Data update
This commit is contained in:
Ingy döt Net
parent
5150844a7d
commit
4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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@ -1,15 +1,52 @@
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fastfunc rev h .
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while h > 0
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r = r * 10 + h mod 10
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h = h div 10
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.
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return r
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.
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fastfunc issqr n .
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h = sqrt n
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if h = floor h : return 1
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return 0
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.
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po = 1
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lim = 1
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a = 0
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fastfunc next n .
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while 1 = 1
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n += 1
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h = n
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nrev = 0
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while h > 0
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nrev = nrev * 10 + h mod 10
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h = h div 10
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if n = lim
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a += 2
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if a = 10
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a = 2
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po *= 10
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.
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n = a * po
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lim = n + po
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.
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if sqrt (n + nrev) mod 1 = 0
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if n - nrev >= 1 and sqrt (n - nrev) mod 1 = 0
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return n
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q = n mod 10
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if a <> 2 or q = 2
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if a <> 4 or q = 0
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if a <> 6 or q = 0 or q = 5
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#
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s9 = (n mod 9 * 2) mod 9
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if s9 <= 1 or s9 = 4 or s9 = 7
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#
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if q <> 1 and q <> 4 and q <> 6 and q <> 9
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h = a - q
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if h <= 1 or h >= 4 and h <= 6
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#
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nrev = rev n
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if issqr (n + nrev) = 1
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if n > nrev and issqr (n - nrev) = 1
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return n
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.
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.
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.
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.
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.
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.
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.
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.
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.
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@ -1,33 +1,31 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">revn</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">nd</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</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: #000000;">nd</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</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;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</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>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">r</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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with javascript_semantics
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function revn(atom n, integer nd)
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atom r = 0
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for i=1 to nd do
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r = r*10+remainder(n,10)
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n = floor(n/10)
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end for
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return r
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end function
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<span style="color: #004080;">integer</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;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">99</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
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<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">revn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nd</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;"><</span><span style="color: #000000;">n</span> <span style="color: #008080;">then</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">r</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)),</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">and</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)),</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<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: %d (%s)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">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>
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<span style="color: #008080;">if</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</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>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">lim</span> <span style="color: #008080;">then</span>
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<span style="color: #000080;font-style:italic;">-- ?{"lim",lim,elapsed(time()-t0)}</span>
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<span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lim</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">+</span><span style="color: #000000;">9</span>
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<span style="color: #000000;">nd</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<!--
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integer nd = 2, count = 0
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atom lim = 99, n = 9, t0 = time()
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while true do
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n += 1
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atom r = revn(n,nd)
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if r<n then
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atom s = n+r,
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d = n-r
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if s=power(floor(sqrt(s)),2)
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and d=power(floor(sqrt(d)),2) then
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count += 1
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printf(1,"%d: %d (%s)\n",{count,n,elapsed(time()-t0)})
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if count=3 then exit end if
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end if
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end if
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if n=lim then
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-- ?{"lim",lim,elapsed(time()-t0)}
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lim = lim*10+9
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nd += 1
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end if
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end while
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@ -1,240 +1,238 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">maxDigits</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">10</span><span style="color: #0000FF;">:</span><span style="color: #000000;">15</span><span style="color: #0000FF;">)</span>
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with javascript_semantics
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constant maxDigits = iff(platform()=JS?10:15)
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<span style="color: #008080;">enum</span> <span style="color: #000000;">COEFF</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">TDXA</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">TDXB</span> <span style="color: #000080;font-style:italic;">-- struct term = {atom coeff, integer idxa, idxb}
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-- (see allTerms below)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">nd</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- number of digits</span>
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<span style="color: #000000;">count</span> <span style="color: #000080;font-style:italic;">-- of solutions found earlier, for lower nd</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">rares</span> <span style="color: #000080;font-style:italic;">-- (cleared after sorting/printing for each nd)</span>
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enum COEFF, TDXA, TDXB -- struct term = {atom coeff, integer idxa, idxb}
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-- (see allTerms below)
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integer nd, -- number of digits
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count -- of solutions found earlier, for lower nd
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sequence rares -- (cleared after sorting/printing for each nd)
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<span style="color: #008080;">function</span> <span style="color: #000000;">to_atom</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- convert digits array to an atom value</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</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;">digits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">10</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</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;">return</span> <span style="color: #000000;">r</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function to_atom(sequence digits)
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-- convert digits array to an atom value
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atom r = 0
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for i=1 to length(digits) do
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r = r * 10 + digits[i]
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end for
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return r
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end function
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<span style="color: #000080;font-style:italic;">-- psq eliminates 52 out of 64 of numbers fairly cheaply, which translates
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-- to approximately 66% of numbers, or around 10% off the overall time.
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-- NB: only tested to 9,007,199,254,740,991, then again I found no more new
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-- bit patterns after just 15^2.</span>
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-- psq eliminates 52 out of 64 of numbers fairly cheaply, which translates
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-- to approximately 66% of numbers, or around 10% off the overall time.
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-- NB: only tested to 9,007,199,254,740,991, then again I found no more new
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-- bit patterns after just 15^2.
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<span style="color: #008080;">constant</span> <span style="color: #000000;">psq</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">int_to_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">#02030213</span><span style="color: #0000FF;">,</span><span style="color: #000000;">32</span><span style="color: #0000FF;">)&</span> <span style="color: #000080;font-style:italic;">-- #0202021202030213 --> bits,</span>
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<span style="color: #7060A8;">int_to_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">#02020212</span><span style="color: #0000FF;">,</span><span style="color: #000000;">32</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- in 32/64-bit compatible way.</span>
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constant psq = int_to_bits(#02030213,32)& -- #0202021202030213 --> bits,
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int_to_bits(#02020212,32) -- in 32/64-bit compatible way.
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<span style="color: #008080;">function</span> <span style="color: #000000;">isSquare</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- determine if n is a perfect square or not</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">psq</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">63</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">return</span> <span style="color: #004600;">false</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function isSquare(atom n) -- determine if n is a perfect square or not
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if psq[and_bits(n,63)+1] then
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atom r = floor(sqrt(n))
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return r * r = n
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end if
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return false
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end function
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">fnpr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">nmr</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">di</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dis</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- generate (n+r) candidates from (n-r) candidates</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dis</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">digits</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nd</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- (the precise why of how this populates digits has eluded me...)</span>
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<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">indices</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;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">candidates</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>
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<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">di</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span>
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<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">a</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</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;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">][</span><span style="color: #000000;">d</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">le</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">di</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</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: #008080;">then</span>
|
||||
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</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: #000000;">digits</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;">di</span><span style="color: #0000FF;">[</span><span style="color: #000000;">le</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">le</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">dx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">le</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">[</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">[</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">10</span>
|
||||
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">di</span><span style="color: #0000FF;">[</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">a</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</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;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">][</span><span style="color: #000000;">d</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">npr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nmr</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">to_atom</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">))*</span><span style="color: #000000;">2</span> <span style="color: #000080;font-style:italic;">-- (npr == 'n + r')</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">isSquare</span><span style="color: #0000FF;">(</span><span style="color: #000000;">npr</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">rares</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">to_atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000080;font-style:italic;">-- (note this gets overwritten by sorted set:)</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;">"working... %2d: %,d\r"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rares</span><span style="color: #0000FF;">),</span><span style="color: #000000;">rares</span><span style="color: #0000FF;">[$]})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #000000;">di</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">di</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">dis</span><span style="color: #0000FF;">[</span><span style="color: #000000;">level</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">di</span><span style="color: #0000FF;">[</span><span style="color: #000000;">level</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
|
||||
<span style="color: #000000;">fnpr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">level</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nmr</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">di</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dis</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</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;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
|
||||
procedure fnpr(integer level, atom nmr, sequence di, dis, candidates, indices, fml, dmd)
|
||||
-- generate (n+r) candidates from (n-r) candidates
|
||||
if level>length(dis) then
|
||||
sequence digits = repeat(0,nd)
|
||||
-- (the precise why of how this populates digits has eluded me...)
|
||||
integer {a,b} = indices[1],
|
||||
c = candidates[1]+1,
|
||||
d = di[1]+1
|
||||
digits[a] = fml[c][d][1]
|
||||
digits[b] = fml[c][d][2]
|
||||
integer le = length(di)
|
||||
if remainder(nd,2) then
|
||||
d = floor(nd/2)+1
|
||||
digits[d] = di[le]
|
||||
le -= 1
|
||||
end if
|
||||
for dx=2 to le do
|
||||
{a,b} = indices[dx]
|
||||
c = candidates[dx]+10
|
||||
d = di[dx]+1
|
||||
digits[a] = dmd[c][d][1]
|
||||
digits[b] = dmd[c][d][2]
|
||||
end for
|
||||
atom npr = nmr + to_atom(reverse(digits))*2 -- (npr == 'n + r')
|
||||
if isSquare(npr) then
|
||||
rares &= to_atom(digits)
|
||||
if platform()!=JS then
|
||||
-- (note this gets overwritten by sorted set:)
|
||||
printf(1,"working... %2d: %,d\r", {count+length(rares),rares[$]})
|
||||
end if
|
||||
end if
|
||||
else
|
||||
di = deep_copy(di)
|
||||
for n=0 to dis[level] do
|
||||
di[level] = n
|
||||
fnpr(level+1, nmr, di, dis, candidates, indices, fml, dmd)
|
||||
end for
|
||||
end if
|
||||
end procedure
|
||||
|
||||
<span style="color: #008080;">procedure</span> <span style="color: #000000;">fnmr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">list</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- generate (n-r) candidates with a given number of digits.</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">list</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">nmr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- (nmr == 'n - r')</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;">terms</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">nmr</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">COEFF</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">nmr</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">isSquare</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nmr</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">candidates</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;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">])-</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">dis</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: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">candidates</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">10</span>
|
||||
<span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dmd</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">])-</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #000000;">dis</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dis</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #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: #008080;">then</span> <span style="color: #000000;">dis</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dis</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000080;font-style:italic;">-- (above generates dis of eg {1,4,7,9} for nd=7, which as far
|
||||
-- as I (lightly) understand it scans for far fewer candidate
|
||||
-- pairs than a {9,9,9,9} would, or something like that.)</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">di</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dis</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #000080;font-style:italic;">-- (di is the current "dis-scan", eg {0,0,0,0} to {1,4,7,9})</span>
|
||||
<span style="color: #000000;">fnpr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nmr</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">di</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dis</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #000000;">candidates</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">candidates</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">n</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;">list</span><span style="color: #0000FF;">[</span><span style="color: #000000;">level</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">candidates</span><span style="color: #0000FF;">[</span><span style="color: #000000;">level</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">list</span><span style="color: #0000FF;">[</span><span style="color: #000000;">level</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">fnmr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">list</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
|
||||
procedure fnmr(sequence terms, list, candidates, indices, fml, dmd, integer level)
|
||||
-- generate (n-r) candidates with a given number of digits.
|
||||
if level>length(list) then
|
||||
atom nmr = 0 -- (nmr == 'n - r')
|
||||
for i=1 to length(terms) do
|
||||
nmr += terms[i][COEFF] * candidates[i]
|
||||
end for
|
||||
if nmr>0 and isSquare(nmr) then
|
||||
integer c = candidates[1]+1,
|
||||
l = length(fml[c])-1
|
||||
sequence dis = {l}
|
||||
for i=2 to length(candidates) do
|
||||
c = candidates[i]+10
|
||||
l = length(dmd[c])-1
|
||||
dis = append(dis,l)
|
||||
end for
|
||||
if remainder(nd,2) then dis = append(dis,9) end if
|
||||
-- (above generates dis of eg {1,4,7,9} for nd=7, which as far
|
||||
-- as I (lightly) understand it scans for far fewer candidate
|
||||
-- pairs than a {9,9,9,9} would, or something like that.)
|
||||
sequence di = repeat(0,length(dis))
|
||||
-- (di is the current "dis-scan", eg {0,0,0,0} to {1,4,7,9})
|
||||
fnpr(1, nmr, di, dis, candidates, indices, fml, dmd)
|
||||
end if
|
||||
else
|
||||
candidates = deep_copy(candidates)
|
||||
for n=1 to length(list[level]) do
|
||||
candidates[level] = list[level][n]
|
||||
fnmr(terms, list, candidates, indices, fml, dmd, level+1)
|
||||
end for
|
||||
end if
|
||||
end procedure
|
||||
|
||||
<span style="color: #008080;">constant</span> <span style="color: #000000;">dl</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> <span style="color: #000080;font-style:italic;">-- all differences (-9..+9 by 1)</span>
|
||||
<span style="color: #000000;">zl</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- zero difference (0 only)</span>
|
||||
<span style="color: #000000;">el</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- even differences (-8 to +8 by 2)</span>
|
||||
<span style="color: #000000;">ol</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> <span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- odd differences (-9..+9 by 2)</span>
|
||||
<span style="color: #000000;">il</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;">0</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- all integers (0..9 by 1)</span>
|
||||
constant dl = tagset(9,-9), -- all differences (-9..+9 by 1)
|
||||
zl = tagset(0, 0), -- zero difference (0 only)
|
||||
el = tagset(8,-8, 2), -- even differences (-8 to +8 by 2)
|
||||
ol = tagset(9,-9, 2), -- odd differences (-9..+9 by 2)
|
||||
il = tagset(9, 0) -- all integers (0..9 by 1)
|
||||
|
||||
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">start</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
|
||||
procedure main()
|
||||
atom start = time()
|
||||
|
||||
<span style="color: #000080;font-style:italic;">-- terms of (n-r) expression for number of digits from 2 to maxdigits</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">allTerms</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">pow</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">maxDigits</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">terms</span> <span style="color: #0000FF;">=</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: #004080;">atom</span> <span style="color: #000000;">p1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pow</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">tdxa</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tdxb</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: #008080;">while</span> <span style="color: #000000;">tdxa</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">tdxb</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">terms</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tdxa</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tdxb</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- {COEFF,TDXA,TDXB}</span>
|
||||
<span style="color: #000000;">p1</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">10</span>
|
||||
<span style="color: #000000;">p2</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</span>
|
||||
<span style="color: #000000;">tdxa</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #000000;">tdxb</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #000000;">allTerms</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">allTerms</span><span style="color: #0000FF;">,</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000080;font-style:italic;">--/*
|
||||
--(This is what the above loop creates:)
|
||||
--pp(allTerms,{pp_Nest,1,pp_StrFmt,3,pp_IntCh,false,pp_IntFmt,"%d",pp_FltFmt,"%d",pp_Maxlen,148})
|
||||
<nowiki>{{</nowiki>{9,0,1<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>99,0,2<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>999,0,3}, {90,1,2<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>9999,0,4}, {990,1,3<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>99999,0,5}, {9990,1,4}, {900,2,3<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>999999,0,6}, {99990,1,5}, {9900,2,4<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>9999999,0,7}, {999990,1,6}, {99900,2,5}, {9000,3,4<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>99999999,0,8}, {9999990,1,7}, {999900,2,6}, {99000,3,5<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>999999999,0,9}, {99999990,1,8}, {9999900,2,7}, {999000,3,6}, {90000,4,5<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>9999999999,0,10}, {999999990,1,9}, {99999900,2,8}, {9999000,3,7}, {990000,4,6<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>99999999999,0,11}, {9999999990,1,10}, {999999900,2,9}, {99999000,3,8}, {9990000,4,7}, {900000,5,6<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>999999999999,0,12}, {99999999990,1,11}, {9999999900,2,10}, {999999000,3,9}, {99990000,4,8}, {9900000,5,7<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>9999999999999,0,13}, {999999999990,1,12}, {99999999900,2,11}, {9999999000,3,10}, {999990000,4,9}, {99900000,5,8}, {9000000,6,7<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>99999999999999,0,14}, {9999999999990,1,13}, {999999999900,2,12}, {99999999000,3,11}, {9999990000,4,10}, {999900000,5,9}, {99000000,6,8<nowiki>}}</nowiki>}
|
||||
--*/
|
||||
-- terms of (n-r) expression for number of digits from 2 to maxdigits
|
||||
sequence allTerms = {}
|
||||
atom pow = 1
|
||||
for r=2 to maxDigits do
|
||||
sequence terms = {}
|
||||
pow *= 10
|
||||
atom p1 = pow, p2 = 1
|
||||
integer tdxa = 0, tdxb = r-1
|
||||
while tdxa < tdxb do
|
||||
terms = append(terms,{p1-p2, tdxa, tdxb}) -- {COEFF,TDXA,TDXB}
|
||||
p1 /= 10
|
||||
p2 *= 10
|
||||
tdxa += 1
|
||||
tdxb -= 1
|
||||
end while
|
||||
allTerms = append(allTerms,terms)
|
||||
end for
|
||||
--/*
|
||||
--(This is what the above loop creates:)
|
||||
--pp(allTerms,{pp_Nest,1,pp_StrFmt,3,pp_IntCh,false,pp_IntFmt,"%d",pp_FltFmt,"%d",pp_Maxlen,148})
|
||||
{{{9,0,1}},
|
||||
{{99,0,2}},
|
||||
{{999,0,3}, {90,1,2}},
|
||||
{{9999,0,4}, {990,1,3}},
|
||||
{{99999,0,5}, {9990,1,4}, {900,2,3}},
|
||||
{{999999,0,6}, {99990,1,5}, {9900,2,4}},
|
||||
{{9999999,0,7}, {999990,1,6}, {99900,2,5}, {9000,3,4}},
|
||||
{{99999999,0,8}, {9999990,1,7}, {999900,2,6}, {99000,3,5}},
|
||||
{{999999999,0,9}, {99999990,1,8}, {9999900,2,7}, {999000,3,6}, {90000,4,5}},
|
||||
{{9999999999,0,10}, {999999990,1,9}, {99999900,2,8}, {9999000,3,7}, {990000,4,6}},
|
||||
{{99999999999,0,11}, {9999999990,1,10}, {999999900,2,9}, {99999000,3,8}, {9990000,4,7}, {900000,5,6}},
|
||||
{{999999999999,0,12}, {99999999990,1,11}, {9999999900,2,10}, {999999000,3,9}, {99990000,4,8}, {9900000,5,7}},
|
||||
{{9999999999999,0,13}, {999999999990,1,12}, {99999999900,2,11}, {9999999000,3,10}, {999990000,4,9}, {99900000,5,8}, {9000000,6,7}},
|
||||
{{99999999999999,0,14}, {9999999999990,1,13}, {999999999900,2,12}, {99999999000,3,11}, {9999990000,4,10}, {999900000,5,9}, {99000000,6,8}}}
|
||||
--*/
|
||||
|
||||
-- map of first minus last digits for 'n' to pairs giving this value</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">fml</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">({},</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (aka 0..9)
|
||||
-- (fml == 'first minus last')</span>
|
||||
<span style="color: #000000;">fml</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: #0000FF;">{{</span><span style="color: #000000;">2</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;">8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">}}</span>
|
||||
<span style="color: #000000;">fml</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: #0000FF;">{{</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">}}</span>
|
||||
<span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">5</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}}</span>
|
||||
<span style="color: #000080;font-style:italic;">-- fml[6] = <nowiki>{{</nowiki>8, 3<nowiki>}}</nowiki> -- (um? - needs longer lists, & that append(lists[4],dl) below)</span>
|
||||
<span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">7</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">}}</span>
|
||||
<span style="color: #000080;font-style:italic;">-- sequence lists = <nowiki>{{</nowiki>{0<nowiki>}}</nowiki>,<nowiki>{{</nowiki>1<nowiki>}}</nowiki>,<nowiki>{{</nowiki>4<nowiki>}}</nowiki>,<nowiki>{{</nowiki>5<nowiki>}}</nowiki>,<nowiki>{{</nowiki>6<nowiki>}}</nowiki>}</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">lists</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}},{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}},{{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">}},{{</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}}}</span>
|
||||
<span style="color: #000080;font-style:italic;">-- map of other digit differences for 'n' to pairs giving this value</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">dmd</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">({},</span><span style="color: #000000;">19</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (aka -9..+9, so add 10 when indexing dmd)
|
||||
-- (dmd == 'digit minus digit')</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">tens</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>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tens</span><span style="color: #0000FF;">+</span><span style="color: #000000;">10</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">ones</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>
|
||||
<span style="color: #000000;">dmd</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: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dmd</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;">tens</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ones</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: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000080;font-style:italic;">--/*
|
||||
--(This is what the above loop creates:)
|
||||
--pp(dmd,{pp_Nest,1,pp_StrFmt,3,pp_IntCh,false})
|
||||
<nowiki>{{</nowiki>{0,9<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>0,8}, {1,9<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>0,7}, {1,8}, {2,9<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>0,6}, {1,7}, {2,8}, {3,9<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>0,5}, {1,6}, {2,7}, {3,8}, {4,9<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>0,4}, {1,5}, {2,6}, {3,7}, {4,8}, {5,9<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>0,3}, {1,4}, {2,5}, {3,6}, {4,7}, {5,8}, {6,9<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>0,2}, {1,3}, {2,4}, {3,5}, {4,6}, {5,7}, {6,8}, {7,9<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>0,0}, {1,1}, {2,2}, {3,3}, {4,4}, {5,5}, {6,6}, {7,7}, {8,8}, {9,9<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>1,0}, {2,1}, {3,2}, {4,3}, {5,4}, {6,5}, {7,6}, {8,7}, {9,8<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>2,0}, {3,1}, {4,2}, {5,3}, {6,4}, {7,5}, {8,6}, {9,7<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>3,0}, {4,1}, {5,2}, {6,3}, {7,4}, {8,5}, {9,6<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>4,0}, {5,1}, {6,2}, {7,3}, {8,4}, {9,5<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>5,0}, {6,1}, {7,2}, {8,3}, {9,4<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>6,0}, {7,1}, {8,2}, {9,3<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>7,0}, {8,1}, {9,2<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>8,0}, {9,1<nowiki>}}</nowiki>,
|
||||
<nowiki>{{</nowiki>9,0<nowiki>}}</nowiki>}
|
||||
--*/</span>
|
||||
<span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</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;">"digits time nth rare numbers:\n"</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: #008080;">while</span> <span style="color: #000000;">nd</span> <span style="color: #0000FF;"><=</span> <span style="color: #000000;">maxDigits</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">rares</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">terms</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">allTerms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nd</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">nd</span><span style="color: #0000FF;">=</span><span style="color: #000000;">4</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">lists</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: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">zl</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">lists</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: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],</span><span style="color: #000000;">ol</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">lists</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: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">],</span><span style="color: #000000;">el</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- lists[4] = append(lists[4],dl) -- if fml[6] = <nowiki>{{</nowiki>8, 3<nowiki>}}</nowiki>
|
||||
-- lists[5] = append(lists[5],ol) -- ""
|
||||
-- lists[4] = append(lists[4],ol) -- else</span>
|
||||
<span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]),</span><span style="color: #000000;">ol</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- else</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">)></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</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;">lists</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000080;font-style:italic;">-- lists[i] = append(lists[i],dl)</span>
|
||||
<span style="color: #000000;">lists</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: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]),</span><span style="color: #000000;">dl</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;">if</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">indices</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">t</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;">terms</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">term</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">t</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000080;font-style:italic;">-- (we may as well make this 1-based while here)</span>
|
||||
<span style="color: #000000;">indices</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">indices</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">term</span><span style="color: #0000FF;">[</span><span style="color: #000000;">TDXA</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">term</span><span style="color: #0000FF;">[</span><span style="color: #000000;">TDXB</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">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;">lists</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">list</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span>
|
||||
<span style="color: #000000;">candidates</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">list</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #000000;">fnmr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">list</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000080;font-style:italic;">-- (re-)output partial results for this nd-set in sorted order:
|
||||
-- rares = sort(rares)</span>
|
||||
<span style="color: #000000;">rares</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rares</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rares</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</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;">"%12s %2d: %,19d \n"</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;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rares</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</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;">" %2d %5s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">nd</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">elapsed_short</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">start</span><span style="color: #0000FF;">)})</span>
|
||||
<span style="color: #000000;">nd</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
|
||||
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
|
||||
<!--
|
||||
-- map of first minus last digits for 'n' to pairs giving this value
|
||||
sequence fml = repeat({},10) -- (aka 0..9)
|
||||
-- (fml == 'first minus last')
|
||||
fml[1] = {{2, 2}, {8, 8}}
|
||||
fml[2] = {{6, 5}, {8, 7}}
|
||||
fml[5] = {{4, 0}}
|
||||
-- fml[6] = {{8, 3}} -- (um? - needs longer lists, & that append(lists[4],dl) below)
|
||||
fml[7] = {{6, 0}, {8, 2}}
|
||||
-- sequence lists = {{{0}},{{1}},{{4}},{{5}},{{6}}}
|
||||
sequence lists = {{{0}},{{1}},{{4}},{{6}}}
|
||||
-- map of other digit differences for 'n' to pairs giving this value
|
||||
sequence dmd = repeat({},19) -- (aka -9..+9, so add 10 when indexing dmd)
|
||||
-- (dmd == 'digit minus digit')
|
||||
for tens=0 to 9 do
|
||||
integer d = tens+10
|
||||
for ones=0 to 9 do
|
||||
dmd[d] = append(dmd[d], {tens,ones})
|
||||
d -= 1
|
||||
end for
|
||||
end for
|
||||
--/*
|
||||
--(This is what the above loop creates:)
|
||||
--pp(dmd,{pp_Nest,1,pp_StrFmt,3,pp_IntCh,false})
|
||||
{{{0,9}},
|
||||
{{0,8}, {1,9}},
|
||||
{{0,7}, {1,8}, {2,9}},
|
||||
{{0,6}, {1,7}, {2,8}, {3,9}},
|
||||
{{0,5}, {1,6}, {2,7}, {3,8}, {4,9}},
|
||||
{{0,4}, {1,5}, {2,6}, {3,7}, {4,8}, {5,9}},
|
||||
{{0,3}, {1,4}, {2,5}, {3,6}, {4,7}, {5,8}, {6,9}},
|
||||
{{0,2}, {1,3}, {2,4}, {3,5}, {4,6}, {5,7}, {6,8}, {7,9}},
|
||||
{{0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}},
|
||||
{{0,0}, {1,1}, {2,2}, {3,3}, {4,4}, {5,5}, {6,6}, {7,7}, {8,8}, {9,9}},
|
||||
{{1,0}, {2,1}, {3,2}, {4,3}, {5,4}, {6,5}, {7,6}, {8,7}, {9,8}},
|
||||
{{2,0}, {3,1}, {4,2}, {5,3}, {6,4}, {7,5}, {8,6}, {9,7}},
|
||||
{{3,0}, {4,1}, {5,2}, {6,3}, {7,4}, {8,5}, {9,6}},
|
||||
{{4,0}, {5,1}, {6,2}, {7,3}, {8,4}, {9,5}},
|
||||
{{5,0}, {6,1}, {7,2}, {8,3}, {9,4}},
|
||||
{{6,0}, {7,1}, {8,2}, {9,3}},
|
||||
{{7,0}, {8,1}, {9,2}},
|
||||
{{8,0}, {9,1}},
|
||||
{{9,0}}}
|
||||
--*/
|
||||
count = 0
|
||||
printf(1,"digits time nth rare numbers:\n")
|
||||
nd = 2
|
||||
while nd <= maxDigits do
|
||||
rares = {}
|
||||
sequence terms = allTerms[nd-1]
|
||||
if nd=4 then
|
||||
lists[1] = append(lists[1],zl)
|
||||
lists[2] = append(lists[2],ol)
|
||||
lists[3] = append(lists[3],el)
|
||||
-- lists[4] = append(lists[4],dl) -- if fml[6] = {{8, 3}}
|
||||
-- lists[5] = append(lists[5],ol) -- ""
|
||||
-- lists[4] = append(lists[4],ol) -- else
|
||||
lists[4] = append(deep_copy(lists[4]),ol) -- else
|
||||
elsif length(terms)>length(lists[1]) then
|
||||
for i=1 to length(lists) do
|
||||
-- lists[i] = append(lists[i],dl)
|
||||
lists[i] = append(deep_copy(lists[i]),dl)
|
||||
end for
|
||||
end if
|
||||
sequence indices = {}
|
||||
for t=1 to length(terms) do
|
||||
sequence term = terms[t]
|
||||
-- (we may as well make this 1-based while here)
|
||||
indices = append(indices,{term[TDXA]+1,term[TDXB]+1})
|
||||
end for
|
||||
for i=1 to length(lists) do
|
||||
sequence list = lists[i],
|
||||
candidates = repeat(0,length(list))
|
||||
fnmr(terms, list, candidates, indices, fml, dmd, 1)
|
||||
end for
|
||||
-- (re-)output partial results for this nd-set in sorted order:
|
||||
-- rares = sort(rares)
|
||||
rares = sort(deep_copy(rares))
|
||||
for i=1 to length(rares) do
|
||||
count += 1
|
||||
printf(1,"%12s %2d: %,19d \n", {"",count,rares[i]})
|
||||
end for
|
||||
printf(1," %2d %5s\n", {nd, elapsed_short(time()-start)})
|
||||
nd += 1
|
||||
end while
|
||||
end procedure
|
||||
main()
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue