Family Day update
This commit is contained in:
Ingy döt Net
parent
aac6731f2c
commit
9ad63ea473
2442 changed files with 39761 additions and 8255 deletions
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@ -1,78 +1,141 @@
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Program HappyNumbers (output);
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// NativeUInt: LongWord 32-Bit-OS/ Uint64 64-Bit-OS
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{$IFDEF FPC}
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{$MODE DELPHI}
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{$OPTIMIZATION ON,Regvar,PEEPHOLE,CSE,ASMCSE}
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{$CODEALIGN proc=32}
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{$OPTIMIZATION ON,All}
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{$ELSE}
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//for Delphi
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{$APPLICATION CONSOLE}
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{$ENDIF}
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//{$DEFINE Use1E9}
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uses
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sysutils,//Timing
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strutils;//Numb2USA
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const
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HighCache = 19*(9*9);//sum sqrdigt of Uint64
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cDigit = 1000;
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base = 10;
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HighCache = 20*(sqr(base-1));//sum of sqr digit of Uint64
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{$IFDEF Use1E9}
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cDigit1 = sqr(base)*sqr(base);//must be power of base
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cDigit2 = Base*sqr(cDigit1);// 1e9
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cMaxPot = 18;
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{$ELSE}
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cDigit1 = base*sqr(base);//must be power of base
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cDigit2 = sqr(cDigit1);// 1e6
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cMaxPot = 14;
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{$ENDIF}
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type
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tCache = array[0..HighCache] of Word;
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tSqrdCache = array[0..cDigit] of Word;
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tSqrdSumCache = array[0..HighCache] of Word;
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tSumSqrDgts = array[0..cDigit2] of word;
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tCache = array[0..2*HighCache] of word;
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tSqrdSumCache = array[0..2*HighCache] of Uint32;
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var
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SumSqrDgts :tSumSqrDgts;
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Cache : tCache;
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SqrdCache :tSqrdCache;
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SqrdSumCache :tSqrdSumCache;
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function find(n: NativeUint;const cache: tCache): boolean;
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var
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i: NativeUint;
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begin
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find := false;
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for i := low(cache) to high(cache) do
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if cache[i] = n then
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find := true;
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writeln(i:10,n:10);
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end;
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SqrdSumCache1,
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SqrdSumCache2 :tSqrdSumCache;
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procedure InitSqrdCache;
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T1,T0 : TDateTime;
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MAX2,Max1 : NativeInt;
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procedure InitSumSqrDgts;
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//calc all sum of squared digits 0..cDigits2
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//using already calculated values
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var
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i,n,sum,r: NativeUint;
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i,j,n,sq,Base1: NativeInt;
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begin
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For i := 0 to cDigit do
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Begin
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sum := 0;
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n := i;
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while n > 0 do
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begin
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r := n;
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n := n div 10;
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r := r-10*n;
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sum := sum + r*r;
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For i := 0 to Base-1 do
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SumSqrDgts[i] := i*i;
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Base1 := Base;
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n := Base;
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repeat
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For i := 1 to base-1 do
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Begin
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sq := SumSqrDgts[i];
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For j := 0 to base1-1 do
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Begin
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SumSqrDgts[n] := sq+SumSqrDgts[j];
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inc(n);
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end;
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end;
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SqrdCache[i] := sum;
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end;
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Base1 := Base1*base;
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until Base1 >= cDigit2;
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SumSqrDgts[n] := 1;
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end;
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function SumSqrdDgt(n: NativeUint): NativeUint;
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function SumSqrdDgt(n: Uint64):NativeUint;inline;
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var
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sum,r: NativeUint;
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r: Uint64;
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begin
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sum := 0;
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while n > cDigit do
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begin
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result := 0;
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while n>cDigit2 do
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Begin
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r := n;
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n := n div cDigit;
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r := r-cDigit*n;
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sum := sum + SqrdCache[r];
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n := n div cDigit2;
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r := r-n*cDigit2;
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inc(result,SumSqrDgts[r]);
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end;
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SumSqrdDgt := sum + SqrdCache[n];
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inc(result,SumSqrDgts[n]);
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end;
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procedure CalcSqrdSumCache1;
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var
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Count : tSqrdSumCache;
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i,sq,result : NativeInt;
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begin
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For i :=High(Count) downto 0 do
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Count[i] := 0;
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//count the manifold
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For i := cDigit1-1 downto 0 do
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inc(count[SumSqrDgts[i]]);
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For i := High(Count) downto 0 do
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if count[i] <> 0 then
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Begin
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Max1 := i;
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BREAK;
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end;
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For sq := 0 to (20-3)*81 do
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Begin
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result := 0;
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For i := Max1 downto 0 do
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inc(result,Count[i]*Cache[sq+i]);
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SqrdSumCache1[sq] := result;
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end;
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end;
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procedure CalcSqrdSumCache2;
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var
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Count : tSqrdSumCache;
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i,sq,result : NativeInt;
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begin
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For i :=High(Count) downto 0 do
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Count[i] := 0;
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For i := cDigit2-1 downto 0 do
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inc(count[SumSqrDgts[i]]);
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For i := High(Count) downto 0 do
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if count[i] <> 0 then
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Begin
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Max2 := i;
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BREAK;
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end;
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For sq := 0 to (20-6)*81 do
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Begin
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result := 0;
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For i := Max2 downto 0 do
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inc(result,Count[i]*Cache[sq+i]);
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SqrdSumCache2[sq] := result;
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end;
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end;
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procedure Inithappy;
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var
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n,s,p : NativeUint;
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Begin
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fillchar(SqrdSumCache,SizeOf(SqrdSumCache),#0);
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InitSqrdCache;
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fillchar(SqrdSumCache1,SizeOf(SqrdSumCache1),#0);
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fillchar(SqrdSumCache2,SizeOf(SqrdSumCache2),#0);
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InitSumSqrDgts;
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fillChar(Cache,SizeOf(Cache),#0);
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Cache[1] := 1;
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For n := 1 to High(Cache) do
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Begin
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@ -100,57 +163,67 @@ Begin
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end;
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end;
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end;
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end;
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function nextCdigits(sqSum: NativeUint):NativeUint;
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var
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i,cnt : LongInt;
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Begin
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cnt:= SqrdSumCache[sqSum];
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If cnt = 0 then
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Begin
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For i := 0 to Cdigit-1 do
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cnt := cnt + Ord(Cache[sqSum+SqrdCache[i]]=1);
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//saving calculation->speed up x100
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SqrdSumCache[sqSum] := cnt;
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end;
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nextCdigits := cnt;
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//mark all unhappy numbers with 0
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For n := 1 to High(Cache) do
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If Cache[n] <> 1 then
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Cache[n] := 0;
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CalcSqrdSumCache1;
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CalcSqrdSumCache2;
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end;
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function is_happy(n: NativeUint): boolean;inline;
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begin
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is_happy := Cache[SumSqrdDgt(n)]=1
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is_happy := Boolean(Cache[SumSqrdDgt(n)])
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end;
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function nthHappy(Limit: NativeUint):NativeUint;
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function nthHappy(Limit: Uint64):Uint64;
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var
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n,
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count : NativeUint;
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d,e,sE: NativeUint;
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begin
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n:= 0;
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count := 0;
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// big steps
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IF limit>cDigit then
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repeat
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inc(count,nextCdigits(SumSqrdDgt(n)));
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inc(n,cDigit);
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until count >= Limit-cDigit;
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// small steps
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repeat
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if is_happy(n) then
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inc(count);
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inc(n);
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until count >= Limit;
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nthHappy:= n-1;
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result := 0;
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d := 0;
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e := 0;
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sE := SumSqrDgts[e];
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//big steps
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while Limit >= cDigit2 do
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begin
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dec(Limit,SqrdSumCache2[SumSqrDgts[d]+sE]);
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inc(result,cDigit2);
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inc(d);
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IF d >=cDigit2 then
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Begin
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inc(e);
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sE := SumSqrdDgt(e);//SumSqrDgts[e];
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d :=0;
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end;
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end;
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//small steps
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while Limit >= cDigit1 do
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Begin
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dec(Limit,SqrdSumCache1[SumSqrdDgt(result)]);
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inc(result,cDigit1);
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end;
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//ONE BY ONE
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while Limit > 0 do
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begin
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dec(Limit,Cache[SumSqrdDgt(result)]);
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inc(result);
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end;
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result -= 1;
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end;
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var
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n, count,Limit: NativeUint;
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n, count :Uint64;
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Limit: NativeUint;
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begin
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write('cDigit1 = ',Numb2USA(IntToStr(cDigit1)));
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writeln(' cDigit2 = ',Numb2USA(IntToStr(cDigit2)));
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T0 := now;
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Inithappy;
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writeln('Init takes ',FormatDateTime(' HH:NN:SS.ZZZ',now-T0));
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n := 1;
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count := 0;
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while count < 8 do
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while count < 10 do
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begin
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if is_happy(n) then
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begin
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@ -161,11 +234,16 @@ begin
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end;
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writeln;
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T0 := now;
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T1 := T0;
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n := 1;
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Limit := 10;// 1En
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Limit := 10;
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repeat
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writeln('10e',n,' nth happy number ',nthHappy(limit):13);
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writeln('1E',n:2,' n.th happy number ',Numb2USA(IntToStr(nthHappy(Limit))):26,
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FormatDateTime(' HH:NN:SS.ZZZ',now-T1));
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T1 := now;
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inc(n);
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Limit := limit*10;
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until n> 8;
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until n> cMaxPot;
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writeln('Total time counting ',FormatDateTime('HH:NN:SS.ZZZ',now-T0));
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end.
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