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Abelian sandpile model/Identity: Difference between revisions

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Abelian sandpile model/Identity (view source)

Revision as of 05:46, 27 March 2021

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→‎{{header|Phix}}: added syntax colouring the hard way
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m (→‎{{header|Phix}}: added syntax colouring the hard way)
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=={{header|Phix}}==
<!--<lang Phix>constant s1 = {"1 2 0",-->
<span style="color: #008080;">constant</span> <span style="color: #000000;">s1</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"1 2 0"</span><span style="color: #0000FF;">,</span>
"2 1 1",
<span style="0color: #008000;">"2 1 31"</span><span style="color: #0000FF;"}>,</span>
<span style="color: #008000;">"0 1 3"</span><span style="color: #0000FF;">},</span>
 
s2 = {"2 1 3",
<span style="color: #000000;">s2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"2 1 3"</span><span style="color: #0000FF;">,</span>
"1 0 1",
<span style="0color: #008000;">"1 0 1"</span><span style="color: #0000FF;"}>,</span>
<span style="color: #008000;">"0 1 0"</span><span style="color: #0000FF;">},</span>
 
s3 = {"3 3 3",
<span style="color: #000000;">s3</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"3 3 3"</span><span style="color: #0000FF;">,</span>
"3 3 3",
<span style="color: #008000;">"3 3 3"}</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"3 3 3"</span><span style="color: #0000FF;">},</span>
 
s3_id = {"2 1 2",
<span style="color: #000000;">s3_id</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"2 1 2"</span><span style="color: #0000FF;">,</span>
"1 0 1",
<span style="2color: #008000;">"1 20 1"</span><span style="color: #0000FF;"}>,</span>
<span style="color: #008000;">"2 1 2"</span><span style="color: #0000FF;">},</span>
 
s4 = {"4 3 3",
<span style="color: #000000;">s4</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"4 3 3"</span><span style="color: #0000FF;">,</span>
"3 1 2",
<span style="0color: #008000;">"3 1 2"</span><span 3style="color: #0000FF;"}>,</span>
<span style="color: #008000;">"0 2 3"</span><span style="color: #0000FF;">}</span>
 
function add(sequence s, t)
<span style="color: #008080;">function</span> <span style="color: #000000;">add</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;">t</span><span style="color: #0000FF;">)</span>
for i=1 to 3 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: #000000;">3</span> <span style="color: #008080;">do</span>
for j=1 to 5 by 2 do
<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: #000000;">5</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
s[i][j] += t[i][j]-'0'
<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;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">t</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: #008000;">'0'</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
return s
<span style="color: #008080;">return</span> <span style="color: #000000;">s</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
function topple(sequence s, integer one=0)
<span style="color: #008080;">function</span> <span style="color: #000000;">topple</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: #004080;">integer</span> <span style="color: #000000;">one</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
for i=1 to 3 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: #000000;">3</span> <span style="color: #008080;">do</span>
for j=1 to 5 by 2 do
<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: #000000;">5</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
if s[i][j]>'3' then
<span style="color: #008080;">if</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;">j</span><span style="color: #0000FF;">]></span><span style="color: #008000;">'3'</span> <span style="color: #008080;">then</span>
s[i][j] -= 4
<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;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">4</span>
if i>1 then s[i-1][j] += 1 end if
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</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;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if i<3 then s[i+1][j] += 1 end if
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;"><</span><span style="color: #000000;">3</span> <span style="color: #008080;">then</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;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if j>1 then s[i][j-2] += 1 end if
<span style="color: #008080;">if</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</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;">j</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if j<5 then s[i][j+2] += 1 end if
<span style="color: #008080;">if</span> <span style="color: #000000;">j</span><span style="color: #0000FF;"><</span><span style="color: #000000;">5</span> <span style="color: #008080;">then</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;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if one=1 then return s end if
<span style="color: #008080;">if</span> <span style="color: #000000;">one</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">s</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
one = -1
<span style="color: #000000;">one</span> <span style="color: #0000FF;">=</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;">for</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
return iff(one=1?{}:iff(one=-1?topple(s):s))
<span style="color: #008080;">return</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">one</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?{}:</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">one</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #000000;">topple</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">):</span><span style="color: #000000;">s</span><span style="color: #0000FF;">))</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
procedure shout(sequence s)
<span style="color: #008080;">procedure</span> <span style="color: #000000;">shout</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
sequence r = repeat("",5)
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</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;">5</span><span style="color: #0000FF;">)</span>
for i=1 to length(s) 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;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
sequence si = s[i]
<span style="color: #004080;">sequence</span> <span style="color: #000000;">si</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>
if string(si) then
<span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">si</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
string ti = repeat(' ',length(si))
<span style="color: #004080;">string</span> <span style="color: #000000;">ti</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: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">si</span><span style="color: #0000FF;">))</span>
r[1] &= ti
<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: #0000FF;">&=</span> <span style="color: #000000;">ti</span>
r[2] &= si
<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: #0000FF;">&=</span> <span style="color: #000000;">si</span>
r[3] &= ti
<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: #0000FF;">&=</span> <span style="color: #000000;">ti</span>
else
<span for jstyle=1 to 3"color: do#008080;">else</span>
<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: #000000;">3</span> <span style="color: #008080;">do</span>
r[j] &= si[j]
<span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">si</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">for</span>
puts(1,join(r,"\n"))
<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;">r</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">))</span>
end procedure
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
 
puts(1,"1. Show avalanche\n\n")
<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;">"1. Show avalanche\n\n"</span><span style="color: #0000FF;">)</span>
sequence s = s4,
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s4</span><span style="color: #0000FF;">,</span>
res = {" ",s}
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</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>
while true do
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
s = topple(s,1)
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">topple</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
if s={} then exit end if
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">={}</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
res &= {" ==> ",s}
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">" ==&gt; "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">}</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
shout(res)
<span style="color: #000000;">shout</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
 
puts(1,"2. Prove s1 + s2 = s2 + s1\n\n")
<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;">"2. Prove s1 + s2 = s2 + s1\n\n"</span><span style="color: #0000FF;">)</span>
shout({" ",s1," + ",s2," = ",topple(add(s1,s2))})
<span style="color: #000000;">shout</span><span style="color: #0000FF;">({</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" + "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" = "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">topple</span><span style="color: #0000FF;">(</span><span style="color: #000000;">add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">))})</span>
shout({" ",s2," + ",s1," = ",topple(add(s2,s1))})
<span style="color: #000000;">shout</span><span style="color: #0000FF;">({</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" + "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" = "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">topple</span><span style="color: #0000FF;">(</span><span style="color: #000000;">add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">))})</span>
 
puts(1,"3. Show that s3 + s3_id == s3\n\n")
<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;">"3. Show that s3 + s3_id == s3\n\n"</span><span style="color: #0000FF;">)</span>
shout({" ",s3," + ",s3_id," = ",topple(add(s3,s3_id))})
<span style="color: #000000;">shout</span><span style="color: #0000FF;">({</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s3</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" + "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s3_id</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" = "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">topple</span><span style="color: #0000FF;">(</span><span style="color: #000000;">add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s3_id</span><span style="color: #0000FF;">))})</span>
 
puts(1,"4. Show that s3_id + s3_id == s3_id\n\n")
<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;">"4. Show that s3_id + s3_id == s3_id\n\n"</span><span style="color: #0000FF;">)</span>
shout({" ",s3_id," + ",s3_id," = ",topple(add(s3_id,s3_id))})</lang>
<span style="color: #000000;">shout</span><span style="color: #0000FF;">({</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s3_id</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" + "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s3_id</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" = "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">topple</span><span style="color: #0000FF;">(</span><span style="color: #000000;">add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s3_id</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s3_id</span><span style="color: #0000FF;">))})</span>
<!--</lang>-->
{{out}}
<pre>
Petelomax
7,818

edits

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