Dominoes: Difference between revisions
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=={{header|Phix}}==
<!--<lang Phix>(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">domino_set</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">set</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">domino_set</span><span style="color: #0000FF;">(),</span>
<span style="color: #000000;">used</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">),</span><span style="color: #000000;">7</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">tags</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">shuffle</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">))),</span>
<span style="color: #000000;">grid</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">unpack</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'?'</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n? ? ? ? ? ? ? ?\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'\n'</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">s</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">clear</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">'?'</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'+'</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">}}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">r</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">13</span>
<span style="color: #008080;">and</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">c</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">15</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">prev</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">prev</span><span style="color: #0000FF;">=</span><span style="color: #008000;">'?'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">' '</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">prev</span><span style="color: #0000FF;">!=</span><span style="color: #008000;">' '</span> <span style="color: #008080;">then</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">restore</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'?'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">rand_grid</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">rem</span><span style="color: #0000FF;">=</span><span style="color: #000000;">28</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rem</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">13</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">14</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'?'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">12</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">15</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'?'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">grid</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">13</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">15</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">flat</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;"><</span><span style="color: #000000;">15</span> <span style="color: #008080;">and</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'?'</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">vert</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;"><</span><span style="color: #000000;">13</span> <span style="color: #008080;">and</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'?'</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
<span style="color: #000000;">opt</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">flat</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">opt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">opt</span><span style="color: #0000FF;">,{{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}}})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">vert</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">opt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">opt</span><span style="color: #0000FF;">,{{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">},{{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">}}})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">opt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">shuffle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">opt</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">opt</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">r2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c3</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">opt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">tile</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">shuffle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">tags</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rem</span><span style="color: #0000FF;">]])</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tile</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]+</span><span style="color: #008000;">'0'</span>
<span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r2</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tile</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]+</span><span style="color: #008000;">'0'</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">reset</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">clear</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">opt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rand_grid</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rem</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">res</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">restore</span><span style="color: #0000FF;">(</span><span style="color: #000000;">reset</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">flat</span> <span style="color: #008080;">or</span> <span style="color: #000000;">vert</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">soln1</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">solnn</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">rem</span><span style="color: #0000FF;">=</span><span style="color: #000000;">28</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rem</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">solnn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">grid</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'\n'</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">"\n\n\n"</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">soln1</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span> <span style="color: #008080;">then</span> <span style="color: #000000;">soln1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">solnn</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">13</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">15</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">flat</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;"><</span><span style="color: #000000;">15</span> <span style="color: #008080;">and</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'?'</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">vert</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;"><</span><span style="color: #000000;">13</span> <span style="color: #008080;">and</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'?'</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">flat</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">R</span><span style="color: #0000FF;">,</span><span style="color: #000000;">C</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">({</span><span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">used</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">][</span><span style="color: #000000;">C</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">used</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">][</span><span style="color: #000000;">C</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">reset</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">clear</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,{{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}})</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rem</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">restore</span><span style="color: #0000FF;">(</span><span style="color: #000000;">reset</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">used</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">][</span><span style="color: #000000;">C</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">vert</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">R</span><span style="color: #0000FF;">,</span><span style="color: #000000;">C</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">({</span><span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">used</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">][</span><span style="color: #000000;">C</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">used</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">][</span><span style="color: #000000;">C</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">reset</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">clear</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,{{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">}})</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rem</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">restore</span><span style="color: #0000FF;">(</span><span style="color: #000000;">reset</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">used</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">][</span><span style="color: #000000;">C</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">flat</span> <span style="color: #008080;">or</span> <span style="color: #000000;">vert</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">count</span> <span style="color: #000080;font-style:italic;">-- (may still be 0)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">g</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">grid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">g</span>
<span style="color: #000000;">g</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #000000;">soln1</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #000000;">solnn</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">soln1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">></span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"...\n\n\n"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">solnn</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d solution%s found (%s)\n\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #008000;">""</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"s"</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unpack</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"05132231 05505246 43036620 06235126 11300245 21433466 64515414"</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rand_grid</span><span style="color: #0000FF;">())</span>
<!--</lang>-->
{{out}}
<pre>
5+6 2+0 0 4 1+4
+ +
3+6 1 3 0 4 2+2
+ +
3 5 6 4 3+2 1 1
+ + + +
3 5 1+1 3+0 0 5
6 0 5+4 3+5 5+2
+ +
4 4 1+3 6 6+0 2
+ +
1+2 6+2 6 5+0 4
1 solution found (0.1s)
6+4 2+2 0+6 5 0
+ +
1+6 2+3 4+1 4 3
2+1 0+2 3+5 5+1
1+3 5+0 5+6 1+0
4+2 6 0 4+0 1+1
+ +
4+4 2 0 5 3+6 3
+ +
6+6 5+2 5 3+3 4
...
6 4 2 2 0 6+5 0
+ + + + + +
1 6 2 3 4 1+4 3
2 1 0 2 3+5 5 1
+ + + + + +
1 3 5 0 5 6 1 0
+ +
4 2 6 0 4 0 1+1
+ + + +
4 4 2 0 5 3 6 3
+ + + +
6+6 5+2 5 3 3 4
2025 solutions found (0.1s)
</pre>
Note that 2025 is not the maximum number of solutions or anything like that, just a higher than average result.
===Extra credit===
Pretty dumb brute force approach, dreadfully slow.
<!--<lang Phix>(phixonline)-->
<span style="color: #008080;">without</span> <span style="color: #008080;">js</span> <span style="color: #000080;font-style:italic;">-- too slow</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">IGNORE</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">CONSIDER</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">NOSYM</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">what</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rem</span><span style="color: #0000FF;">=</span><span style="color: #000000;">28</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">doubles</span><span style="color: #0000FF;">=</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rem</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">total</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">13</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">15</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">flat</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;"><</span><span style="color: #000000;">15</span> <span style="color: #008080;">and</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'?'</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">vert</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;"><</span><span style="color: #000000;">13</span> <span style="color: #008080;">and</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'?'</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
<span style="color: #000000;">opt</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">flat</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">opt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">opt</span><span style="color: #0000FF;">,{{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}}})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">vert</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">opt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">opt</span><span style="color: #0000FF;">,{{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">},{{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">}}})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">opt</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">r2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c3</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">opt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">reset</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">clear</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">opt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">what</span><span style="color: #0000FF;">=</span><span style="color: #000000;">IGNORE</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">total</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">(</span><span style="color: #000000;">what</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rem</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">what</span><span style="color: #0000FF;">=</span><span style="color: #000000;">CONSIDER</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">doubles</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">total</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">doubles</span><span style="color: #0000FF;">*</span><span style="color: #000000;">count</span><span style="color: #0000FF;">(</span><span style="color: #000000;">what</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rem</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">doubles</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rem</span><span style="color: #0000FF;">></span><span style="color: #000000;">doubles</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">total</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">rem</span><span style="color: #0000FF;">-</span><span style="color: #000000;">doubles</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">count</span><span style="color: #0000FF;">(</span><span style="color: #000000;">what</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rem</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">doubles</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">else</span> <span style="color: #000080;font-style:italic;">-- NOSYM</span>
<span style="color: #000000;">total</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">rem</span><span style="color: #0000FF;">*</span><span style="color: #000000;">count</span><span style="color: #0000FF;">(</span><span style="color: #000000;">what</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rem</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">restore</span><span style="color: #0000FF;">(</span><span style="color: #000000;">reset</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">flat</span> <span style="color: #008080;">or</span> <span style="color: #000000;">vert</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">total</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">total</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Arrangements ignoring values: %,d\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">(</span><span style="color: #000000;">IGNORE</span><span style="color: #0000FF;">))</span>
<span style="color: #000080;font-style:italic;">--printf(1,"Arrangements considering values: %d\n",count(CONSIDER)) -- too slow</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Arrangements ignoring symmetry: %g\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">(</span><span style="color: #000000;">NOSYM</span><span style="color: #0000FF;">))</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
<!--</lang>-->
{{out}}
<pre>
Arrangements ignoring values: 1,292,697
Arrangements ignoring symmetry: 1.05798e+44
"2 minutes and 37s"
</pre>
|
Revision as of 19:09, 17 November 2021
Warning: If you are looking for pizza delivery you have come to the wrong page. Bloody Google (other search engines are available).
Take a box of dominoes give them a good shuffle and then arrange them in diverse orientations such that they form a rectangle with 7 rows of 8 columns. Make a tableau of the face values e.g.
05132231 05505246 43036620 06235126 11300245 21433466 64515414
Now torment your computer by making it identify where each domino is.
Do this for the above tableau and one of your own construction.
Extra credit:
How many ways are there to arrange dominoes in an 8x7 rectangle, first ignoring their values, then considering their values, and finally considering values but ignoring value symmetry, i.e. transposing 5 and 4.
F#
<lang fsharp> // Dominoes: Nigel Galloway. November 17th., 2021. let cP (n:seq<uint64 list * uint64>) g=seq{for y,n in n do for g in g do let l=n^^^g in if n+g=l then yield (g::y,l)} let rec fG n g=match g with h::t->fG(cP n h)t |_->fst(Seq.head n) let solve(N:int[])=let fG=let y=fG [([],0UL)]([for g in 0..47->((N.[g],N.[g+8]),(1UL<<<g)+(1UL<<<g+8))]@[for n in 0..6 do for g in n*8..n*8+6->((N.[g],N.[g+1]),(1UL<<<g)+(1UL<<<g+1))]
|>List.groupBy(fun((n,g),_)->(min n g,max n g))|>List.sort|>List.map(fun(_,n)->n|>List.map(fun(n,g)->g))) in (fun n g->if List.contains((1UL<<<n)+(1UL<<<g)) y then "+" else " ") N|>Array.chunkBySize 8|>Array.iteri(fun n g->let n=n*8 in [0..6]|>List.iter(fun y->printf $"%d{g.[y]}%s{fG(n+y)(n+y+1)}"); printfn $"%d{g.[7]}"; [0..7]|>List.iter(fun g->printf $"%s{fG(n+g)(n+g+8)} "); printfn "")
solve [|0;5;1;3;2;2;3;1;
0;5;5;0;5;2;4;6; 4;3;0;3;6;6;2;0; 0;6;2;3;5;1;2;6; 1;1;3;0;0;2;4;5; 2;1;4;3;3;4;6;6; 6;4;5;1;5;4;1;4|]
</lang>
- Output:
0+5 1+3 2 2+3 1 + + 0 5+5 0 5 2+4 6 + + 4 3 0 3 6+6 2 0 + + + + 0 6 2 3+5 1 2 6 + + 1 1 3 0+0 2 4 5 + + + + 2 1 4 3+3 4 6 6 + + 6 4+5 1+5 4 1+4
<lang fsharp> solve [|5;6;2;0;0;4;1;4;
3;6;1;3;0;4;2;2; 3;5;6;4;3;2;1;1; 3;5;1;1;3;0;0;5; 6;0;5;4;3;5;5;2; 4;4;1;3;6;6;0;2; 1;2;6;2;6;5;0;4|]
</lang>
- Output:
5+6 2+0 0 4 1+4 + + 3+6 1 3 0 4 2+2 + + 3 5 6 4 3+2 1 1 + + + + 3 5 1+1 3+0 0 5 6 0 5+4 3+5 5+2 + + 4 4 1+3 6 6+0 2 + + 1+2 6+2 6 5+0 4
Phix
with javascript_semantics function domino_set() sequence set = {} for i=0 to 6 do for j=i to 6 do set = append(set,{i,j}) end for end for return set end function sequence set = domino_set(), used = repeat(repeat(false,7),7), tags = shuffle(tagset(length(set))), grid function unpack(sequence s) s = split(s,' ') s = apply(true,join,{s,'?'}) s = join(s,"\n? ? ? ? ? ? ? ?\n") s = split(s,'\n') return s end function function clear(integer r, c, sequence s) if grid[r][c]!='?' then ?9/0 end if grid[r][c]='+' sequence res = {{r,c}} for i=1 to length(s) do {r,c} = s[i] if r>=1 and r<=13 and c>=1 and c<=15 then integer prev = grid[r][c] if prev='?' then grid[r][c] = ' ' res = append(res,{r,c}) elsif prev!=' ' then ?9/0 end if end if end for return res end function procedure restore(sequence s) for i=1 to length(s) do integer {r,c} = s[i] grid[r][c] = '?' end for end procedure function rand_grid(integer rem=28) if rem=0 then for r=1 to 13 by 2 do for c=2 to 14 by 2 do grid[r][c] = '?' end for end for for r=2 to 12 by 2 do for c=1 to 15 by 2 do grid[r][c] = '?' end for end for return grid end if for r=1 to 13 by 2 do for c=1 to 15 by 2 do bool flat = (c<15 and grid[r,c+1]='?'), vert = (r<13 and grid[r+1,c]='?') sequence res = {}, opt = {} if flat then opt = append(opt,{{r,c+2,r,c+1},{{r,c-1},{r,c+3},{r-1,c},{r-1,c+2},{r+1,c},{r+1,c+2}}}) end if if vert then opt = append(opt,{{r+2,c,r+1,c},{{r-1,c},{r,c-1},{r+2,c-1},{r,c+1},{r+2,c+1},{r+3,c}}}) end if opt = shuffle(opt) for i=1 to length(opt) do integer {r2,c2,r3,c3} = opt[i][1] sequence tile = shuffle(set[tags[rem]]) grid[r][c] = tile[1]+'0' grid[r2][c2] = tile[2]+'0' sequence reset = clear(r3,c3,opt[i][2]) res = rand_grid(rem-1) if length(res) then return res end if restore(reset) end for if flat or vert then return {} end if end for end for return {} end function string soln1 = "" string solnn = "" function solve(integer rem=28) if rem=0 then solnn = join(grid,'\n')&"\n\n\n" if soln1 = "" then soln1 = solnn end if return 1 end if for r=1 to 13 by 2 do for c=1 to 15 by 2 do bool flat = (c<15 and grid[r,c+1]='?'), vert = (r<13 and grid[r+1,c]='?') integer count = 0 if flat then integer {R,C} = sort({grid[r][c]-'0'+1,grid[r][c+2]-'0'+1}) if not used[R][C] then used[R][C] = true sequence reset = clear(r,c+1,{{r,c-1},{r,c+3},{r-1,c},{r-1,c+2},{r+1,c},{r+1,c+2}}) count += solve(rem-1) restore(reset) used[R][C] = false end if end if if vert then integer {R,C} = sort({grid[r][c]-'0'+1,grid[r+2][c]-'0'+1}) if not used[R][C] then used[R][C] = true sequence reset = clear(r+1,c,{{r-1,c},{r,c-1},{r+2,c-1},{r,c+1},{r+2,c+1},{r+3,c}}) count += solve(rem-1) restore(reset) used[R][C] = false end if end if if flat or vert then return count -- (may still be 0) end if end for end for return 0 end function procedure test(sequence g) grid = g g = {} soln1 = "" solnn = "" atom t0 = time() integer n = solve() puts(1,soln1) if n>1 then if n>2 then puts(1,"...\n\n\n") end if puts(1,solnn) end if printf(1,"%d solution%s found (%s)\n\n\n",{n,iff(n=1?"":"s"),elapsed(time()-t0)}) end procedure test(unpack("05132231 05505246 43036620 06235126 11300245 21433466 64515414")) test(rand_grid())
- Output:
5+6 2+0 0 4 1+4 + + 3+6 1 3 0 4 2+2 + + 3 5 6 4 3+2 1 1 + + + + 3 5 1+1 3+0 0 5 6 0 5+4 3+5 5+2 + + 4 4 1+3 6 6+0 2 + + 1+2 6+2 6 5+0 4 1 solution found (0.1s) 6+4 2+2 0+6 5 0 + + 1+6 2+3 4+1 4 3 2+1 0+2 3+5 5+1 1+3 5+0 5+6 1+0 4+2 6 0 4+0 1+1 + + 4+4 2 0 5 3+6 3 + + 6+6 5+2 5 3+3 4 ... 6 4 2 2 0 6+5 0 + + + + + + 1 6 2 3 4 1+4 3 2 1 0 2 3+5 5 1 + + + + + + 1 3 5 0 5 6 1 0 + + 4 2 6 0 4 0 1+1 + + + + 4 4 2 0 5 3 6 3 + + + + 6+6 5+2 5 3 3 4 2025 solutions found (0.1s)
Note that 2025 is not the maximum number of solutions or anything like that, just a higher than average result.
Extra credit
Pretty dumb brute force approach, dreadfully slow.
without js -- too slow enum IGNORE, CONSIDER, NOSYM function count(integer what, rem=28, doubles=6) if rem=0 then return 1 end if atom total = 0 for r=1 to 13 by 2 do for c=1 to 15 by 2 do bool flat = (c<15 and grid[r,c+1]='?'), vert = (r<13 and grid[r+1,c]='?') sequence res = {}, opt = {} if flat then opt = append(opt,{{r,c+2,r,c+1},{{r,c-1},{r,c+3},{r-1,c},{r-1,c+2},{r+1,c},{r+1,c+2}}}) end if if vert then opt = append(opt,{{r+2,c,r+1,c},{{r-1,c},{r,c-1},{r+2,c-1},{r,c+1},{r+2,c+1},{r+3,c}}}) end if for i=1 to length(opt) do integer {r2,c2,r3,c3} = opt[i][1] sequence reset = clear(r3,c3,opt[i][2]) if what=IGNORE then total += count(what,rem-1) elsif what=CONSIDER then if doubles then total += doubles*count(what,rem-1,doubles-1) end if if rem>doubles then total += 2*(rem-doubles)*count(what,rem-1,doubles) end if else -- NOSYM total += 2*rem*count(what,rem-1) end if restore(reset) end for if flat or vert then return total end if end for end for return total end function atom t0 = time() printf(1,"Arrangements ignoring values: %,d\n",count(IGNORE)) --printf(1,"Arrangements considering values: %d\n",count(CONSIDER)) -- too slow printf(1,"Arrangements ignoring symmetry: %g\n",count(NOSYM)) ?elapsed(time()-t0)
- Output:
Arrangements ignoring values: 1,292,697 Arrangements ignoring symmetry: 1.05798e+44 "2 minutes and 37s"