">r</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mspace" style="margin-right:0.05555555555555555em;"></span><span class="mbin"><span class="mord"><span class="mord mathrm">m</span><span class="mord mathrm">o</span><span class="mord mathrm">d</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mspace" style="margin-right:0.05555555555555555em;"></span><span class="mord text"><span class="mord">W</span></span></span></span></span></span></span>
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<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi><mo>=</mo><mrow><mo fence="true">⌊</mo><mfrac><mi>r</mi><mtext>H</mtext></mfrac><mo fence="true">⌋</mo></mrow></mrow><annotation encoding="application/x-tex">
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\it y = \left\lfloor\frac{r}{\text H}\right\rfloor
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</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8359999999999999em;vertical-align:-0.686em;"></span><span class="mord"><span class="mord mathit">y</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">⌊</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.10756em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">H</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathit">r</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">⌋</span></span></span></span></span></span></span></span></p>
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<p>The code equivalent to this in Python is below:</p>
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<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kn">import</span> <span class="nn">random</span>
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<span class="c1"># r <= 0 <= W*H
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</span><span class="n">r</span> <span class="o">=</span> <span class="n">random</span><span class="p">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">W</span><span class="o">*</span><span class="n">H</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
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<span class="c1"># x = r mod W
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</span><span class="n">x</span> <span class="o">=</span> <span class="n">r</span> <span class="o">%</span> <span class="n">W</span>
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<span class="c1"># y = floor(r/H); note the special syntax python has for this operation
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</span><span class="n">y</span> <span class="o">=</span> <span class="n">r</span> <span class="o">//</span> <span class="n">H</span>
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</code></pre></div></div>
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<p>So that’s that, we can put this in a big ‘ol for loop and generate an arbitrary <em>n</em> number of bombs given a width and height of a Minesweeper board.</p>
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<h2 id="cascading-tile-revealing">Cascading Tile Revealing</h2>
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<p>This one is hard to describe;
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I am adapting this from <a href="https://leetcode.com/problems/minesweeper/">leetcode.com</a>.
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Whenever a player clicks a tile, the following logic should be used:</p>
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<ol>
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<li>If a mine is revealed, the game is over. (obviously)</li>
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<li>If a tile with <em>no</em> adjacent mines is revealed, recursively reveal all eight adjacent tiles.</li>
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<li>If a tile with one or more adjacent mines is revealed, display the number of mines next to it.</li>
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</ol>
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<p>Here is the code in Python for this algorithm.</p>
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<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="k">def</span> <span class="nf">reveal_square</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">board</span><span class="p">,</span> <span class="n">alread_revealed</span><span class="p">):</span>
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<span class="c1"># if already checked
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</span> <span class="k">if</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="n">already_revealed</span><span class="p">:</span>
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<span class="k">return</span>
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<span class="c1"># if it's a bomb
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</span> <span class="k">if</span> <span class="n">board</span><span class="p">[</span><span class="n">x</span><span class="p">][</span><span class="n">y</span><span class="p">]</span> <span class="o">==</span> <span class="s">'B'</span><span class="p">:</span>
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<span class="n">you_lose</span><span class="p">()</span>
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<span class="k">return</span>
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<span class="c1"># if the bomb number is more than 0
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</span> <span class="n">already_revealed</span><span class="p">.</span><span class="n">append</span><span class="p">((</span><span class="n">nx</span><span class="p">,</span> <span class="n">ny</span><span class="p">))</span>
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<span class="c1"># from -1 to 1
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</span> <span class="k">for</span> <span class="n">xd</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">):</span>
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<span class="k">for</span> <span class="n">yd</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">):</span>
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<span class="c1"># skip if it is this the center tile
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</span> <span class="k">if</span> <span class="n">x</span><span class="o">+</span><span class="n">xd</span> <span class="o">==</span> <span class="n">x</span> <span class="ow">and</span> <span class="n">y</span><span class="o">+</span><span class="n">yd</span> <span class="o">==</span> <span class="n">y</span><span class="p">:</span>
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<span class="k">continue</span>
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<span class="c1"># recursively check the adjacent square
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</span> <span class="n">reveal</span><span class="p">(</span><span class="n">x</span><span class="o">+</span><span class="n">xd</span><span class="p">,</span> <span class="n">y</span><span class="o">+</span><span class="n">yd</span><span class="p">,</span> <span class="n">board</span><span class="p">,</span> <span class="n">already_revealed</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">already_revealed</span>
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</code></pre></div></div>
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<p>This has no checks for valid squares, but it’s the general idea.
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This function returns an array of tile coordinates which should be revealed.</p>
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<h2 id="conclusion">Conclusion</h2>
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<p>I wrote this because in the first place because I was writing my own Minesweeper game.
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I hope that this helps you with getting the general idea of a Minesweeper game.
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The completed version of this game is available on my <a href="https://lamegames.tait.tech/">lamegames</a> site.
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Let me know what you think!</p>
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<p>Happy hacking!</p>
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