Data commit

Task/M-bius-function/Delphi/m-bius-function.delphi

@@ -0,0 +1,107 @@
+function IsPrime(N: int64): boolean;
+{Fast, optimised prime test}
+var I,Stop: int64;
+begin
+if (N = 2) or (N=3) then Result:=true
+else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
+else
+     begin
+     I:=5;
+     Stop:=Trunc(sqrt(N+0.0));
+     Result:=False;
+     while I<=Stop do
+           begin
+           if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit;
+           Inc(I,6);
+           end;
+     Result:=True;
+     end;
+end;
+
+
+
+function GetNextPrime(var Start: integer): integer;
+{Get the next prime number after Start}
+{Start is passed by "reference," so the
+{original variable is incremented}
+begin
+repeat Inc(Start)
+until IsPrime(Start);
+Result:=Start;
+end;
+
+
+type TIntArray = array of integer;
+
+
+procedure StoreNumber(N: integer; var IA: TIntArray);
+{Expand and store number in array}
+begin
+SetLength(IA,Length(IA)+1);
+IA[High(IA)]:=N;
+end;
+
+
+procedure GetPrimeFactors(N: integer; var Facts: TIntArray);
+{Get all the prime factors of a number}
+var I: integer;
+begin
+I:=2;
+repeat
+	begin
+	if (N mod I) = 0 then
+		begin
+		StoreNumber(I,Facts);
+		N:=N div I;
+		end
+	else GetNextPrime(I);
+	end
+until N=1;
+end;
+
+
+
+function HasDuplicates(IA: TIntArray): boolean;
+{Look for duplicates factors in array}
+var I: integer;
+begin
+Result:=True;
+for I:=0 to Length(IA)-1 do
+ if IA[I]=IA[I+1] then exit;
+Result:=False;
+end;
+
+
+function Moebius(N: integer): integer;
+{Get moebius function of number}
+var I: integer;
+var Factors: TIntArray;
+var Even,Square: boolean;
+begin
+{Collect all prime factors}
+SetLength(Factors,0);
+GetPrimeFactors(N,Factors);
+{Are there an even number of factors?}
+Even:=(Length(Factors) and 1)=0;
+{If there are duplicates, there are perfect squares}
+Square:=HasDuplicates(Factors);
+{Return the Moebius function value}
+if Square then Result:=0
+else if Even then Result:=1
+else Result:=-1;
+end;
+
+procedure TestMoebiusFactors(Memo: TMemo);
+{Test Moebius function for 1..200-1}
+var N,M: integer;
+var S: string;
+begin
+S:='';
+for N:=1 to 199 do
+	begin
+	M:=Moebius(N);
+	S:=S+Format('%3d',[M]);
+	if (N mod 20)=19 then S:=S+#$0D#$0A
+	end;
+Memo.Text:=S;
+end;