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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@ -30,10 +30,10 @@ H2:=H1;
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if (k and 1)<>0 then H2:=H2 div 10;
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{Reverse H2 and add to H1}
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while H2>0 do
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begin
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H1:=H1 * 10 + (H2 mod 10);
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H2:=H2 div 10;
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end;
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begin
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H1:=H1 * 10 + (H2 mod 10);
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H2:=H2 div 10;
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end;
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Result:=H1;
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end;
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@ -47,20 +47,20 @@ begin
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R1:=0;
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{Step through number of digits}
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for Result:=1 to 36 do
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begin
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{Calculate new Range step: 9,9,90,90,90,900,900...}
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if (Result and 1)<>0 then Step:=9 * Trunc(Power(10,Result div 2));
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{Calculate R2}
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R2:=(R1 + Step)-1;
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{See if N falls between R1 and R2}
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if (N>=R1) and (N<=R2) then
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begin
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{Calculate offset and exit}
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Offset:=(N - R1)+1;
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exit;
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end;
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R1:=R2+1;
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end;
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begin
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{Calculate new Range step: 9,9,90,90,90,900,900...}
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if (Result and 1)<>0 then Step:=9 * Trunc(Power(10,Result div 2));
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{Calculate R2}
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R2:=(R1 + Step)-1;
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{See if N falls between R1 and R2}
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if (N>=R1) and (N<=R2) then
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begin
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{Calculate offset and exit}
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Offset:=(N - R1)+1;
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exit;
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end;
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R1:=R2+1;
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end;
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end;
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@ -83,20 +83,20 @@ SetLength(Pals,Count);
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Inx:=0;
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{Handle palindromes up to 18 digits}
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for D:=1 to 18 do
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begin
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{Get maximum count for palindrom of D digits}
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if (D and 1)=1 then Max:=Trunc(Power(10,(D + 1) div 2))
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else Max:=Trunc(Power(10,D div 2));
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{Step through all the numbers half the size of the number of digits}
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for I:=1 to Max-Max div 10 do
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begin
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{Store palindrome}
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Pals[Inx]:=GetNKPalindrome(I,D);
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Inc(Inx);
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{Exit when array is full}
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if Inx>=Count then break;
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end;
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end;
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begin
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{Get maximum count for palindrom of D digits}
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if (D and 1)=1 then Max:=Trunc(Power(10,(D + 1) div 2))
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else Max:=Trunc(Power(10,D div 2));
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{Step through all the numbers half the size of the number of digits}
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for I:=1 to Max-Max div 10 do
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begin
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{Store palindrome}
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Pals[Inx]:=GetNKPalindrome(I,D);
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Inc(Inx);
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{Exit when array is full}
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if Inx>=Count then break;
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end;
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end;
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end;
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@ -139,20 +139,20 @@ Result:='Ending in: '+IntToStr(EndDigit)+CRLF;
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Cnt:=0;
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{Get palindromes and test them}
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for I:=0 to high(Integer) do
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begin
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{Get next palinedrome}
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P:=GetNthPalindrome(I);
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{Is Gapful and has specified EndDigit}
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if IsGapFul(P) and HasEndDigit(P,EndDigit) then
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begin
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Inc(Cnt);
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{Display it}
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Result:=Result+Format('%8d',[P]);
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if (Cnt mod 5)=0 then Result:=Result+CRLF;
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{Break when finished}
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if Cnt>=Max then break;
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end;
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end;
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begin
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{Get next palinedrome}
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P:=GetNthPalindrome(I);
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{Is Gapful and has specified EndDigit}
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if IsGapFul(P) and HasEndDigit(P,EndDigit) then
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begin
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Inc(Cnt);
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{Display it}
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Result:=Result+Format('%8d',[P]);
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if (Cnt mod 5)=0 then Result:=Result+CRLF;
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{Break when finished}
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if Cnt>=Max then break;
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end;
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end;
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end;
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@ -169,24 +169,24 @@ Result:='Ending in: '+IntToStr(EndDigit)+CRLF;
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{Get count number of items}
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Inx:=0;
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for I:=0 to Count-1 do
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begin
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{Keep getting palindromes until}
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{they Gapful and have specified last digit}
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repeat
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begin
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P:=GetNthPalindrome(Inx);
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Inc(Inx);
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end
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until IsGapFul(P) and HasEndDigit(P,EndDigit);
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{Save item}
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IA[I]:=P;
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end;
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begin
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{Keep getting palindromes until}
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{they Gapful and have specified last digit}
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repeat
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begin
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P:=GetNthPalindrome(Inx);
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Inc(Inx);
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end
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until IsGapFul(P) and HasEndDigit(P,EndDigit);
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{Save item}
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IA[I]:=P;
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end;
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{Get last items}
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for I:=Count-Last to Count-1 do
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begin
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Result:=Result+Format('%12d',[IA[I]]);
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if (I mod 5)=4 then Result:=Result+CRLF;
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end;
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begin
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Result:=Result+Format('%12d',[IA[I]]);
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if (I mod 5)=4 then Result:=Result+CRLF;
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end;
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end;
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@ -1,60 +1,62 @@
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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;">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>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
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<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>
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<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>
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<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>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">e</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 reverse_n(atom s)
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atom e = 0
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while s>0 do
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e = e*10 + remainder(s,10)
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s = floor(s/10)
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end while
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return e
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end function
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<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>
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<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>
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constant mx = 1000,
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data = {{1, 20, repeat("%6d",3)&
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repeat("%7d",13)&
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repeat("%8d",4)},
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{86, 100, repeat("%9d",15)},
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{991, 1000, repeat("%11d",10)}}
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<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>
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include builtins\ordinal.e
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<span style="color: #008080;">function</span> <span style="color: #000000;">digit</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">results</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
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<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>
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<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)
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-- (obvs. 64-bit phix is fine with 19 digits, but 32-bit ain't)</span>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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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: #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>
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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;">mx</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">results</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;">for</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;">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>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">if</span> <span style="color: #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>
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<span style="color: #008080;">return</span> <span style="color: #000000;">results</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function digit(sequence results, integer d)
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integer count = 0, pow = 1, fl = d*11
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for nd=3 to 15 do -- (number of digits, usually quits early)
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-- (obvs. 64-bit phix is fine with 19 digits, but 32-bit ain't)
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bool odd = (remainder(nd,2)==1)
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for s=d*pow to (d+1)*pow-1 do -- (eg 300 to 399)
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integer e = reverse_n(s)
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for m=0 to iff(odd?9:0) do -- (1 or 10 iterations)
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atom p = e + iff(odd ? s*pow*100+m*pow*10
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: s*pow*10)
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if remainder(p,fl)==0 then -- gapful!
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count += 1
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results[count][d] = p
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if count==mx then return results end if
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end if
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end for
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end for
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if odd then pow *= 10 end if
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end for
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if count<mx then ?9/0 end if -- oh dear...
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return results
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end function
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
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<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>
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<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>
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<span style="color: #000000;">results</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">digit</span><span style="color: #0000FF;">(</span><span style="color: #000000;">results</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</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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procedure main()
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sequence results = repeat(repeat({},9),mx)
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for d=1 to 9 do -- (the start/end digit)
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results = digit(results,d)
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end for
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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;">data</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
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<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 (> 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: #7060A8;">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: #7060A8;">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>
|
||||
<!--
|
||||
for i=1 to length(data) do
|
||||
{integer s, integer e, sequence fmts} = data[i]
|
||||
printf(1,"%,d%s to %,d%s palindromic gapful numbers (> 100) ending with:\n", {s,ord(s),e,ord(e)})
|
||||
for d=1 to 9 do
|
||||
printf(1,"%d:",d)
|
||||
for j=s to e do
|
||||
printf(1,fmts[j-s+1],results[j][d])
|
||||
end for
|
||||
printf(1,"\n")
|
||||
end for
|
||||
printf(1,"\n")
|
||||
end for
|
||||
end procedure
|
||||
main()
|
||||
|
|
|
|||
|
|
@ -1,188 +1,186 @@
|
|||
(phixonline)-->
|
||||
<span style="color: #000080;font-style:italic;">--
|
||||
-- demo\rosetta\Palindromic_gapful_numbers.exw
|
||||
-- ===========================================
|
||||
--
|
||||
-- Astonishingly this is all done with standard precision numbers, <2^53.
|
||||
-- I will credit [[Self_numbers#AppleScript]] and comment by Nigel Galloway
|
||||
-- on the talk page for ideas that inspired me.
|
||||
--
|
||||
-- A palindrome such as 9459549 can be constructed/broken down into
|
||||
-- 9000009
|
||||
-- 400040
|
||||
-- 50500
|
||||
-- 9000
|
||||
--
|
||||
-- Further, 9459549 rem 99 is the same as
|
||||
-- (the sum of rem 99 on all of those pieces) rem 99
|
||||
--
|
||||
-- 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
|
||||
-- is the same as (4 rem 99[already known])*10 rem 99 [smaller nos].
|
||||
--
|
||||
-- Also, when filling a "hole", such as the final 9, we find
|
||||
-- v
|
||||
-- 9450549 rem 99 = 9
|
||||
-- 9451549 rem 99 = 19,
|
||||
-- 9452549 rem 99 = 29,
|
||||
-- 9453549 rem 99 = 39,
|
||||
-- 9454549 rem 99 = 49,
|
||||
-- 9455549 rem 99 = 59,
|
||||
-- 9456549 rem 99 = 69,
|
||||
-- 9457549 rem 99 = 79,
|
||||
-- 9458549 rem 99 = 89, and
|
||||
-- 9459549 rem 99 = 0,
|
||||
-- ^
|
||||
-- in this case only the '9' fits.
|
||||
--
|
||||
-- But actually we can predict what will fit from the partial sum of
|
||||
-- prior pieces rem 99, ie 9000009..50500, and the same can be said
|
||||
-- when filling the 505-sized hole - what will "fit" depends not on
|
||||
-- what the "outer" actually are, but what their sum rem 99 is, and
|
||||
-- likewise for larger and larger holes.
|
||||
-- If we later find ourselves looking at the same size hole, with
|
||||
-- the same outer rem and the same rem 99 outmost requirement, we
|
||||
-- would know instantly how many things are going to fit.
|
||||
-- True, keeping full lists as the holes got bigger would probably
|
||||
-- consume memory almost as fast as an SR-71, but a single count,
|
||||
-- albeit one keyed on 4 conditions, we can cope. It turns out that
|
||||
-- even by the 10^15th scan, we only hit 17,579 variations anyway.
|
||||
-- As we stumble across larger and larger holes, what we learn can
|
||||
-- be used to skip more and more similar, such that finding the
|
||||
-- ten millionth item is almost as fast as the first millionth, as
|
||||
-- opposed to the times 10 that you'd normally expect.
|
||||
--
|
||||
-- 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,
|
||||
-- but that's ok because many smaller but still quite big holes
|
||||
-- will probably be skipped.
|
||||
--</span>
|
||||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
|
||||
--
|
||||
-- demo\rosetta\Palindromic_gapful_numbers.exw
|
||||
-- ===========================================
|
||||
--
|
||||
-- Astonishingly this is all done with standard precision numbers, <2^53.
|
||||
-- I will credit Self_numbers#AppleScript and comment by Nigel Galloway
|
||||
-- on the talk page for ideas that inspired me.
|
||||
--
|
||||
-- A palindrome such as 9459549 can be constructed/broken down into
|
||||
-- 9000009
|
||||
-- 400040
|
||||
-- 50500
|
||||
-- 9000
|
||||
--
|
||||
-- Further, 9459549 rem 99 is the same as
|
||||
-- (the sum of rem 99 on all of those pieces) rem 99
|
||||
--
|
||||
-- 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
|
||||
-- is the same as (4 rem 99[already known])*10 rem 99 [smaller nos].
|
||||
--
|
||||
-- Also, when filling a "hole", such as the final 9, we find
|
||||
-- v
|
||||
-- 9450549 rem 99 = 9
|
||||
-- 9451549 rem 99 = 19,
|
||||
-- 9452549 rem 99 = 29,
|
||||
-- 9453549 rem 99 = 39,
|
||||
-- 9454549 rem 99 = 49,
|
||||
-- 9455549 rem 99 = 59,
|
||||
-- 9456549 rem 99 = 69,
|
||||
-- 9457549 rem 99 = 79,
|
||||
-- 9458549 rem 99 = 89, and
|
||||
-- 9459549 rem 99 = 0,
|
||||
-- ^
|
||||
-- in this case only the '9' fits.
|
||||
--
|
||||
-- But actually we can predict what will fit from the partial sum of
|
||||
-- prior pieces rem 99, ie 9000009..50500, and the same can be said
|
||||
-- when filling the 505-sized hole - what will "fit" depends not on
|
||||
-- what the "outer" actually are, but what their sum rem 99 is, and
|
||||
-- likewise for larger and larger holes.
|
||||
-- If we later find ourselves looking at the same size hole, with
|
||||
-- the same outer rem and the same rem 99 outmost requirement, we
|
||||
-- would know instantly how many things are going to fit.
|
||||
-- True, keeping full lists as the holes got bigger would probably
|
||||
-- consume memory almost as fast as an SR-71, but a single count,
|
||||
-- albeit one keyed on 4 conditions, we can cope. It turns out that
|
||||
-- even by the 10^15th scan, we only hit 17,579 variations anyway.
|
||||
-- As we stumble across larger and larger holes, what we learn can
|
||||
-- be used to skip more and more similar, such that finding the
|
||||
-- ten millionth item is almost as fast as the first millionth, as
|
||||
-- opposed to the times 10 that you'd normally expect.
|
||||
--
|
||||
-- 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,
|
||||
-- but that's ok because many smaller but still quite big holes
|
||||
-- will probably be skipped.
|
||||
--
|
||||
with javascript_semantics
|
||||
|
||||
<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>
|
||||
<span style="color: #000080;font-style:italic;">-- ie <nowiki>{{</nowiki>{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1<nowiki>}}</nowiki>,
|
||||
-- <nowiki>{{</nowiki>2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2<nowiki>}}</nowiki>,
|
||||
-- <nowiki>{{</nowiki>3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3<nowiki>}}</nowiki>,
|
||||
-- <nowiki>{{</nowiki>4}, {4}, {4}, {4}, {4}, {4}, {4}, {4}, {4<nowiki>}}</nowiki>,
|
||||
-- <nowiki>{{</nowiki>5}, {5}, {5}, {5}, {5}, {5}, {5}, {5}, {5<nowiki>}}</nowiki>,
|
||||
-- <nowiki>{{</nowiki>6}, {6}, {6}, {6}, {6}, {6}, {6}, {6}, {6<nowiki>}}</nowiki>,
|
||||
-- <nowiki>{{</nowiki>7}, {7}, {7}, {7}, {7}, {7}, {7}, {7}, {7<nowiki>}}</nowiki>,
|
||||
-- <nowiki>{{</nowiki>8}, {8}, {8}, {8}, {8}, {8}, {8}, {8}, {8<nowiki>}}</nowiki>,
|
||||
-- <nowiki>{{</nowiki>9}, {9}, {9}, {9}, {9}, {9}, {9}, {9}, {9<nowiki>}}</nowiki>}
|
||||
-- aka 1 rem 11 .. 1 rem 99 are all 1,
|
||||
-- .. 9 rem 11 .. 9 rem 99 are all 9.
|
||||
-- each gets extended with 10 rem 11 .. 10 rem 99,
|
||||
-- 100 rem 11 .. 100 rem 99,
|
||||
-- ... .. 900 rem 99, etc.
|
||||
-- (not really worth trying to take advantage of any cycles
|
||||
-- that might appear in such a relatively small table, as
|
||||
-- it will be at most (on 64-bit) 9 * 9 * 42.)
|
||||
--</span>
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">rmdrn</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>
|
||||
<span style="color: #000080;font-style:italic;">--
|
||||
-- digit is the outer 0..9 (obvs 0 always yields 0),
|
||||
-- gap is zeroes between (-1,0,1,2,.. for eg 1,11,101,1001),
|
||||
-- pow is trailing zeros (0,1,2,.. for eg 101,1010,10100),
|
||||
-- n is 1..9 for 11..99
|
||||
-- eg rmdrn(4,3,2,1) yields remainder(4000400,11), but
|
||||
-- that === remainder(remainder(4000000,11)+
|
||||
-- remainder( 400,11),11), and
|
||||
-- if k = remainder(4*10^(m-1),11) [already known] then
|
||||
-- remainder(4*10^m,11) === remainder(k*10,11), so
|
||||
-- we only need to keep a small table for each [digit][n].
|
||||
-- Thus we avoid maths on 10^42-ish numbers/needing gmp.
|
||||
--</span>
|
||||
<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>
|
||||
<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>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">cdn</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: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdn</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>
|
||||
<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: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- (kill refcount)</span>
|
||||
<span style="color: #000000;">cdn</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdn</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: #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: #000000;">cdn</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<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;">cdn</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;">cdn</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>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
sequence cache = columnize(repeat(columnize({tagset(9)}),9))
|
||||
-- ie {{{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}},
|
||||
-- {{2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}},
|
||||
-- {{3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}},
|
||||
-- {{4}, {4}, {4}, {4}, {4}, {4}, {4}, {4}, {4}},
|
||||
-- {{5}, {5}, {5}, {5}, {5}, {5}, {5}, {5}, {5}},
|
||||
-- {{6}, {6}, {6}, {6}, {6}, {6}, {6}, {6}, {6}},
|
||||
-- {{7}, {7}, {7}, {7}, {7}, {7}, {7}, {7}, {7}},
|
||||
-- {{8}, {8}, {8}, {8}, {8}, {8}, {8}, {8}, {8}},
|
||||
-- {{9}, {9}, {9}, {9}, {9}, {9}, {9}, {9}, {9}}}
|
||||
-- aka 1 rem 11 .. 1 rem 99 are all 1,
|
||||
-- .. 9 rem 11 .. 9 rem 99 are all 9.
|
||||
-- each gets extended with 10 rem 11 .. 10 rem 99,
|
||||
-- 100 rem 11 .. 100 rem 99,
|
||||
-- ... .. 900 rem 99, etc.
|
||||
-- (not really worth trying to take advantage of any cycles
|
||||
-- that might appear in such a relatively small table, as
|
||||
-- it will be at most (on 64-bit) 9 * 9 * 42.)
|
||||
--
|
||||
function rmdrn(integer digit, gap, pow, n)
|
||||
--
|
||||
-- digit is the outer 0..9 (obvs 0 always yields 0),
|
||||
-- gap is zeroes between (-1,0,1,2,.. for eg 1,11,101,1001),
|
||||
-- pow is trailing zeros (0,1,2,.. for eg 101,1010,10100),
|
||||
-- n is 1..9 for 11..99
|
||||
-- eg rmdrn(4,3,2,1) yields remainder(4000400,11), but
|
||||
-- that === remainder(remainder(4000000,11)+
|
||||
-- remainder( 400,11),11), and
|
||||
-- if k = remainder(4*10^(m-1),11) [already known] then
|
||||
-- remainder(4*10^m,11) === remainder(k*10,11), so
|
||||
-- we only need to keep a small table for each [digit][n].
|
||||
-- Thus we avoid maths on 10^42-ish numbers/needing gmp.
|
||||
--
|
||||
if digit=0 then return 0 end if
|
||||
integer nn = n*11, g
|
||||
sequence cdn = cache[digit][n]
|
||||
while length(cdn)<gap+pow+2 do
|
||||
cache[digit][n] = 0 -- (kill refcount)
|
||||
cdn &= remainder(cdn[$]*10,nn)
|
||||
cache[digit][n] = cdn
|
||||
end while
|
||||
g = iff(gap=-1 ? 0 : cdn[gap+pow+2])
|
||||
return remainder(g + cdn[pow+1],nn)
|
||||
end function
|
||||
|
||||
<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>
|
||||
integer skipd = new_dict()
|
||||
|
||||
<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>
|
||||
<span style="color: #000080;font-style:italic;">--
|
||||
-- pals: results (passing it up grants it automatic pass-by-reference status, which may help speedwise)
|
||||
-- lhs: eg "945" of a potential 9459549 result
|
||||
-- palcount, to_skip, count: self explanatory (aka got/ignore/target)
|
||||
-- l: length of inner to be filled in
|
||||
-- r: remainder of outer, eg remainder(9400049,11), built from rmdrn()
|
||||
-- p: left shift (should in fact always equal length(lhs), I think)
|
||||
-- dd: outermost 1..9 (despite the name, it's a single digit)
|
||||
--</span>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<span style="color: #000000;">palcount</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">skip</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #000000;">skip</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
<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>
|
||||
<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;">rmdrn</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>
|
||||
<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>
|
||||
<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>
|
||||
<span style="color: #000000;">palcount</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</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: #000000;">skip</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<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: #7060A8;">deep_copy</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>
|
||||
<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: #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>
|
||||
<span style="color: #000000;">skip</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">skipn</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<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>
|
||||
<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>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<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>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
function palindromicgapfuls(sequence pals, string lhs, atom palcount, to_skip, count, integer l, r, p, dd)
|
||||
--
|
||||
-- pals: results (passing it up grants it automatic pass-by-reference status, which may help speedwise)
|
||||
-- lhs: eg "945" of a potential 9459549 result
|
||||
-- palcount, to_skip, count: self explanatory (aka got/ignore/target)
|
||||
-- l: length of inner to be filled in
|
||||
-- r: remainder of outer, eg remainder(9400049,11), built from rmdrn()
|
||||
-- p: left shift (should in fact always equal length(lhs), I think)
|
||||
-- dd: outermost 1..9 (despite the name, it's a single digit)
|
||||
--
|
||||
sequence key = {l,r,p,dd}
|
||||
integer node = getd_index(key,skipd)
|
||||
atom skip = iff(node==null?count:getd_by_index(node,skipd)), skipn
|
||||
if node!=null and (palcount+skip)<to_skip then
|
||||
palcount += skip
|
||||
else
|
||||
skip = 0
|
||||
for d=0 to 9 do
|
||||
integer r2 = remainder(r+rmdrn(d,l-2,p,dd),dd*11)
|
||||
if l<=2 then
|
||||
if r2=0 then
|
||||
palcount += 1
|
||||
if palcount<=to_skip then
|
||||
skip += 1
|
||||
else
|
||||
pals = append(deep_copy(pals),lhs&repeat(d+'0',l)&reverse(lhs))
|
||||
end if
|
||||
end if
|
||||
else
|
||||
{pals,palcount,skipn} = palindromicgapfuls(pals,lhs&(d+'0'),palcount,to_skip,count,l-2,r2,p+1,dd)
|
||||
skip += skipn
|
||||
end if
|
||||
if palcount==count then exit end if
|
||||
end for
|
||||
if palcount<to_skip then setd(key,skip,skipd) end if
|
||||
end if
|
||||
return {pals,palcount,skip}
|
||||
end function
|
||||
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">pals</span> <span style="color: #0000FF;">=</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: #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>
|
||||
<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>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rmdrn</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>
|
||||
<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>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">pals</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
function collect(integer digit, atom count, keep)
|
||||
atom to_skip = count - keep,
|
||||
palcount = 0, l = 3
|
||||
sequence pals = {}
|
||||
string lhs = ""&(digit+'0') -- ie "1" or "2" .. or "9"
|
||||
while palcount < count do
|
||||
integer r = rmdrn(digit,l-2,0,digit)
|
||||
{pals,palcount} = palindromicgapfuls(pals,lhs,palcount,to_skip,count,l-2,r,1,digit)
|
||||
l += 1
|
||||
end while
|
||||
return pals
|
||||
end function
|
||||
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<span style="color: #000080;font-style:italic;">-- {1_000_000_000_000_000,1,2,4}, -- (matches AppleScript)</span>
|
||||
<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
|
||||
-- (any further and you'd need mpfr just to hold counts)</span>
|
||||
constant tests = {{20,20,1,9},{100,15,1,9},{1000,10,1,9},{10_000,5,1,9},
|
||||
{100_000,1,1,9},{1_000_000,1,1,9},{10_000_000,1,1,9},
|
||||
{100_000_000,1,9,9},{1000_000_000,1,9,9},{10_000_000_000,1,9,9},
|
||||
{100_000_000_000,1,9,9},{1000_000_000_000,1,9,9},
|
||||
{10_000_000_000_000,1,9,9},{100_000_000_000_000,1,9,9},
|
||||
{1_000_000_000_000_000,1,9,9},
|
||||
-- {1_000_000_000_000_000,1,2,4}, -- (matches AppleScript)
|
||||
{10_000_000_000_000_000_000,1,9,9}} -- 64 bit only
|
||||
-- (any further and you'd need mpfr just to hold counts)
|
||||
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<!--
|
||||
atom t0 = time(), count, keep, start, finish
|
||||
for i=1 to length(tests)-(machine_bits()!=64) do
|
||||
{count, keep, start, finish} = tests[i]
|
||||
string r = iff(count==keep?sprintf("First %d",{count}):
|
||||
iff(keep>1?sprintf("Last %d of first %,d",{keep,count})
|
||||
:sprintf("%,dth",{count}))),
|
||||
s = iff(keep=1?"":"s")
|
||||
printf(1,"%s palindromic gapful number%s ending with:\n", {r,s})
|
||||
sequence tags = tagset(finish,start),
|
||||
res = apply(true,collect,{tags,count,keep})
|
||||
string fmt = sprintf("%%%ds",max(apply(join(res,{}),length)))
|
||||
for j=1 to length(res) do
|
||||
printf(1,"%d: %s\n",{tags[j],join(apply(true,sprintf,{{fmt},res[j]})," ")})
|
||||
end for
|
||||
puts(1,"\n")
|
||||
end for
|
||||
printf(1,"Completed in %s\n",elapsed(time()-t0))
|
||||
|
|
|
|||
|
|
@ -1,6 +1,6 @@
|
|||
// 10,True --> 101,111,121,131,141,151,161,171,181,191,202, ..
|
||||
// 10,False --> 1001,1111,1221,1331,1441,1551,1661,1771,1881,..
|
||||
fcn createPalindromeW(start,oddLength){ //--> iterator
|
||||
fcn createPalindromeW(start,oddLength){ //--> iterator
|
||||
[start..].tweak('wrap(z){
|
||||
p,n := z,z;
|
||||
if(oddLength) n/=10;
|
||||
|
|
@ -8,7 +8,7 @@ fcn createPalindromeW(start,oddLength){ //--> iterator
|
|||
p
|
||||
})
|
||||
}
|
||||
fcn palindromicGapfulW(endsWith){ //--> iterator
|
||||
fcn palindromicGapfulW(endsWith){ //--> iterator
|
||||
po,pe := createPalindromeW(10,True), createPalindromeW(10,False);
|
||||
div:=endsWith*10 + endsWith;
|
||||
Walker.zero().tweak('wrap{
|
||||
|
|
|
|||
|
|
@ -5,6 +5,6 @@ fcn palGT(n,N,sz){ palindromicGapfulW(n).drop(N-sz).walk(sz) } // worker thread
|
|||
foreach N,sz in (T( T(100_000,1) )){
|
||||
println("\nLast %d of %,d palindromic gapful numbers:".fmt(sz,N));
|
||||
[1..9].apply('wrap(n){ palGT.future(n,N,sz) }) // create threads
|
||||
.apply("noop") // wait for threads to finish
|
||||
.apply("noop") // wait for threads to finish
|
||||
: pgpp(_);
|
||||
}
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue