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game_pins.html
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<!DOCTYPE html>
<html>
<head><meta charset="utf-8" />
<title>game_pins</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>
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<div class=" highlight hl-ipython2"><pre><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
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<h4 id="Necessary-functions">Necessary functions<a class="anchor-link" href="#Necessary-functions">¶</a></h4>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">createBoard</span><span class="p">():</span>
<span class="n">board</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">flipud</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">tril</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">bool</span><span class="p">)))</span>
<span class="n">board</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="bp">False</span>
<span class="k">return</span> <span class="n">board</span>
<span class="c"># x y </span>
<span class="c"># 0 4</span>
<span class="c"># 1 3</span>
<span class="c"># 2 2</span>
<span class="c"># 3 1</span>
<span class="c"># 4 0</span>
<span class="k">def</span> <span class="nf">isPin</span><span class="p">(</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="c"># if queried outside of the board just return True</span>
<span class="k">if</span><span class="p">(</span><span class="n">x</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">x</span> <span class="o">></span> <span class="mi">4</span> <span class="ow">or</span> <span class="n">y</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">y</span> <span class="o">></span> <span class="mi">4</span> <span class="o">-</span> <span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">True</span>
<span class="k">return</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="k">def</span> <span class="nf">generatePossibleMovesForField</span><span class="p">(</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="c"># 6 directions: +x, -x, +y, -y, +xy, -xy</span>
<span class="n">possibleMoves</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="c"># if position to check is empty</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">isPin</span><span class="p">(</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="k">return</span> <span class="n">possibleMoves</span>
<span class="c"># not clause comes first because the odds are </span>
<span class="c"># that we are going to make a lot of comparisons </span>
<span class="c"># outside of the board so it will be more efficient</span>
<span class="c"># +x</span>
<span class="k">if</span><span class="p">(</span><span class="ow">not</span> <span class="n">isPin</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="n">x</span><span class="o">+</span><span class="mi">2</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="ow">and</span> <span class="n">isPin</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="n">x</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">y</span><span class="p">)):</span>
<span class="n">possibleMoves</span><span class="o">.</span><span class="n">append</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">x</span><span class="o">+</span><span class="mi">2</span><span class="p">,</span><span class="n">y</span><span class="p">))</span>
<span class="c"># -x</span>
<span class="k">if</span><span class="p">(</span><span class="ow">not</span> <span class="n">isPin</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="n">x</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="ow">and</span> <span class="n">isPin</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="n">x</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">y</span><span class="p">)):</span>
<span class="n">possibleMoves</span><span class="o">.</span><span class="n">append</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">x</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="n">y</span><span class="p">))</span>
<span class="c"># +y</span>
<span class="k">if</span><span class="p">(</span><span class="ow">not</span> <span class="n">isPin</span><span class="p">(</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="o">+</span><span class="mi">2</span><span class="p">)</span> <span class="ow">and</span> <span class="n">isPin</span><span class="p">(</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="o">+</span><span class="mi">1</span><span class="p">)):</span>
<span class="n">possibleMoves</span><span class="o">.</span><span class="n">append</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">x</span><span class="p">,</span><span class="n">y</span><span class="o">+</span><span class="mi">2</span><span class="p">))</span>
<span class="c"># -y</span>
<span class="k">if</span><span class="p">(</span><span class="ow">not</span> <span class="n">isPin</span><span class="p">(</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="o">-</span><span class="mi">2</span><span class="p">)</span> <span class="ow">and</span> <span class="n">isPin</span><span class="p">(</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="o">-</span><span class="mi">1</span><span class="p">)):</span>
<span class="n">possibleMoves</span><span class="o">.</span><span class="n">append</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">x</span><span class="p">,</span><span class="n">y</span><span class="o">-</span><span class="mi">2</span><span class="p">))</span>
<span class="c"># +x-y</span>
<span class="k">if</span><span class="p">(</span><span class="ow">not</span> <span class="n">isPin</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="n">x</span><span class="o">+</span><span class="mi">2</span><span class="p">,</span> <span class="n">y</span><span class="o">-</span><span class="mi">2</span><span class="p">)</span> <span class="ow">and</span> <span class="n">isPin</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="n">x</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">y</span><span class="o">-</span><span class="mi">1</span><span class="p">)):</span>
<span class="n">possibleMoves</span><span class="o">.</span><span class="n">append</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">x</span><span class="o">+</span><span class="mi">2</span><span class="p">,</span><span class="n">y</span><span class="o">-</span><span class="mi">2</span><span class="p">))</span>
<span class="c"># -x+y</span>
<span class="k">if</span><span class="p">(</span><span class="ow">not</span> <span class="n">isPin</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="n">x</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="n">y</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span> <span class="ow">and</span> <span class="n">isPin</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="n">x</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">y</span><span class="o">+</span><span class="mi">1</span><span class="p">)):</span>
<span class="n">possibleMoves</span><span class="o">.</span><span class="n">append</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">x</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="n">y</span><span class="o">+</span><span class="mi">2</span><span class="p">))</span>
<span class="k">return</span> <span class="n">possibleMoves</span>
<span class="k">def</span> <span class="nf">generateAllPossibleMovesForBoard</span><span class="p">(</span><span class="n">board</span><span class="p">):</span>
<span class="n">possibleMoves</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">5</span><span class="p">):</span>
<span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">5</span><span class="o">-</span><span class="n">x</span><span class="p">):</span>
<span class="n">possibleMoves</span> <span class="o">+=</span> <span class="n">generatePossibleMovesForField</span><span class="p">(</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="k">return</span> <span class="n">possibleMoves</span>
<span class="k">def</span> <span class="nf">makeMove</span><span class="p">(</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="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">):</span>
<span class="n">board</span> <span class="o">=</span> <span class="n">board</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">isPin</span><span class="p">(</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="ow">or</span> <span class="ow">not</span> <span class="n">isPin</span><span class="p">(</span><span class="n">board</span><span class="p">,(</span><span class="n">x</span><span class="o">+</span><span class="n">xx</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">,(</span><span class="n">y</span><span class="o">+</span><span class="n">yy</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span> <span class="ow">or</span> <span class="n">isPin</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s">'Invalid move x={} y={} xx={} yy={}'</span><span class="o">.</span><span class="n">format</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">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">))</span>
<span class="k">return</span> <span class="bp">None</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="bp">False</span>
<span class="n">board</span><span class="p">[(</span><span class="n">x</span><span class="o">+</span><span class="n">xx</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">][(</span><span class="n">y</span><span class="o">+</span><span class="n">yy</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="bp">False</span>
<span class="n">board</span><span class="p">[</span><span class="n">xx</span><span class="p">][</span><span class="n">yy</span><span class="p">]</span> <span class="o">=</span> <span class="bp">True</span>
<span class="k">return</span> <span class="n">board</span>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">bt</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">count</span><span class="p">,</span> <span class="n">boards</span><span class="p">):</span>
<span class="c"># print(c.astype(int))</span>
<span class="n">boards</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">boards</span><span class="p">)</span>
<span class="n">boards</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
<span class="c"># if count % 100 == 0: </span>
<span class="c"># print count</span>
<span class="n">possibleMoves</span> <span class="o">=</span> <span class="n">generateAllPossibleMovesForBoard</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">c</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">print</span><span class="p">(</span><span class="s">'MADE IT'</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span><span class="bp">True</span><span class="p">,</span> <span class="n">count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">boards</span><span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">possibleMoves</span><span class="p">:</span> <span class="k">return</span> <span class="p">(</span><span class="bp">False</span><span class="p">,</span> <span class="n">count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">boards</span><span class="p">)</span>
<span class="k">for</span> <span class="n">possibleMove</span> <span class="ow">in</span> <span class="n">possibleMoves</span><span class="p">:</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">makeMove</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="o">*</span><span class="n">possibleMove</span><span class="p">)</span>
<span class="n">isWin</span><span class="p">,</span> <span class="n">count</span><span class="p">,</span> <span class="n">winningBoards</span> <span class="o">=</span> <span class="n">bt</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">count</span><span class="p">,</span> <span class="n">boards</span><span class="p">)</span>
<span class="k">if</span> <span class="n">isWin</span><span class="p">:</span>
<span class="k">return</span> <span class="p">(</span><span class="bp">True</span><span class="p">,</span> <span class="n">count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">winningBoards</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span><span class="bp">False</span><span class="p">,</span> <span class="n">count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">boards</span><span class="p">)</span>
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<h4 id="Solution">Solution<a class="anchor-link" href="#Solution">¶</a></h4>
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<div class=" highlight hl-ipython2"><pre><span class="n">board</span> <span class="o">=</span> <span class="n">createBoard</span><span class="p">()</span>
<span class="n">isWin</span><span class="p">,</span> <span class="n">count</span><span class="p">,</span> <span class="n">winningBoards</span> <span class="o">=</span> <span class="n">bt</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="mi">0</span><span class="p">,[])</span>
<span class="k">print</span><span class="p">(</span><span class="s">'Steps to win: {}'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">count</span><span class="p">))</span>
<span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">winningBoards</span><span class="p">:</span>
<span class="k">print</span> <span class="n">b</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s">''</span><span class="p">)</span>
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<pre>MADE IT
Steps to win: 354
[[0 1 1 1 1]
[1 1 1 1 0]
[1 1 1 0 0]
[1 1 0 0 0]
[1 0 0 0 0]]
[[1 0 0 1 1]
[1 1 1 1 0]
[1 1 1 0 0]
[1 1 0 0 0]
[1 0 0 0 0]]
[[1 0 1 0 0]
[1 1 1 1 0]
[1 1 1 0 0]
[1 1 0 0 0]
[1 0 0 0 0]]
[[1 1 1 0 0]
[1 0 1 1 0]
[1 0 1 0 0]
[1 1 0 0 0]
[1 0 0 0 0]]
[[1 0 0 1 0]
[1 0 1 1 0]
[1 0 1 0 0]
[1 1 0 0 0]
[1 0 0 0 0]]
[[1 0 0 1 0]
[1 1 0 0 0]
[1 0 1 0 0]
[1 1 0 0 0]
[1 0 0 0 0]]
[[1 0 0 1 0]
[0 0 1 0 0]
[1 0 1 0 0]
[1 1 0 0 0]
[1 0 0 0 0]]
[[1 0 0 0 0]
[0 0 0 0 0]
[1 1 1 0 0]
[1 1 0 0 0]
[1 0 0 0 0]]
[[1 0 0 0 0]
[1 0 0 0 0]
[0 1 1 0 0]
[0 1 0 0 0]
[1 0 0 0 0]]
[[0 0 0 0 0]
[0 0 0 0 0]
[1 1 1 0 0]
[0 1 0 0 0]
[1 0 0 0 0]]
[[0 0 0 0 0]
[0 0 0 1 0]
[1 1 0 0 0]
[0 0 0 0 0]
[1 0 0 0 0]]
[[0 0 0 0 0]
[0 0 0 1 0]
[0 0 1 0 0]
[0 0 0 0 0]
[1 0 0 0 0]]
[[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 1 0 0 0]
[1 0 0 0 0]]
[[0 0 0 0 0]
[0 0 0 0 0]
[0 0 1 0 0]
[0 0 0 0 0]
[0 0 0 0 0]]
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<h4 id="Tests">Tests<a class="anchor-link" href="#Tests">¶</a></h4>
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<div class="prompt input_prompt">In [35]:</div>
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<div class=" highlight hl-ipython2"><pre><span class="n">board</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">bool</span><span class="p">)</span>
<span class="n">board</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">board</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">board</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">isWin</span><span class="p">,</span> <span class="n">count</span><span class="p">,</span> <span class="n">winningBoards</span> <span class="o">=</span> <span class="n">bt</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="mi">0</span><span class="p">,[])</span>
<span class="k">print</span><span class="p">(</span><span class="n">count</span><span class="p">)</span>
<span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">winningBoards</span><span class="p">:</span>
<span class="k">print</span> <span class="n">b</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">)</span>
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<pre>MADE IT
4
[[1 0 1 1 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]]
[[1 1 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]]
[[0 0 1 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]]
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<div class=" highlight hl-ipython2"><pre><span class="n">board</span> <span class="o">=</span> <span class="n">createBoard</span><span class="p">()</span>
<span class="k">print</span><span class="p">(</span><span class="n">board</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">))</span>
<span class="k">print</span><span class="p">(</span><span class="n">generateAllPossibleMovesForBoard</span><span class="p">(</span><span class="n">board</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">board</span> <span class="o">=</span> <span class="n">makeMove</span><span class="p">(</span><span class="n">board</span><span class="p">,</span> <span class="o">*</span><span class="n">generateAllPossibleMovesForBoard</span><span class="p">(</span><span class="n">board</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span><span class="c"># 0, 2, 0, 0)</span>
<span class="k">print</span><span class="p">(</span><span class="n">board</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">))</span>
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<pre>[[0 1 1 1 1]
[1 1 1 1 0]
[1 1 1 0 0]
[1 1 0 0 0]
[1 0 0 0 0]]
(0, 2, 0, 0)
[[1 0 0 1 1]
[1 1 1 1 0]
[1 1 1 0 0]
[1 1 0 0 0]
[1 0 0 0 0]]
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<div class=" highlight hl-ipython2"><pre><span class="n">board</span> <span class="o">=</span> <span class="n">createBoard</span><span class="p">()</span>
<span class="k">print</span><span class="p">(</span><span class="n">board</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">))</span>
<span class="n">generatePossibleMovesForField</span><span class="p">(</span><span class="n">board</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
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<pre>[[0 1 1 1 1]
[1 1 1 1 0]
[1 1 1 0 0]
[1 1 0 0 0]
[1 0 0 0 0]]
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<pre>[(2, 0, 0, 0)]</pre>
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<div class=" highlight hl-ipython2"><pre><span class="n">board</span> <span class="o">=</span> <span class="n">createBoard</span><span class="p">()</span>
<span class="n">board</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="bp">True</span>
<span class="n">board</span><span class="p">[</span><span class="mi">3</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="bp">False</span>
<span class="k">print</span><span class="p">(</span><span class="n">board</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">))</span>
<span class="n">generatePossibleMovesForField</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
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<pre>[[1 1 1 1 1]
[1 1 1 1 0]
[1 1 1 0 0]
[1 0 0 0 0]
[1 0 0 0 0]]
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<pre>[(1, 3, 3, 1)]</pre>
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<div class=" highlight hl-ipython2"><pre><span class="n">board</span> <span class="o">=</span> <span class="n">createBoard</span><span class="p">()</span>
<span class="n">board</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="bp">True</span>
<span class="n">board</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">4</span><span class="p">]</span> <span class="o">=</span> <span class="bp">False</span>
<span class="n">board</span><span class="p">[</span><span class="mi">4</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="bp">False</span>
<span class="k">print</span><span class="p">(</span><span class="n">board</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</span><span class="p">))</span>
<span class="n">generatePossibleMovesForField</span><span class="p">(</span><span class="n">board</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
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<pre>[[1 1 1 1 0]
[1 1 1 1 0]
[1 1 1 0 0]
[1 1 0 0 0]
[0 0 0 0 0]]
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<pre>[(2, 2, 4, 0), (2, 2, 0, 4)]</pre>
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