Pentomino tiling: Difference between revisions
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Apart from the shape table creation, the solving part is a translation of Go.<br> |
Apart from the shape table creation, the solving part is a translation of Go.<br> |
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I also added a fast unsolveable() check routine, not that it desperately needed it. |
I also added a fast unsolveable() check routine, not that it desperately needed it. |
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<lang Phix> |
<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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......I................................................................ |
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<span style="color: #008080;">constant</span> <span style="color: #000000;">pentominoes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #008000;">""" |
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......I.....L......N.........................................Y......... |
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. |
......I................................................................ |
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......I.....L......N.........................................Y......... |
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. |
.FF...I.....L.....NN....PP....TTT...........V.....W....X....YY.....ZZ.. |
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FF....I.....L.....N.....PP.....T....U.U.....V....WW...XXX....Y.....Z... |
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----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- |
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.F....I.....LL....N.....P......T....UUU...VVV...WW.....X.....Y....ZZ..."""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'\n'</span><span style="color: #0000FF;">)</span> |
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<span style="color: #000080;font-style:italic;">----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- </span> |
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function get_shapes() |
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sequence res = {} |
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<span style="color: #008080;">function</span> <span style="color: #000000;">get_shapes</span><span style="color: #0000FF;">()</span> |
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for offset=0 to length(pentominoes[1]) by 6 do |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
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-- |
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<span style="color: #008080;">for</span> <span style="color: #000000;">offset</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pentominoes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">by</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span> |
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-- scan left/right, and up/down, both ways, to give 8 orientations |
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<span style="color: #000080;font-style:italic;">-- |
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-- (computes the equivalent of those hard-coded tables in |
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-- scan left/right, and up/down, both ways, to give 8 orientations |
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-- other examples, albeit in a slightly different order.) |
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-- (computes the equivalent of those hard-coded tables in |
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-- |
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-- other examples, albeit in a slightly different order.) |
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sequence shape = {} |
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--</span> |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">shapes</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
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for orientation=0 to 7 do |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">letter</span> |
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sequence this = {} |
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<span style="color: #008080;">for</span> <span style="color: #000000;">orientation</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">7</span> <span style="color: #008080;">do</span> |
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bool found = false |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">shape</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
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integer fr, fc |
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<span style="color: #004080;">bool</span> <span style="color: #000000;">found</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span> |
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for r=1 to 5 do |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">fr</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fc</span> |
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for c=1 to 5 do |
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<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;">5</span> <span style="color: #008080;">do</span> |
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integer rr = iff(and_bits(orientation,#01)?6-r:r), |
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<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;">5</span> <span style="color: #008080;">do</span> |
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cc = iff(and_bits(orientation,#02)?6-c:c) |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">rr</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">orientation</span><span style="color: #0000FF;">,</span><span style="color: #000000;">#01</span><span style="color: #0000FF;">)?</span><span style="color: #000000;">6</span><span style="color: #0000FF;">-</span><span style="color: #000000;">r</span><span style="color: #0000FF;">:</span><span style="color: #000000;">r</span><span style="color: #0000FF;">),</span> |
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if and_bits(orientation,#04) then {rr,cc} = {cc,rr} end if |
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<span style="color: #000000;">cc</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">orientation</span><span style="color: #0000FF;">,</span><span style="color: #000000;">#02</span><span style="color: #0000FF;">)?</span><span style="color: #000000;">6</span><span style="color: #0000FF;">-</span><span style="color: #000000;">c</span><span style="color: #0000FF;">:</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</span> |
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integer ch = pentominoes[rr,offset+cc] |
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">orientation</span><span style="color: #0000FF;">,</span><span style="color: #000000;">#04</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">rr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cc</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">cc</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rr</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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if ch!='.' then |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pentominoes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">offset</span><span style="color: #0000FF;">+</span><span style="color: #000000;">cc</span><span style="color: #0000FF;">]</span> |
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if not found then |
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<span style="color: #008080;">if</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">!=</span><span style="color: #008000;">'.'</span> <span style="color: #008080;">then</span> |
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{found,fr,fc,letter} = {true,r,c,ch} |
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<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">found</span> <span style="color: #008080;">then</span> |
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else |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">found</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fc</span><span style="color: #0000FF;">,</span><span style="color: #000000;">letter</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #004600;">true</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;">ch</span><span style="color: #0000FF;">}</span> |
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this &= {r-fr,c-fc} |
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<span style="color: #008080;">else</span> |
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<span style="color: #000000;">shape</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;">fr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">fc</span><span style="color: #0000FF;">}</span> |
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end if |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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if not find(this,shape) then |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shape</span><span style="color: #0000FF;">,</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
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end if |
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<span style="color: #000000;">shapes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">,</span><span style="color: #000000;">shape</span><span style="color: #0000FF;">)</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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res = append(res,{letter&"",shape}) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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end for |
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<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;">letter</span><span style="color: #0000FF;">&</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">})</span> |
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return res |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">res</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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constant shapes = get_shapes(), |
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nRows = 8, |
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<span style="color: #008080;">constant</span> <span style="color: #000000;">shapes</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_shapes</span><span style="color: #0000FF;">(),</span> |
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nCols = 8 |
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<span style="color: #000000;">nRows</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">,</span> |
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<span style="color: #000000;">nCols</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">8</span> |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">grid</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: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nCols</span><span style="color: #0000FF;">),</span><span style="color: #000000;">nRows</span><span style="color: #0000FF;">),</span> |
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<span style="color: #000000;">placed</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: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">))</span> |
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">re_place</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">o</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: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">)</span> |
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<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;">ch</span> |
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<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;">o</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span> |
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<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;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">o</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: #0000FF;">=</span> <span style="color: #000000;">ch</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span> |
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<span style="color: #008080;">function</span> <span style="color: #000000;">can_place</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">o</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: #000000;">ch</span><span style="color: #0000FF;">)</span> |
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sequence grid = repeat(repeat(' ',nCols),nRows), |
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<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;">o</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span> |
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placed = repeat(false,length(shapes)) |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">o</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> |
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<span style="color: #000000;">y</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> |
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function can_place(sequence o, integer r, c, ch) |
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<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;"><</span><span style="color: #000000;">1</span> <span style="color: #008080;">or</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">></span><span style="color: #000000;">nCols</span> |
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for i=1 to length(o) by 2 do |
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<span style="color: #008080;">or</span> <span style="color: #000000;">y</span><span style="color: #0000FF;"><</span><span style="color: #000000;">1</span> <span style="color: #008080;">or</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">></span><span style="color: #000000;">nRows</span> |
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integer x := c + o[i+1], |
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<span style="color: #008080;">or</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">y</span><span style="color: #0000FF;">][</span><span style="color: #000000;">x</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">' '</span> <span style="color: #008080;">then</span> |
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y := r + o[i] |
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<span style="color: #008080;">return</span> <span style="color: #004600;">false</span> |
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if x<1 or x>nCols |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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or y<1 or y>nRows |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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or grid[y][x]!=' ' then |
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<span style="color: #000000;">re_place</span><span style="color: #0000FF;">(</span><span style="color: #000000;">o</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;">ch</span><span style="color: #0000FF;">)</span> |
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return false |
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<span style="color: #008080;">return</span> <span style="color: #004600;">true</span> |
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end if |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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end for |
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grid[r][c] = ch |
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<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;">pos</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">numPlaced</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> |
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for i=1 to length(o) by 2 do |
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<span style="color: #008080;">if</span> <span style="color: #000000;">numPlaced</span> <span style="color: #0000FF;">==</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">shapes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
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grid[r+o[i]][c+o[i+1]] = ch |
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<span style="color: #008080;">return</span> <span style="color: #004600;">true</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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return true |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">row</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">/</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> |
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end function |
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<span style="color: #000000;">col</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span> |
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<span style="color: #008080;">if</span> <span style="color: #000000;">grid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">row</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">' '</span> <span style="color: #008080;">then</span> |
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procedure un_place(sequence o, integer r, c) |
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<span style="color: #008080;">return</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">numPlaced</span><span style="color: #0000FF;">)</span> |
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grid[r][c] = ' ' |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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for i=1 to length(o) by 2 do |
|||
<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;">shapes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
|||
grid[r+o[i]][c+o[i+1]] = ' ' |
|||
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">placed</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> |
|||
end for |
|||
<span style="color: #004080;">integer</span> <span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">shapes</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: #000000;">1</span><span style="color: #0000FF;">]</span> |
|||
end procedure |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">j</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;">shapes</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;">do</span> |
|||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">o</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">shapes</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;">j</span><span style="color: #0000FF;">]</span> |
|||
function solve(integer pos=0, numPlaced=0) |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">can_place</span><span style="color: #0000FF;">(</span><span style="color: #000000;">o</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
|||
if numPlaced == length(shapes) then |
|||
<span style="color: #000000;">placed</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span> |
|||
return true |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">numPlaced</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
|||
end if |
|||
<span style="color: #008080;">return</span> <span style="color: #004600;">true</span> |
|||
integer row = floor(pos/8)+1, |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
col = mod(pos,8)+1 |
|||
<span style="color: #000000;">re_place</span><span style="color: #0000FF;">(</span><span style="color: #000000;">o</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">)</span> |
|||
if grid[row][col]!=' ' then |
|||
<span style="color: #000000;">placed</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span> |
|||
return solve(pos+1, numPlaced) |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
end if |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
for i=1 to length(shapes) do |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
if not placed[i] then |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
integer ch = shapes[i][1][1] |
|||
<span style="color: #008080;">return</span> <span style="color: #004600;">false</span> |
|||
for j=1 to length(shapes[i][2]) do |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
sequence o = shapes[i][2][j] |
|||
if can_place(o, row, col, ch) then |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">unsolveable</span><span style="color: #0000FF;">()</span> |
|||
placed[i] = true |
|||
<span style="color: #000080;font-style:italic;">-- |
|||
if solve(pos+1, numPlaced+1) then |
|||
-- The only unsolvable grids seen have |
|||
return true |
|||
-- -.- or -..- or -... at edge/corner, |
|||
end if |
|||
-- - -- --- - |
|||
-- or somewhere in the middle a -.- |
|||
placed[i] = false |
|||
-- - |
|||
-- |
|||
end for |
|||
-- Simply place all shapes at all positions/orientations, |
|||
end if |
|||
-- all the while checking for any untouchable cells. |
|||
end for |
|||
--</span> |
|||
return false |
|||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">griddled</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">grid</span><span style="color: #0000FF;">)</span> |
|||
end function |
|||
<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;">8</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;">8</span> <span style="color: #008080;">do</span> |
|||
function unsolveable() |
|||
<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: #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;">shapes</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
|||
-- The only unsolvable grids seen have |
|||
<span style="color: #004080;">integer</span> <span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">shapes</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: #000000;">1</span><span style="color: #0000FF;">]</span> |
|||
-- -.- or -..- or -... at edge/corner, |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">j</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;">shapes</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;">do</span> |
|||
-- - -- --- - |
|||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">o</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">shapes</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;">j</span><span style="color: #0000FF;">]</span> |
|||
-- or somewhere in the middle a -.- |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">can_place</span><span style="color: #0000FF;">(</span><span style="color: #000000;">o</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;">ch</span><span style="color: #0000FF;">)</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;">griddled</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> |
|||
-- Simply place all shapes at all positions/orientations, |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">k</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;">o</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span> |
|||
-- all the while checking for any untouchable cells. |
|||
<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;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">' '</span> |
|||
-- |
|||
<span style="color: #000000;">griddled</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span> |
|||
sequence griddled = grid |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
for r=1 to 8 do |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
for c=1 to 8 do |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
if grid[r][c]=' ' then |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
for i=1 to length(shapes) do |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">griddled</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: #008080;">return</span> <span style="color: #004600;">true</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
integer ch = shapes[i][1][1] |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
for j=1 to length(shapes[i][2]) do |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
sequence o = shapes[i][2][j] |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
if can_place(o, r, c, ch) then |
|||
<span style="color: #008080;">return</span> <span style="color: #004600;">false</span> |
|||
grid[r][c] = ' ' |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
griddled[r][c] = '-' |
|||
for k=1 to length(o) by 2 do |
|||
<span style="color: #008080;">procedure</span> <span style="color: #000000;">add_four_randomly</span><span style="color: #0000FF;">()</span> |
|||
grid[r+o[k]][c+o[k+1]] = ' ' |
|||
<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> |
|||
griddled[r+o[k]][c+o[k+1]] = '-' |
|||
<span style="color: #008080;">while</span> <span style="color: #000000;">count</span><span style="color: #0000FF;"><</span><span style="color: #000000;">4</span> <span style="color: #008080;">do</span> |
|||
end for |
|||
<span style="color: #004080;">integer</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">rand</span><span style="color: #0000FF;">(</span><span style="color: #000000;">8</span><span style="color: #0000FF;">),</span> |
|||
end if |
|||
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">rand</span><span style="color: #0000FF;">(</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)</span> |
|||
end for |
|||
<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> |
|||
end for |
|||
<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> |
|||
if griddled[r][c]!='-' then return true end if |
|||
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> |
|||
end if |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
end for |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
|||
end for |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span> |
|||
return false |
|||
end function |
|||
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span> |
|||
<span style="color: #000000;">add_four_randomly</span><span style="color: #0000FF;">()</span> |
|||
procedure add_four_randomly() |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">unsolveable</span><span style="color: #0000FF;">()</span> <span style="color: #008080;">then</span> |
|||
integer count = 0 |
|||
<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;">"No solution\n"</span><span style="color: #0000FF;">)</span> |
|||
while count<4 do |
|||
<span style="color: #008080;">else</span> |
|||
integer r = rand(8), |
|||
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">()</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> |
|||
c = rand(8) |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
if grid[r][c]=' ' then |
|||
<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: #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"</span><span style="color: #0000FF;">)</span> |
|||
grid[r][c] = '-' |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span> |
|||
count += 1 |
|||
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span> |
|||
end if |
|||
<!--</lang>--> |
|||
end while |
|||
end procedure |
|||
procedure main() |
|||
add_four_randomly() |
|||
if unsolveable() then |
|||
puts(1,"No solution\n") |
|||
else |
|||
if not solve() then ?9/0 end if |
|||
end if |
|||
puts(1,join(grid,"\n")&"\n") |
|||
end procedure |
|||
main()</lang> |
|||
{{out}} |
{{out}} |
||
<pre> |
<pre> |