Data commit
This commit is contained in:
Ingy döt Net
parent
7387c8f97b
commit
cb5bb5e222
199093 changed files with 3378972 additions and 0 deletions
498
Task/Cyclops-numbers/Pascal/cyclops-numbers.pas
Normal file
498
Task/Cyclops-numbers/Pascal/cyclops-numbers.pas
Normal file
|
|
@ -0,0 +1,498 @@
|
|||
program cyclops;
|
||||
{$IFDEF FPC}
|
||||
{$MODE DELPHI}
|
||||
{$OPTIMIZATION ON,ALL}
|
||||
{$CodeAlign proc=32,loop=1}
|
||||
{$ENDIF}
|
||||
//extra https://oeis.org/A136098/b136098.txt take ~37 s( TIO.RUN )
|
||||
uses
|
||||
sysutils;
|
||||
const
|
||||
BIGLIMIT = 10*1000*1000;
|
||||
|
||||
type
|
||||
//number in base 9
|
||||
tnumdgts = array[0..10] of byte;
|
||||
tpnumdgts = pByte;
|
||||
tnum9 = packed record
|
||||
nmdgts : tnumdgts;
|
||||
nmMaxDgtIdx :byte;
|
||||
nmNum : uint32;
|
||||
end;
|
||||
tCN = record
|
||||
cnRight,
|
||||
cnLeft : tNum9;
|
||||
cnNum : Uint64;
|
||||
cndigits,
|
||||
cnIdx : Uint32;
|
||||
end;
|
||||
tCyclopsList = array of Uint64;
|
||||
|
||||
procedure InitCycNum(var cn:tCN);forward;
|
||||
|
||||
var
|
||||
cnMin,cnPow10Shift,cnPow9 : array[0..15] of Uint64;
|
||||
Cyclops :tCyclopsList;
|
||||
|
||||
function IndexToCyclops(n:Uint64):tCN;
|
||||
//zero-based index
|
||||
var
|
||||
dgtCnt,i,num : UInt32;
|
||||
q,p9: Uint64;
|
||||
Begin
|
||||
InitCycNum(result);
|
||||
if n = 0 then
|
||||
EXIT;
|
||||
result.cnIdx := n;
|
||||
dgtCnt := 0;
|
||||
|
||||
repeat
|
||||
p9 := sqr(cnPow9[dgtCnt]);
|
||||
if n < p9 then
|
||||
break;
|
||||
n -= p9;
|
||||
inc(dgtCnt)
|
||||
until dgtcnt>10;
|
||||
dec(dgtCnt);
|
||||
with result do
|
||||
Begin
|
||||
with cnRight do
|
||||
Begin
|
||||
nmMaxDgtIdx := dgtCnt;
|
||||
For i := 0 to dgtCnt do
|
||||
begin
|
||||
q := n DIV 9;
|
||||
nmdgts[i] := n-9*q;
|
||||
n := q;
|
||||
end;
|
||||
num :=0;
|
||||
For i := dgtcnt downto 0 do
|
||||
num := num*10+nmdgts[i]+1;
|
||||
nmNum:= num;
|
||||
cnNum := num;
|
||||
end;
|
||||
|
||||
with cnLeft do
|
||||
Begin
|
||||
nmMaxDgtIdx := dgtCnt;
|
||||
For i := 0 to dgtCnt do
|
||||
begin
|
||||
q := n DIV 9;
|
||||
nmdgts[i] := n-9*q;
|
||||
n := q;
|
||||
end;
|
||||
num :=0;
|
||||
For i := dgtcnt downto 0 do
|
||||
num := num*10+nmdgts[i]+1;
|
||||
nmNum:= num;
|
||||
cnNum += num*cnPow10Shift[dgtCnt];
|
||||
cndigits := dgtCnt;
|
||||
end;
|
||||
end;
|
||||
end;
|
||||
|
||||
procedure Out_Cyclops(const cl:tCyclopsList;colw,colc:NativeInt);
|
||||
var
|
||||
i,n : NativeInt;
|
||||
Begin
|
||||
n := High(cl);
|
||||
If n > 100 then
|
||||
n := 100;
|
||||
For i := 0 to n do
|
||||
begin
|
||||
write(cl[i]:colw);
|
||||
if (i+1) mod colc = 0 then
|
||||
writeln;
|
||||
end;
|
||||
if (i+1) mod colc <> 0 then
|
||||
writeln;
|
||||
if n< High(cl) then
|
||||
writeln(High(cl)+1,' : ',cl[High(cl)]);
|
||||
end;
|
||||
|
||||
procedure InitCnMinPow;
|
||||
//min = (0,1,11,111,1111,11111,111111,1111111,11111111,...);
|
||||
var
|
||||
i,min,pow,pow9 : Uint64;
|
||||
begin
|
||||
min := 0;
|
||||
pow := 100;
|
||||
pow9 := 1;
|
||||
For i :=0 to High(cnMin) do
|
||||
begin
|
||||
cnMin[i] := min;
|
||||
min := 10*min+1;
|
||||
cnPow10Shift[i] := pow;
|
||||
pow *= 10;
|
||||
cnPow9[i] := pow9;
|
||||
pow9 *= 9;
|
||||
end;
|
||||
end;
|
||||
|
||||
procedure ClearNum9(var tn:tNum9;idx:Uint32);
|
||||
begin
|
||||
fillchar(tn,SizeOf(tn),#0);
|
||||
tn.nmNum := cnMin[idx+1];
|
||||
end;
|
||||
|
||||
Procedure InitCycNum(var cn:tCN);
|
||||
Begin
|
||||
with cn do
|
||||
Begin
|
||||
cndigits := 0;
|
||||
ClearNum9(cnLeft,0);
|
||||
ClearNum9(cnRight,0);
|
||||
cnNum := 0;
|
||||
cnIdx := 0;
|
||||
end;
|
||||
end;
|
||||
|
||||
procedure IncNum9(var tn:tNum9);
|
||||
var
|
||||
idx,fac,n: Uint32;
|
||||
begin
|
||||
idx := 0;
|
||||
with tn do
|
||||
Begin
|
||||
fac := 1;
|
||||
n := nmdgts[0]+1;
|
||||
inc(nmNum);
|
||||
repeat
|
||||
if n < 9 then
|
||||
break;
|
||||
inc(nmNum,fac);
|
||||
nmdgts[idx] :=0;
|
||||
inc(idx);
|
||||
fac *= 10;
|
||||
n := nmdgts[idx]+1;
|
||||
until idx > nmMaxDgtIdx;
|
||||
If idx > High(nmdgts) then
|
||||
EXIT;
|
||||
nmdgts[idx] := n;
|
||||
if nmMaxDgtIdx<Idx then
|
||||
nmMaxDgtIdx := Idx;
|
||||
end;
|
||||
end;
|
||||
|
||||
procedure NextCycNum(var cycnum:tCN);
|
||||
begin
|
||||
with cycnum do
|
||||
Begin
|
||||
if cnIdx <> 0 then
|
||||
begin
|
||||
//increment right digits
|
||||
IncNum9(cnRight);
|
||||
if cnRight.nmMaxDgtIdx > cndigits then
|
||||
Begin
|
||||
//set right digits to minimum
|
||||
ClearNum9(cnRight,cndigits);
|
||||
//increment left digits
|
||||
IncNum9(cnLeft);
|
||||
//One more digit ?
|
||||
if cnLeft.nmMaxDgtIdx > cndigits then
|
||||
Begin
|
||||
inc(cndigits);
|
||||
ClearNum9(cnLeft,cndigits);
|
||||
ClearNum9(cnRight,cndigits);
|
||||
if cndigits>High(tnumdgts) then
|
||||
cndigits := High(tnumdgts);
|
||||
end;
|
||||
end;
|
||||
cnNum := cnLeft.nmNum*cnPow10Shift[cndigits]+cnRight.nmNUm;
|
||||
inc(cnIdx);
|
||||
end
|
||||
else
|
||||
Begin
|
||||
cnNum := 101;
|
||||
cnIdx := 1;
|
||||
end;
|
||||
end;
|
||||
end;
|
||||
|
||||
procedure MakePalinCycNum(var cycnum:tCN);
|
||||
//make right to be palin of left
|
||||
var
|
||||
n,dgt : Uint32;
|
||||
i,j:NativeInt;
|
||||
Begin
|
||||
n := 0;
|
||||
with cycnum do
|
||||
Begin
|
||||
i := 0;
|
||||
For j := cnDigits downto 0 do
|
||||
begin
|
||||
dgt := cnLeft.nmdgts[i];
|
||||
cnRight.nmdgts[j] := dgt;
|
||||
n := 10*n+(dgt+1);
|
||||
inc(i);
|
||||
end;
|
||||
cnRight.nmNum := n;
|
||||
cnNum := cnLeft.nmNum*cnPow10Shift[cndigits]+n;
|
||||
end;
|
||||
end;
|
||||
|
||||
procedure IncLeftCn(var cn:tCN);
|
||||
Begin
|
||||
with cn do
|
||||
Begin
|
||||
//set right digits to minimum
|
||||
ClearNum9(cnRight,cndigits);
|
||||
//increment left digits
|
||||
IncNum9(cnLeft);
|
||||
//One more digit ?
|
||||
if cnLeft.nmMaxDgtIdx > cndigits then
|
||||
Begin
|
||||
inc(cndigits);
|
||||
ClearNum9(cnLeft,cndigits);
|
||||
ClearNum9(cnRight,cndigits);
|
||||
if cndigits>High(tnumdgts) then
|
||||
cndigits := High(tnumdgts);
|
||||
end;
|
||||
cnNum := cnLeft.nmNum*cnPow10Shift[cndigits]+cnRight.nmNUm;
|
||||
end;
|
||||
end;
|
||||
|
||||
function isPalinCycNum(const cycnum:tCN):boolean;
|
||||
var
|
||||
i,j:NativeInt;
|
||||
Begin
|
||||
with cycnum do
|
||||
Begin
|
||||
i := cnDigits;
|
||||
j := 0;
|
||||
repeat
|
||||
result := (cnRight.nmdgts[i]=cnLeft.nmdgts[j]);
|
||||
if not(result) then
|
||||
BREAK;
|
||||
dec(i);
|
||||
inc(j);
|
||||
until i<0;
|
||||
end;
|
||||
end;
|
||||
|
||||
function FirstCyclops(cnt:NativeInt):tCN;
|
||||
var
|
||||
i: NativeInt;
|
||||
begin
|
||||
setlength(Cyclops,cnt);
|
||||
i := 0;
|
||||
InitCycNum(result);
|
||||
while i < cnt do
|
||||
begin
|
||||
Cyclops[i] := result.cnNum;
|
||||
inc(i);
|
||||
NextCycNum(result);
|
||||
end;
|
||||
repeat
|
||||
NextCycNum(result);
|
||||
inc(i);
|
||||
until result.cnNum> BIGLIMIT;
|
||||
end;
|
||||
|
||||
function isPrime(n:Uint64):boolean;
|
||||
var
|
||||
p,q : Uint64;
|
||||
Begin
|
||||
{
|
||||
if n< 4 then
|
||||
Begin
|
||||
if n < 2 then
|
||||
EXIT(false);
|
||||
EXIT(true);
|
||||
end;
|
||||
if n = 5 then
|
||||
exit(true);}
|
||||
if (n AND 1 = 0) then
|
||||
EXIT(false);
|
||||
q := n div 3;
|
||||
if n - 3*q = 0 then
|
||||
EXIT(false);
|
||||
p := 5;
|
||||
{$CodeAlign loop=1}
|
||||
repeat
|
||||
q := n div p;
|
||||
if n-q*p = 0 then
|
||||
EXIT(false);
|
||||
p += 2;
|
||||
q := n div p;
|
||||
if n-q*p = 0 then
|
||||
EXIT(false);
|
||||
if q < p then
|
||||
break;
|
||||
p += 4;
|
||||
until false;
|
||||
EXIT(true);
|
||||
end;
|
||||
|
||||
function FirstPrimeCyclops(cnt:NativeInt):tCN;
|
||||
var
|
||||
i: NativeInt;
|
||||
begin
|
||||
i := 0;
|
||||
setlength(Cyclops,cnt);
|
||||
InitCycNum(result);
|
||||
while i<cnt do
|
||||
begin
|
||||
if isPrime(result.cnNum) then
|
||||
Begin
|
||||
Cyclops[i] := result.cnNum;
|
||||
inc(i);
|
||||
end;
|
||||
NextCycNum(result);
|
||||
end;
|
||||
repeat
|
||||
if isPrime(result.cnNum) then
|
||||
begin;
|
||||
inc(i);
|
||||
if result.cnNum > BIGLIMIT then
|
||||
BREAK;
|
||||
end;
|
||||
NextCycNum(result);
|
||||
until false;
|
||||
result.cnIdx := i;
|
||||
end;
|
||||
|
||||
function FirstBlindPrimeCyclops(cnt:NativeInt):tCN;
|
||||
var
|
||||
n: Uint64;
|
||||
i: NativeInt;
|
||||
isPr:Boolean;
|
||||
begin
|
||||
i := 0;
|
||||
setlength(Cyclops,cnt);
|
||||
InitCycNum(result);
|
||||
while i< cnt do
|
||||
begin
|
||||
with result do
|
||||
if isPrime(cnNum) then
|
||||
Begin
|
||||
n:= cnRight.nmNum;
|
||||
if cndigits > 0 then
|
||||
n += cnLeft.nmNum*cnPow10Shift[cndigits-1]
|
||||
else
|
||||
n += cnLeft.nmNum*10;
|
||||
if isPrime(n) then
|
||||
Begin
|
||||
Cyclops[i] := cnNum;
|
||||
inc(i);
|
||||
end;
|
||||
end;
|
||||
NextCycNum(result);
|
||||
end;
|
||||
repeat
|
||||
with result do
|
||||
if isPrime(cnNum) then
|
||||
Begin
|
||||
n:= cnRight.nmNum;
|
||||
if cndigits > 0 then
|
||||
n += cnLeft.nmNum*cnPow10Shift[cndigits-1]
|
||||
else
|
||||
n += cnLeft.nmNum*10;
|
||||
isPr:= isPrime(n);
|
||||
inc(i,Ord(isPr));
|
||||
if isPr AND (cnNum > BIGLIMIT) then
|
||||
BREAK;
|
||||
end;
|
||||
NextCycNum(result);
|
||||
until false;
|
||||
result.cnIdx := i;
|
||||
end;
|
||||
|
||||
function FirstPalinPrimeCyclops(cnt:NativeInt):tCN;
|
||||
var
|
||||
i: NativeInt;
|
||||
begin
|
||||
i := 0;
|
||||
setlength(Cyclops,cnt);
|
||||
InitCycNum(result);
|
||||
while i< cnt do
|
||||
Begin
|
||||
MakePalinCycNum(result);
|
||||
with result do
|
||||
if isPrime(cnNum) then
|
||||
Begin
|
||||
Cyclops[i] := cnNum;
|
||||
inc(i);
|
||||
end;
|
||||
IncLeftCn(result);
|
||||
while Not(result.cnLeft.nmdgts[result.cnDigits]+1 in [1,3,7,9]) do
|
||||
IncLeftCn(result);
|
||||
end;
|
||||
|
||||
repeat
|
||||
MakePalinCycNum(result);
|
||||
with result do
|
||||
if isPrime(cnNum) then
|
||||
begin
|
||||
inc(i);
|
||||
if cnNum >BIGLIMIT then
|
||||
break;
|
||||
end;
|
||||
IncLeftCn(result);
|
||||
while Not(result.cnLeft.nmdgts[result.cnDigits]+1 in [1,3,7,9]) do
|
||||
IncLeftCn(result);
|
||||
until false;
|
||||
result.cnIdx := i;
|
||||
end;
|
||||
|
||||
var
|
||||
cycnum:tCN;
|
||||
T0 : Int64;
|
||||
cnt : NativeUint;
|
||||
begin
|
||||
InitCnMinPow;
|
||||
|
||||
cnt := 50;
|
||||
writeln('The first ',cnt,' cyclops numbers are:');
|
||||
cycnum := FirstCyclops(cnt);
|
||||
Out_Cyclops(Cyclops,5,10);
|
||||
writeln('First such number > ',BIGLIMIT,' is ',cycnum.cnNum,
|
||||
' at zero-based index ',cycnum.cnIdx);
|
||||
writeln;
|
||||
|
||||
cnt := 50;
|
||||
writeln('The first ',cnt,' prime cyclops numbers are:');
|
||||
T0 := GetTickCount64;
|
||||
cycnum := FirstPrimeCyclops(cnt);
|
||||
T0 := GetTickCOunt64-T0;
|
||||
Out_Cyclops(Cyclops,7,10);
|
||||
writeln('First such number > ',BIGLIMIT,' is ',cycnum.cnNum,
|
||||
' at one-based index ',cycnum.cnIdx);
|
||||
writeln(cycnum.cnIdx,'.th = ',cycnum.cnNum,' in ',T0/1000:6:3,' s');
|
||||
writeln;
|
||||
|
||||
cnt := 50;
|
||||
writeln('The first ',cnt,' blind prime cyclops numbers are:');
|
||||
T0 := GetTickCount64;
|
||||
cycnum := FirstBlindPrimeCyclops(cnt);
|
||||
T0 := GetTickCOunt64-T0;
|
||||
Out_Cyclops(Cyclops,7,10);
|
||||
writeln('First such number > ',BIGLIMIT,' is ',cycnum.cnNum,
|
||||
' at one-based index ',cycnum.cnIdx);
|
||||
writeln(cycnum.cnIdx,'.th = ',cycnum.cnNum,' in ',T0/1000:6:3,' s');
|
||||
writeln;
|
||||
|
||||
cnt := 50;
|
||||
writeln('The first ',cnt,' palindromatic prime cyclops numbers are:');
|
||||
cycnum := FirstPalinPrimeCyclops(cnt);
|
||||
Out_Cyclops(Cyclops,15,5);
|
||||
writeln('First such number > ',BIGLIMIT,' is ',cycnum.cnNum,
|
||||
' at one-based index ',cycnum.cnIdx);
|
||||
writeln;
|
||||
|
||||
cnt := 100;
|
||||
repeat
|
||||
write(cnt:17,'.th = ');
|
||||
if cnt <= 10*1000 then
|
||||
Begin
|
||||
InitCycNum(cycnum);
|
||||
repeat
|
||||
NextCycNum(cycnum);
|
||||
until cycnum.cnIdx = cnt;
|
||||
write(cycnum.cnNum);
|
||||
end;
|
||||
cycnum:= IndexToCyclops(cnt);
|
||||
writeln(' calc ',cycnum.cnNum);
|
||||
cnt *= 10;
|
||||
until cnt >1000*1000*1000*1000*1000;
|
||||
end.
|
||||
Loading…
Add table
Add a link
Reference in a new issue