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Ingy döt Net
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61
Task/Happy-numbers/Pascal/happy-numbers-1.pas
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61
Task/Happy-numbers/Pascal/happy-numbers-1.pas
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Program HappyNumbers (output);
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uses
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Math;
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function find(n: integer; cache: array of integer): boolean;
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var
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i: integer;
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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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end;
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function is_happy(n: integer): boolean;
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var
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cache: array of integer;
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sum: integer;
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begin
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setlength(cache, 1);
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repeat
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sum := 0;
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while n > 0 do
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begin
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sum := sum + (n mod 10)**2;
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n := n div 10;
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end;
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if sum = 1 then
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begin
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is_happy := true;
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break;
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end;
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if find(sum, cache) then
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begin
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is_happy := false;
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break;
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end;
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n := sum;
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cache[high(cache)]:= sum;
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setlength(cache, length(cache)+1);
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until false;
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end;
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var
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n, count: integer;
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begin
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n := 1;
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count := 0;
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while count < 8 do
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begin
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if is_happy(n) then
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begin
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inc(count);
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write(n, ' ');
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end;
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inc(n);
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end;
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writeln;
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end.
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249
Task/Happy-numbers/Pascal/happy-numbers-2.pas
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249
Task/Happy-numbers/Pascal/happy-numbers-2.pas
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Program HappyNumbers (output);
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{$IFDEF FPC}
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{$MODE DELPHI}
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{$OPTIMIZATION ON,All}
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{$ELSE}
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{$APPLICATION CONSOLE}
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{$ENDIF}
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//{$DEFINE Use1E9}
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uses
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sysutils,//Timing
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strutils;//Numb2USA
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const
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base = 10;
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HighCache = 20*(sqr(base-1));//sum of sqr digit of Uint64
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{$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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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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SqrdSumCache1,
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SqrdSumCache2 :tSqrdSumCache;
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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,j,n,sq,Base1: NativeInt;
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begin
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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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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: Uint64):NativeUint;inline;
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var
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r: Uint64;
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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 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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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(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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If Cache[n] = 0 then
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Begin
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//start a linked list
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Cache[n] := n;
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p := n;
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s := SumSqrdDgt(p);
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while Cache[s] = 0 do
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Begin
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Cache[s] := p;
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p := s;
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s := SumSqrdDgt(p);
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end;
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//mark linked list backwards as happy number
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IF Cache[s] = 1 then
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Begin
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repeat
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s := Cache[p];
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Cache[p] := 1;
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p := s;
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until s = n;
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Cache[n] := 1;
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end;
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end;
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end;
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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 := Boolean(Cache[SumSqrdDgt(n)])
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end;
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function nthHappy(Limit: Uint64):Uint64;
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var
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d,e,sE: NativeUint;
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begin
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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 :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 < 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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inc(count);
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write(n, ' ');
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end;
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inc(n);
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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;
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repeat
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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> 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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