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Ingy döt Net
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199093 changed files with 3378972 additions and 0 deletions
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program NdN;
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//Narcissistic decimal number
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const
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Base = 10;
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MaxDigits = 16;
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type
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tDigit = 0..Base-1;
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tcntDgt= 0..MaxDigits-1;
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var
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powDgt : array[tDigit] of NativeUint;
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PotdgtPos: array[tcntDgt] of NativeUint;
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UpperSum : array[tcntDgt] of NativeUint;
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tmpSum,
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tmpN,
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actPot : NativeUint;
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procedure InitPowDig;
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var
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i,j : NativeUint;
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Begin
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j := 1;
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For i := 0 to High(tDigit) do
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Begin
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powDgt[i] := i;
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PotdgtPos[i] := j;
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j := j*Base;
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end;
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actPot := 0;
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end;
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procedure NextPowDig;
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var
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i,j : NativeUint;
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Begin
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// Next power of digit = i ^ actPot,always 0 = 0 , 1 = 1
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For i := 2 to High(tDigit) do
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powDgt[i] := powDgt[i]*i;
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// number of digits times 9 ^(max number of digits)
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j := powDgt[High(tDigit)];
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For i := 0 to High(UpperSum) do
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UpperSum[i] := (i+1)*j;
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inc(actPot);
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end;
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procedure OutPutNdN(n:NativeUint);
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Begin
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write(n,' ');
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end;
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procedure NextDgtSum(dgtPos,i,sumPowDgt,n:NativeUint);
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begin
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//unable to reach sum
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IF (sumPowDgt+UpperSum[dgtPos]) < n then
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EXIT;
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repeat
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tmpN := n+PotdgtPos[dgtPos]*i;
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tmpSum := sumPowDgt+powDgt[i];
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//unable to get smaller
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if tmpSum > tmpN then
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EXIT;
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IF tmpSum = tmpN then
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OutPutNdN(tmpSum);
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IF dgtPos>0 then
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NextDgtSum(dgtPos-1,0,tmpSum,tmpN);
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inc(i);
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until i >= Base;
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end;
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var
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i : NativeUint;
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Begin
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InitPowDig;
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For i := 1 to 9 do
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Begin
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write(' length ',actPot+1:2,': ');
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//start with 1 in front, else you got i-times 0 in front
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NextDgtSum(actPot,1,0,0);
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writeln;
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NextPowDig;
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end;
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end.
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@ -0,0 +1,202 @@
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program PowerOwnDigits;
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{$IFDEF FPC}
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{$MODE DELPHI}{$OPTIMIZATION ON,ALL}{$COPERATORS ON}
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{$ELSE}{$APPTYPE CONSOLE}{$ENDIF}
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uses
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SysUtils;
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const
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MAXBASE = 10;
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MaxDgtVal = MAXBASE - 1;
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MaxDgtCount = 19;
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type
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tDgtCnt = 0..MaxDgtCount;
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tValues = 0..MaxDgtVal;
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tUsedDigits = array[0..23] of Int8;
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tpUsedDigits = ^tUsedDigits;
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tPower = array[tValues] of Uint64;
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var
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PowerDgt: array[tDgtCnt] of tPower;
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Min10Pot : array[tDgtCnt] of Uint64;
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gblUD : tUsedDigits;
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CombIdx: array of Int8;
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Numbers : array of Uint64;
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rec_cnt : NativeInt;
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procedure OutUD(const UD:tUsedDigits);
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var
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i : integer;
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begin
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For i in tValues do
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write(UD[i]:3);
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writeln;
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For i := 0 to MaxDgtCount do
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write(CombIdx[i]:3);
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writeln;
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end;
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function InitCombIdx(ElemCount: Byte): pbyte;
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begin
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setlength(CombIdx, ElemCount + 1);
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Fillchar(CombIdx[0], sizeOf(CombIdx[0]) * (ElemCount + 1), #0);
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Result := @CombIdx[0];
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Fillchar(gblUD[0], sizeOf(gblUD[0]) * (ElemCount + 1), #0);
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gblUD[0]:= 1;
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end;
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function Init(ElemCount:byte):pByte;
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var
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pP1,Pp2 : pUint64;
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i, j: Int32;
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begin
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Min10Pot[0]:= 0;
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Min10Pot[1]:= 1;
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for i := 2 to High(tDgtCnt) do
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Min10Pot[i]:=Min10Pot[i-1]*MAXBASE;
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pP1 := @PowerDgt[low(tDgtCnt)];
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for i in tValues do
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pP1[i] := 1;
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pP1[0] := 0;
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for j := low(tDgtCnt) + 1 to High(tDgtCnt) do
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Begin
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pP2 := @PowerDgt[j];
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for i in tValues do
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pP2[i] := pP1[i]*i;
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pP1 := pP2;
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end;
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result := InitCombIdx(ElemCount);
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gblUD[0]:= 1;
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end;
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function GetPowerSum(minpot:nativeInt;digits:pbyte;var UD :tUsedDigits):NativeInt;
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var
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pPower : pUint64;
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res,r : Uint64;
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dgt :Int32;
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begin
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r := Min10Pot[minpot];
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dgt := minpot;
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res := 0;
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pPower := @PowerDgt[minpot,0];
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repeat
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dgt -=1;
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res += pPower[digits[dgt]];
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until dgt=0;
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//check if res within bounds of digitCnt
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result := 0;
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if (res<r) or (res>r*MAXBASE) then EXIT;
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//convert res into digits
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repeat
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r := res DIV MAXBASE;
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result+=1;
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UD[res-r*MAXBASE]-= 1;
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res := r;
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until r = 0;
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end;
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procedure calcNum(minPot:Int32;digits:pbyte);
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var
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UD :tUsedDigits;
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res: Uint64;
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i: nativeInt;
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begin
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UD := gblUD;
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If GetPowerSum(minpot,digits,UD) <>0 then
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Begin
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//don't check 0
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i := 1;
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repeat
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If UD[i] <> 0 then
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Break;
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i +=1;
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until i > MaxDgtVal;
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if i > MaxDgtVal then
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begin
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res := 0;
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for i := minpot-1 downto 0 do
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res += PowerDgt[minpot,digits[i]];
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setlength(Numbers, Length(Numbers) + 1);
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Numbers[high(Numbers)] := res;
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end;
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end;
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end;
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function NextCombWithRep(pComb: pByte;pUD :tpUsedDigits;MaxVal, ElemCount: UInt32): boolean;
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var
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i,dgt: NativeInt;
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begin
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i := -1;
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repeat
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i += 1;
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dgt := pComb[i];
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if dgt < MaxVal then
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break;
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dec(pUD^[dgt]);
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until i >= ElemCount;
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Result := i >= ElemCount;
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if i = 0 then
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begin
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dec(pUD^[dgt]);
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dgt +=1;
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pComb[i] := dgt;
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inc(pUD^[dgt]);
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end
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else
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begin
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//decrements digit 0 too.This is false, but not checked.
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dec(pUD^[dgt]);
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dgt +=1;
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pUD^[dgt]:=i+1;
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repeat
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pComb[i] := dgt;
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i -= 1;
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until i < 0;
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end;
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end;
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var
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digits : pByte;
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T0 : Int64;
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tmp: Uint64;
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i, j : Int32;
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begin
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digits := Init(MaxDgtCount);
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T0 := GetTickCount64;
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rec_cnt := 0;
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// i > 0
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For i := 2 to MaxDgtCount do
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Begin
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digits := InitCombIdx(MaxDgtCount);
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repeat
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calcnum(i,digits);
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inc(rec_cnt);
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until NextCombWithRep(digits,@gblUD,MaxDgtVal,i);
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writeln(i:3,' digits with ',Length(Numbers):3,' solutions in ',GetTickCount64-T0:5,' ms');
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end;
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T0 := GetTickCount64-T0;
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writeln(rec_cnt,' recursions');
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//sort
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for i := 0 to High(Numbers) - 1 do
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for j := i + 1 to High(Numbers) do
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if Numbers[j] < Numbers[i] then
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begin
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tmp := Numbers[i];
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Numbers[i] := Numbers[j];
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Numbers[j] := tmp;
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end;
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setlength(Numbers, j + 1);
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for i := 0 to High(Numbers) do
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writeln(i+1:3,Numbers[i]:20);
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setlength(Numbers, 0);
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setlength(CombIdx,0);
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{$IFDEF WINDOWS}
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readln;
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{$ENDIF}
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end.
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