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Palindromic gapful numbers: Difference between revisions

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Palindromic gapful numbers (view source)

Revision as of 13:41, 19 April 2021

43,680 bytes added ,  3 years ago
m
→‎{{header|Phix}}: added syntax colouring the hard way, also checked the final AppleScript 2..4 checks (all good!)
(→‎{{header|AppleScript}}: →‎Translation of Phix "Ludicrously fast …": 6.5-fold speed increase by dumping NSMutableDictionary altogether. Several minor tweaks and comment changes.)
m (→‎{{header|Phix}}: added syntax colouring the hard way, also checked the final AppleScript 2..4 checks (all good!))
Line 2,913:
{{trans|Go}}
Translation of Go, but trimmed back to bare minimum: you should not expect this to fare particularly well at the 10_000_000-level against the likes of Go/Pascal, though it should fare reasonably well against lesser beings... The version below beats 'em all, though, for now.
<!--<lang Phix>function reverse_n(atom s)-->
<span style="color: #008080;">function</span> <span style="color: #000000;">reverse_n</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
atom e = 0
<span style="color: #004080;">atom</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
while s>0 do
<span style="color: #008080;">while</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
e = e*10 + remainder(s,10)
<span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span> <span style="color: #0000FF;">+</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
s = floor(s/10)
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
return e
<span style="color: #008080;">return</span> <span style="color: #000000;">e</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">mx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1000</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">data</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"%7d "</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">86</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">100</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"%8d "</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">991</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1000</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"%10d "</span><span style="color: #0000FF;">}}</span>
<span style="color: #008080;">include</span> <span style="color: #000000;">builtins</span><span style="color: #0000FF;">\</span><span style="color: #7060A8;">ordinal</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
constant mx = 1000,
data = {{1, 20, "%7d "}, {86, 100, "%8d "}, {991, 1000, "%10d "}}
 
include builtins\ordinal.e
 
procedure main()
sequence results = repeat(repeat({},9),mx)
for d=1 to 9 do -- (the start/end digit)
integer count = 0, pow = 1, fl = d*11
for nd=3 to 15 do -- (number of digits, usually quits early)
-- (obvs. 64-bit phix is fine with 19 digits, but 32-bit ain't)
bool odd = (remainder(nd,2)==1)
for s=d*pow to (d+1)*pow-1 do -- (eg 300 to 399)
integer e = reverse_n(s)
for m=0 to iff(odd?9:0) do -- (1 or 10 iterations)
atom p = e + iff(odd ? s*pow*100+m*pow*10
: s*pow*10)
if remainder(p,fl)==0 then -- gapful!
count += 1
results[count][d] = p
-- (see? goto /is/ sometimes useful :-))
if count==mx then #ilASM{jmp :outer} end if
end if
end for
end for
if odd then pow *= 10 end if
end for
if count<mx then ?9/0 end if -- oh dear...
#ilASM{::outer}
end for
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
for i=1 to length(data) do
<span style="color: #004080;">sequence</span> <span style="color: #000000;">results</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: #000000;">9</span><span style="color: #0000FF;">),</span><span style="color: #000000;">mx</span><span style="color: #0000FF;">)</span>
{integer s, integer e, string fmt} = data[i]
<span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (the start/end digit)</span>
printf(1,"%,d%s to %,d%s palindromic gapful numbers (> 100) ending with:\n", {s,ord(s),e,ord(e)})
<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: #0000FF;">,</span> <span style="color: #000000;">pow</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fl</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">*</span><span style="color: #000000;">11</span>
for d=1 to 9 do
<span style="color: #008080;">for</span> <span style="color: #000000;">nd</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #000000;">15</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (number of digits, usually quits early)
printf(1,"%d: ",d)
-- (obvs. 64-bit phix is fine with 19 digits, but 32-bit ain't)</span>
for j=s to e do
<span style="color: #004080;">bool</span> <span style="color: #000000;">odd</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nd</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)==</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
printf(1,fmt,results[j][d])
<span style="color: #008080;">for</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #000000;">d</span><span style="color: #0000FF;">*</span><span style="color: #000000;">pow</span> <span style="color: #008080;">to</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">pow</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (eg 300 to 399)</span>
end for
<span style="color: #004080;">integer</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">reverse_n</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
printf(1,"\n")
<span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">odd</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: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (1 or 10 iterations)</span>
end for
<span style="color: #004080;">atom</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">+</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">odd</span> <span style="color: #0000FF;">?</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">*</span><span style="color: #000000;">pow</span><span style="color: #0000FF;">*</span><span style="color: #000000;">100</span><span style="color: #0000FF;">+</span><span style="color: #000000;">m</span><span style="color: #0000FF;">*</span><span style="color: #000000;">pow</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span>
printf(1,"\n")
<span style="color: #0000FF;">:</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">*</span><span style="color: #000000;">pow</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fl</span><span style="color: #0000FF;">)==</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- gapful!</span>
end procedure
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
main()</lang>
<span style="color: #000000;">results</span><span style="color: #0000FF;">[</span><span style="color: #000000;">count</span><span style="color: #0000FF;">][</span><span style="color: #000000;">d</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span>
<span style="color: #000080;font-style:italic;">-- (see? goto /is/ sometimes useful :-))</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">==</span><span style="color: #000000;">mx</span> <span style="color: #008080;">then</span> #ilASM{jmp :outer} <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;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">odd</span> <span style="color: #008080;">then</span> <span style="color: #000000;">pow</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</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;">if</span> <span style="color: #000000;">count</span><span style="color: #0000FF;"><</span><span style="color: #000000;">mx</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: #000080;font-style:italic;">-- oh dear...</span>
#ilASM{::outer}
<span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">data</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">{</span><span style="color: #004080;">integer</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">data</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</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;">"%,d%s to %,d%s palindromic gapful numbers (&gt; 100) ending with:\n"</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;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</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: "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">s</span> <span style="color: #008080;">to</span> <span style="color: #000000;">e</span> <span style="color: #008080;">do</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: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">results</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">d</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">"\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">"\n"</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;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</lang>-->
{{out}}
<pre style="font-size: 11px">
Line 3,006 ⟶ 3,008:
Astonishingly this is all done with standard precision numbers, &lt; 2<sup><small>53</small></sup>. You realise this is like ten thousand times the ''square'' of the previous limits, and still far faster.<br>
I will credit [[Self_numbers#AppleScript]] and the comment by Nigel Galloway on the talk page for ideas that inspired me.
<!--<lang Phix>(phixonline)-->
<lang Phix>-- demo/rosetta/Palindromic_gapful_numbers.exw
<span style="color: #000080;font-style:italic;">-- demo/rosetta/Palindromic_gapful_numbers.exw
--
--
-- A palindrome such as 9459549 can be constructed/broken down into
-- Astonishingly this is all done with standard precision numbers, &lt;2^53.
-- 9000009
-- I will credit https://rosettacode.org/wiki/Self_numbers#AppleScript and
-- 400040
-- the comment by Nigel Galloway on the talk page for ideas that inspired me.
-- 50500
--
-- 9000
-- A palindrome such as 9459549 can be constructed/broken down into
--
-- 9000009
-- Further, 9459549 rem 99 is the same as
-- (the sum of rem 99 on all of those pieces) rem 99 400040
-- 50500
--
-- 9000
-- Finding eg 400040 rem 99 can also be simplified, it is of course the
--
-- same as (400000 rem 99 + 40 rem 99) rem 99, and further 40 rem 99
-- Further, 9459549 rem 99 is the same as (4 rem 99[already known])*10 rem 99 [smaller nos].
-- (the sum of rem 99 on all of those pieces) rem 99
--
--
-- Also, when filling a "hole", such as the final 9, we find
-- Finding eg 400040 rem 99 can also be simplified, it is of v course the
-- same as (400000 rem 99 + 40 9450549rem 99) rem 99, =and 9further 40 rem 99
-- is the same as (4 rem 99[already 9451549known])*10 rem 99 =[smaller 19,nos].
--
-- 9452549 rem 99 = 29,
-- Also, when filling a "hole", such as the final 9, we find
-- 9453549 rem 99 = 39,
-- 9454549 rem 99 =v 49,
-- 94555499450549 rem 99 = 59,9
-- 94565499451549 rem 99 = 6919,
-- 94575499452549 rem 99 = 7929,
-- 94585499453549 rem 99 = 8939, and
-- 94595499454549 rem 99 = 049,
-- 9455549 rem 99 ^= 59,
-- 9456549 rem 99 = 69,
-- in this case only the '9' fits.
-- 9457549 rem 99 = 79,
--
-- 9458549 rem 99 = 89, and
-- But actually we can predict what will fit from the partial sum of
-- prior pieces rem 99, ie 9000009..50500, and the same9459549 canrem be99 said= 0,
-- when filling the 505-sized hole - what will "fit" depends not on ^
-- in this case only the '9' fits.
-- what the "outer" actually are, but what their sum rem 99 is, and
--
-- likewise for larger and larger holes.
-- But Ifactually we latercan findpredict ourselveswhat lookingwill atfit thefrom samethe sizepartial hole,sum withof
-- the sameprior outerpieces rem 99, ie 9000009..50500, and the same remcan 99 outmost requirement,be wesaid
-- when filling the 505-sized hole - what will "fit" depends not on
-- would know instantly how many things are going to fit.
-- what the "outer" actually are, but what their sum rem 99 is, and
-- True, keeping full lists as the holes got bigger would probably
-- likewise for larger and larger holes.
-- consume memory almost as fast as an SR-71, but a single count,
-- If we later find ourselves looking at the same size hole, with
-- albeit one keyed on 4 conditions, we can cope. It turns out that
-- the same outer rem and the same rem 99 outmost requirement, we
-- even by the 10^19th scan, we only hit 24,791 variations anyway.
-- would know instantly how many things are going to fit.
-- As we stumble across larger and larger holes, what we learn can
-- True, keeping full lists as the holes got bigger would probably
-- be used to skip more and more similar, such that finding the
-- tenconsume millionth item ismemory almost as fast as thean first millionthSR-71, asbut a single count,
-- albeit one keyed on 4 conditions, we can cope. It turns out that
-- opposed to the times 10 that you'd normally expect.
-- even by the 10^15th scan, we only hit 17,579 variations anyway.
--
-- Note thatAs if Iwe stumble across alarger holeand thatlarger willholes, fitwhat morewe thanlearn I'mcan
-- preparedbe used to fully skip, Imore startand goingmore throughsimilar, thingssuch one-by-one,that finding the
-- ten millionth item is almost as fast as the first millionth, as
-- but that's ok because many smaller but still quite big holes
-- opposed to the times 10 that you'd normally expect.
-- will probably be skipped.
--
-- Note that if I stumble across a hole that will fit more than I'm
 
-- prepared to fully skip, I start going through things one-by-one,
sequence cache = columnize(repeat(columnize({tagset(9)}),9))
-- but that's ok because many smaller but still quite big holes
-- ie {{{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}},
-- will probably be skipped.
-- {{2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}},
--</span>
-- {{3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}},
-- {{4}, {4}, {4}, {4}, {4}, {4}, {4}, {4}, {4}},
<span style="color: #004080;">sequence</span> <span style="color: #000000;">cache</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">({</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)}),</span><span style="color: #000000;">9</span><span style="color: #0000FF;">))</span>
-- {{5}, {5}, {5}, {5}, {5}, {5}, {5}, {5}, {5}},
<span style="color: #000080;font-style:italic;">-- ie {{6{1}, {61}, {61}, {61}, {61}, {61}, {61}, {61}, {61}},
-- {{72}, {72}, {72}, {72}, {72}, {72}, {72}, {72}, {72}},
-- {{83}, {83}, {83}, {83}, {83}, {83}, {83}, {83}, {83}},
-- {{94}, {94}, {94}, {94}, {94}, {94}, {94}, {94}, {9}4}},
-- aka 1 rem 11 .. 1 rem{{5}, 99{5}, are{5}, all{5}, 1{5}, {5}, {5}, {5}, {5}},
-- .. 9 rem 11 .. 9{{6}, rem{6}, 99{6}, are{6}, all{6}, 9.{6}, {6}, {6}, {6}},
-- {{7}, {7}, {7}, {7}, {7}, {7}, {7}, {7}, {7}},
-- each gets extended with 10 rem 11 .. 10 rem 99,
-- {{8}, {8}, {8}, {8}, {8}, {8}, {8}, {8}, 100 rem 11 .. 100 rem 99{8}},
-- {{9}, {9}, {9}, {9}, {9}, {9}, {9}, ... .. 900 rem 99{9}, etc.{9}}}
-- aka 1 rem 11 .. 1 rem 99 are all 1,
-- (not really worth trying to take advantage of any cycles
-- that.. might9 appearrem in11 such.. a9 relativelyrem small99 table,are asall 9.
-- each itgets willextended bewith at10 mostrem (on11 64-bit).. 910 *rem 9 * 42.)99,
-- 100 rem 11 .. 100 rem 99,
--
-- ... .. 900 rem 99, etc.
function rmdr(integer digit, gap, pow, n)
-- (not really worth trying to take advantage of any cycles
--
-- that might appear in such a relatively small table, as
-- digit is the outer 0..9 (obvs 0 always yields 0),
-- it will be at most (on 64-bit) 9 * 9 * 42.)
-- gap is zeroes between (-1,0,1,2,.. for eg 1,11,101,1001),
--</span>
-- pow is trailing zeros (0,1,2,.. for eg 101,1010,10100),
<span style="color: #008080;">function</span> <span style="color: #000000;">rmdr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">digit</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">gap</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">pow</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
-- n is 1..9 for 11..99
<span style="color: #000080;font-style:italic;">--
-- eg rmdr(4,3,2,1) yields remainder(4000400,11), but
-- digit is the outer 0..9 (obvs 0 always yields 0),
-- that === remainder(remainder(4000000,11)+
-- gap is zeroes between (-1,0,1,2,.. for eg 1,11,101,1001),
-- remainder( 400,11),11), and
-- pow is trailing zeros (0,1,2,.. for eg 101,1010,10100),
-- if k = remainder(4*10^(m-1),11) [already known] then
-- n is 1..9 for 11..99
-- remainder(4*10^m,11) === remainder(k*10,11), so
-- eg rmdr(4,3,2,1) yields remainder(4000400,11), but
-- we only need to keep a small table for each [digit][n].
-- that === remainder(remainder(4000000,11)+
-- Thus we avoid maths on 10^42-size numbers/needing gmp.
-- remainder( 400,11),11), and
--
-- if k = remainder(4*10^(m-1),11) [already known] then
if digit=0 then return 0 end if
-- remainder(4*10^m,11) === remainder(k*10,11), so
integer nn = n*11
-- we only need to keep a small table for each [digit][n].
while length(cache[digit][n])<gap+pow+2 do
-- Thus we avoid maths on 10^42-ish numbers/needing gmp.
cache[digit][n] &= remainder(cache[digit][n][$]*10,nn)
--</span>
end while
<span style="color: #008080;">if</span> <span style="color: #000000;">digit</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;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
integer g = iff(gap=-1?0:cache[digit][n][gap+pow+2])
<span style="color: #004080;">integer</span> <span style="color: #000000;">nn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">g</span>
return remainder(g+cache[digit][n][pow+1],nn)
<span style="color: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cache</span><span style="color: #0000FF;">[</span><span style="color: #000000;">digit</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">])<</span><span style="color: #000000;">gap</span><span style="color: #0000FF;">+</span><span style="color: #000000;">pow</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
end function
<span style="color: #000000;">cache</span><span style="color: #0000FF;">[</span><span style="color: #000000;">digit</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cache</span><span style="color: #0000FF;">[</span><span style="color: #000000;">digit</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][$]*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">)</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
integer skipd = new_dict()
<span style="color: #000000;">g</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">gap</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">1</span> <span style="color: #0000FF;">?</span> <span style="color: #000000;">0</span> <span style="color: #0000FF;">:</span> <span style="color: #000000;">cache</span><span style="color: #0000FF;">[</span><span style="color: #000000;">digit</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">gap</span><span style="color: #0000FF;">+</span><span style="color: #000000;">pow</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span>
 
<span style="color: #008080;">return</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">g</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">cache</span><span style="color: #0000FF;">[</span><span style="color: #000000;">digit</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">pow</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">)</span>
function palindromicgapfuls(sequence pals, string lhs, atom palcount, to_skip, count, integer l, r, p, dd)
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
--
-- pals: results (passing it up grants it automatic pass-by-reference status, which may help speedwise)
<span style="color: #004080;">integer</span> <span style="color: #000000;">skipd</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">new_dict</span><span style="color: #0000FF;">()</span>
-- lhs: eg "945" of a potential 9459549 result
-- palcount, to_skip, count: self explanatory (aka got/ignore/target)
<span style="color: #008080;">function</span> <span style="color: #000000;">palindromicgapfuls</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">pals</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">lhs</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">palcount</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">to_skip</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dd</span><span style="color: #0000FF;">)</span>
-- l: length of inner to be filled in
<span style="color: #000080;font-style:italic;">--
-- r: remainder of outer, eg remainder(9400049,11), built from rmdr()
-- pals: results (passing it up grants it automatic pass-by-reference status, which may help speedwise)
-- p: left shift (should in fact always equal length(lhs), I think)
-- lhs: eg "945" of a potential 9459549 result
-- dd: outermost 1..9 (despite the name, it's a single digit)
-- palcount, to_skip, count: self explanatory (aka got/ignore/target)
--
-- l: length of inner to be filled in
sequence key = {l,r,p,dd}
-- r: remainder of outer, eg remainder(9400049,11), built from rmdr()
integer node = getd_index(key,skipd)
-- p: left shift (should in fact always equal length(lhs), I think)
atom skip = iff(node==null?count:getd_by_index(node,skipd))
-- dd: outermost 1..9 (despite the name, it's a single digit)
if node!=null and (palcount+skip)<to_skip then
--</span>
palcount += skip
<span style="color: #004080;">sequence</span> <span style="color: #000000;">key</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dd</span><span style="color: #0000FF;">}</span>
else
<span style="color: #004080;">integer</span> <span style="color: #000000;">node</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd_index</span><span style="color: #0000FF;">(</span><span style="color: #000000;">key</span><span style="color: #0000FF;">,</span><span style="color: #000000;">skipd</span><span style="color: #0000FF;">)</span>
skip = 0
<span style="color: #004080;">atom</span> <span style="color: #000000;">skip</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">node</span><span style="color: #0000FF;">==</span><span style="color: #004600;">null</span><span style="color: #0000FF;">?</span><span style="color: #000000;">count</span><span style="color: #0000FF;">:</span><span style="color: #7060A8;">getd_by_index</span><span style="color: #0000FF;">(</span><span style="color: #000000;">node</span><span style="color: #0000FF;">,</span><span style="color: #000000;">skipd</span><span style="color: #0000FF;">)),</span> <span style="color: #000000;">skipn</span>
for d=0 to 9 do
<span style="color: #008080;">if</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">!=</span><span style="color: #004600;">null</span> <span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">palcount</span><span style="color: #0000FF;">+</span><span style="color: #000000;">skip</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">to_skip</span> <span style="color: #008080;">then</span>
integer r2 = remainder(r+rmdr(d,l-2,p,dd),dd*11)
<span style="color: #000000;">palcount</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">skip</span>
if l<=2 then
<span style="color: #008080;">else</span>
if r2=0 then
<span style="color: #000000;">skip</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
palcount += 1
<span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
if palcount<=to_skip then
<span style="color: #004080;">integer</span> <span style="color: #000000;">r2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">rmdr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dd</span><span style="color: #0000FF;">),</span><span style="color: #000000;">dd</span><span style="color: #0000FF;">*</span><span style="color: #000000;">11</span><span style="color: #0000FF;">)</span>
skip += 1
<span style="color: #008080;">if</span> <span style="color: #000000;">l</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
else
<span style="color: #008080;">if</span> <span style="color: #000000;">r2</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
pals = append(pals,lhs&repeat(d+'0',l)&reverse(lhs))
<span style="color: #000000;">palcount</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
end if
<span style="color: #008080;">if</span> <span style="color: #000000;">palcount</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">to_skip</span> <span style="color: #008080;">then</span>
end if
<span style="color: #000000;">skip</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
else
<span style="color: #008080;">else</span>
{pals,palcount,atom skipn} = palindromicgapfuls(pals, lhs&(d+'0'), palcount, to_skip, count, l-2, r2, p+1, dd)
<span style="color: #000000;">pals</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pals</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lhs</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">)&</span><span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lhs</span><span style="color: #0000FF;">))</span>
skip += skipn
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if palcount==count then exit end if
<span style="color: #008080;">else</span>
end for
<span style="color: #0000FF;">{</span><span style="color: #000000;">pals</span><span style="color: #0000FF;">,</span><span style="color: #000000;">palcount</span><span style="color: #0000FF;">,</span><span style="color: #000000;">skipn</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">palindromicgapfuls</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pals</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">lhs</span><span style="color: #0000FF;">&(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">palcount</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">to_skip</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dd</span><span style="color: #0000FF;">)</span>
if palcount<to_skip then setd(key,skip,skipd) end if
<span style="color: #000000;">skip</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">skipn</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
return {pals,palcount,skip}
<span style="color: #008080;">if</span> <span style="color: #000000;">palcount</span><span style="color: #0000FF;">==</span><span style="color: #000000;">count</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>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
 
<span style="color: #008080;">if</span> <span style="color: #000000;">palcount</span><span style="color: #0000FF;"><</span><span style="color: #000000;">to_skip</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">setd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">key</span><span style="color: #0000FF;">,</span><span style="color: #000000;">skip</span><span style="color: #0000FF;">,</span><span style="color: #000000;">skipd</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
function collect(integer digit, atom count, keep)
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
atom to_skip = count - keep,
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">pals</span><span style="color: #0000FF;">,</span><span style="color: #000000;">palcount</span><span style="color: #0000FF;">,</span><span style="color: #000000;">skip</span><span style="color: #0000FF;">}</span>
palcount = 0, l = 3
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
sequence pals = {}
string lhs = ""&(digit+'0') -- ie "1" or "2" .. or "9"
<span style="color: #008080;">function</span> <span style="color: #000000;">collect</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">digit</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">keep</span><span style="color: #0000FF;">)</span>
while palcount < count do
<span style="color: #004080;">atom</span> <span style="color: #000000;">to_skip</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">keep</span><span style="color: #0000FF;">,</span>
integer r = rmdr(digit,l-2,0,digit)
<span style="color: #000000;">palcount</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3</span>
{pals,palcount} = palindromicgapfuls(pals,lhs,palcount,to_skip,count,l-2,r,1,digit)
<span style="color: #004080;">sequence</span> <span style="color: #000000;">pals</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
l += 1
<span style="color: #004080;">string</span> <span style="color: #000000;">lhs</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span><span style="color: #0000FF;">&(</span><span style="color: #000000;">digit</span><span style="color: #0000FF;">+</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- ie "1" or "2" .. or "9"</span>
end while
<span style="color: #008080;">while</span> <span style="color: #000000;">palcount</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">count</span> <span style="color: #008080;">do</span>
return pals
<span style="color: #004080;">integer</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rmdr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">digit</span><span style="color: #0000FF;">)</span>
end function
<span style="color: #0000FF;">{</span><span style="color: #000000;">pals</span><span style="color: #0000FF;">,</span><span style="color: #000000;">palcount</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">palindromicgapfuls</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pals</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lhs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">palcount</span><span style="color: #0000FF;">,</span><span style="color: #000000;">to_skip</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</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;">digit</span><span style="color: #0000FF;">)</span>
 
<span style="color: #000000;">l</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
constant tests = {{20,20,1},{100,15,1},{1000,10,1},{10_000,5,1},
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
{100_000,1,1},{1_000_000,1,1},{10_000_000,1,1},
<span style="color: #008080;">return</span> <span style="color: #000000;">pals</span>
{100_000_000,1,9},{1000_000_000,1,9},{10_000_000_000,1,9},
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
{100_000_000_000,1,9},{1000_000_000_000,1,9},
{10_000_000_000_000,1,9},{100_000_000_000_000,1,9},
<span style="color: #008080;">constant</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">10_000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},</span>
{1000_000_000_000_000,1,9},
<span style="color: #0000FF;">{</span><span style="color: #000000;">100_000</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><span style="color: #000000;">9</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1_000_000</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><span style="color: #000000;">9</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">10_000_000</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><span style="color: #000000;">9</span><span style="color: #0000FF;">},</span>
{10_000_000_000_000_000_000,1,9}} -- 64 bit only
<span style="color: #0000FF;">{</span><span style="color: #000000;">100_000_000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1000_000_000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">10_000_000_000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},</span>
-- (any further and you'd need mpfr just to hold counts)
<span style="color: #0000FF;">{</span><span style="color: #000000;">100_000_000_000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1000_000_000_000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},</span>
 
<span style="color: #0000FF;">{</span><span style="color: #000000;">10_000_000_000_000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">100_000_000_000_000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},</span>
atom t0 = time(), count, keep, start
<span style="color: #0000FF;">{</span><span style="color: #000000;">1_000_000_000_000_000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},</span>
for i=1 to length(tests)-(machine_bits()!=64) do
<span style="color: #000080;font-style:italic;">-- {1_000_000_000_000_000,1,2,4}, -- (matches AppleScript)</span>
{count, keep, start} = tests[i]
<span style="color: #0000FF;">{</span><span style="color: #000000;">10_000_000_000_000_000_000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">}}</span> <span style="color: #000080;font-style:italic;">-- 64 bit only
atom from = count-keep+1
-- (any further and you'd need mpfr just to hold counts)</span>
string r = iff(count==keep?sprintf("First %d",{count}):
iff(keep>1?sprintf("Last %d of first %,d",{keep,count})
<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: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">keep</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">start</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">finish</span>
:sprintf("%,dth",{count}))),
<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;">tests</span><span style="color: #0000FF;">)-(</span><span style="color: #7060A8;">machine_bits</span><span style="color: #0000FF;">()!=</span><span style="color: #000000;">64</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
s = iff(keep=1?"":"s")
<span style="color: #0000FF;">{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">keep</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">start</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">finish</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
printf(1,"%s palindromic gapful number%s ending with:\n", {r,s})
<span style="color: #004080;">string</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count</span><span style="color: #0000FF;">==</span><span style="color: #000000;">keep</span><span style="color: #0000FF;">?</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"First %d"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">}):</span>
sequence tags = tagset(9,start),
<span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">keep</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"Last %d of first %,d"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">keep</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">})</span>
res = apply(true,collect,{tags,count,keep})
<span style="color: #0000FF;">:</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%,dth"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">}))),</span>
string fmt = sprintf("%%%ds",max(apply(join(res,{}),length)))
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">keep</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>
for j=1 to length(res) do
<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;">"%s palindromic gapful number%s ending with:\n"</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;">s</span><span style="color: #0000FF;">})</span>
printf(1,"%d: %s\n",{tags[j],join(apply(true,sprintf,{{fmt},res[j]})," ")})
<span style="color: #004080;">sequence</span> <span style="color: #000000;">tags</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">finish</span><span style="color: #0000FF;">,</span><span style="color: #000000;">start</span><span style="color: #0000FF;">),</span>
end for
<span style="color: #000000;">res</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: #000000;">collect</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">tags</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">keep</span><span style="color: #0000FF;">})</span>
puts(1,"\n")
<span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%%%ds"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,{}),</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">)))</span>
end for
<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;">res</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
printf(1,"Completed in %s\n",elapsed(time()-t0))</lang>
<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: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">tags</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #7060A8;">join</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;">sprintf</span><span style="color: #0000FF;">,{{</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">},</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]}),</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</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"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">"Completed in %s\n"</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 style="font-size: 11px">
Petelomax
7,830

edits

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