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How can I mark an integer into thousands and hundreds?
Just say I have an integer 12345678910, then I want to change it into a money value like 12.345.678.910.
I try the following code but it is not working.
procedure TForm1.Button1Click(Sender: TObject);
var
j,iPos,i, x, y : integer;
sTemp, original, hasil, data : string;
begin
original := edit1.Text;
sTemp := '';
j := length(edit1.Text);
i := 3;
while i < j do
begin
insert('.',original, (j-i));
edit1.Text := original;
j := length(edit1.Text);
for x := 1 to y do
begin
i := i + ( i + x );
end;
end;
edit2.Text := original;
There is System.SysUtils.Format call in Delphi http://docwiki.embarcadero.com/Libraries/Tokyo/en/System.SysUtils.Format.
This call understand 'm' character as money specific formatter.
Try code like this:
Value := 12345678910;
FormattedStr := Format('Money = %m', [Value])
By default Format will use systemwide format settings, if you have to override default system settings, see official docs:
The conversion is controlled by the CurrencyString, CurrencyFormat,
NegCurrFormat, ThousandSeparator, DecimalSeparator, and
CurrencyDecimals global variables or their equivalent in a
TFormatSettings data structure. If the format string contains a
precision specifier, it overrides the value given by the
CurrencyDecimals global variable or its TFormatSettings equivalent.
This function does what you specify:
function FormatThousandsSeparators(Value: Int64): string;
var
Index: Integer;
begin
Result := IntToStr(Value);
Index := Length(Result) - 3;
while Index > 0 do
begin
Insert('.', Result, Index + 1);
Dec(Index, 3);
end;
end;
Note that your example 12345678910 does not fit into a 32 bit signed integer value which is why I used Int64.
This function does not handle negative values correctly. For instance, it returns '-.999' when passed -999. That can be dealt with like so:
function FormatThousandsSeparators(Value: Int64): string;
var
Index: Integer;
Negative: Boolean;
begin
Negative := Value < 0;
Result := IntToStr(Abs(Value));
Index := Length(Result) - 3;
while Index > 0 do
begin
Insert('.', Result, Index + 1);
Dec(Index, 3);
end;
if Negative then
Result := '-' + Result;
end;
i know now, its so simple. just use
showMessage(formatFloat('#.###.00', strToFloat(original)));
but thanks Remy, you opened my mind.
I was trying to implement the following recursive formula to my code
but to my surprise it turns out that after implementing this to DELPHI, I get an error due to division by zero. I am 98% sure that my knot vector is correctly calculated, which in a way means there shouldn't be any divisions by zero. I am 70% sure that the recursive formula is correctly implemented, for that reason I am posting my code here:
program project1;
uses
SysUtils;
Type
TRealPoint = record
x: single;
y: single;
end;
type
TSample = Class(TObject)
public
KnotVector: array of single;
FitPoints: array of TRealPoint;
Degree: integer;
constructor Create; overload;
function Coefficient(i, p: integer; Knot: single): single;
procedure GetKnots;
destructor Destroy; overload;
end;
constructor TSample.Create;
begin
inherited;
end;
function TSample.Coefficient(i, p: integer; Knot: single): single;
var
s1, s2: single;
begin
If (p = 0) then
begin
If (KnotVector[i] <= Knot) And (Knot < KnotVector[i+1]) then Result := 1.0
else Result := 0.0;
end
else
begin
s1 := (Knot - KnotVector[i])*Coefficient(i, p-1, Knot)/(KnotVector[i+p] - KnotVector[i]); //THIS LINE ERRORS due to division by zero ???
s2 := (KnotVector[i+p+1]-Knot)*Coefficient(i+1,p-1,Knot)/(KnotVector[i+p+1]-KnotVector[i+1]);
Result := s1 + s2;
end;
end;
procedure TSample.GetKnots();
var
KnotValue: single;
i, MaxKnot: integer;
begin
// KNOTS
KnotValue:= 0.0;
SetLength(KnotVector, Length(FitPoints) + 1 + Degree);
MaxKnot:= Length(KnotVector) - (2*Degree + 1);
for i := Low(KnotVector) to High(KnotVector) do
begin
if i <= (Degree) then KnotVector[i] := KnotValue / MaxKnot
else if i > Length(FitPoints) then KnotVector[i] := KnotValue / MaxKnot
else
begin
KnotValue := KnotValue + 1.0;
KnotVector[i] := KnotValue / MaxKnot;
end;
end;
end;
destructor TSample.Destroy;
begin
inherited;
end;
var
i, j: integer;
Test: TSample;
N: array of array of single;
begin
Test := TSample.Create;
//define degree
Test.Degree := 3;
//random fit points
j := 15;
SetLength(Test.FitPoints, j + 1 + Test.Degree);
For i := Low(Test.FitPoints) to High(Test.FitPoints) do
begin
Test.FitPoints[i].x := Random()*2000;
Test.FitPoints[i].y := Random()*2000;
end;
//get knot vector
Test.GetKnots;
//get coefficients
SetLength(N, j+1, j+1);
For j := Low(N) to High(N) do
begin
For i := Low(N[j]) to High(N[j]) do
begin
N[j, i] := Test.Coefficient(i,3,Test.KnotVector[j]);
write(floattostrf(N[j,i], ffFixed, 2, 2) + ', ');
end;
writeln();
end;
readln();
Test.Free;
end.
Basically I'm not sure how to continue. I would need the values of matrix N (see this link) of basis coefficients but somehow using the formula from this link leads me to division by zero.
So... Is there a totally different way how to calculate those coefficients or what is the problem here?
UPDATE
Instead of using my own idea i tried to implement the algorithm from here as suggested by Dsm in the comments. As a result, there is no more divison by zero, but the result is totally unexpected anyways.
For n + 1 = 10 random fit points with spline degree 3 the basis matrix N (see link) is singular - as seen from the attached image.
Instead of that I would expect the matrix to be band matrix. Anyway, here is my updated code:
program project1;
uses
SysUtils;
Type
TRealPoint = record
x: single;
y: single;
end;
type
TMatrix = array of array of double;
type
TSample = Class(TObject)
public
KnotVector: array of double;
FitPoints: array of TRealPoint;
SplineDegree: integer;
Temp: array of double;
A: TMatrix;
procedure GetKnots;
function GetBasis(Parameter: double): boolean;
procedure FormBasisMatrix;
end;
procedure TSample.GetKnots();
var
i, j: integer;
begin
// KNOTS
//https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/INT-APP/PARA-knot-generation.html
SetLength(KnotVector, Length(FitPoints) + SplineDegree + 1);
for i := Low(KnotVector) to High(KnotVector) do
begin
if i <= SplineDegree then KnotVector[i] := 0
else if i <= (High(KnotVector) - SplineDegree - 1) then KnotVector[i] := (i - SplineDegree) / (Length(FitPoints) - SplineDegree)
else KnotVector[i] := 1;
end;
end;
function TSample.GetBasis(Parameter: double): boolean;
var
m, d, k: integer;
FirstTerm, SecondTerm: double;
begin
//http://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve-coef.html
Result := False;
//initialize to 0
SetLength(Temp, Length(FitPoints));
For m := Low(Temp) to High(Temp) do Temp[m] := 0.0;
//special cases
If Abs(Parameter - KnotVector[0]) < 1e-8 then
begin
Temp[0] := 1;
end
else if Abs(Parameter - KnotVector[High(KnotVector)]) < 1e-8 then
begin
Temp[High(Temp)] := 1;
end
else
begin
//find knot span [u_k, u_{k+1})
for k := Low(KnotVector) to High(KnotVector) do if Abs(KnotVector[k] - Parameter) < 1e-8 then break;
Temp[k] := 1.0;
for d := 1 to SplineDegree do
begin
Temp[k - d] := (KnotVector[k + 1] - Parameter) * Temp[k - d + 1] / (KnotVector[k + 1] - KnotVector[k - d + 1]);
for m := k - d + 1 to k - 1 do
begin
FirstTerm := (Parameter - KnotVector[m]) / (KnotVector[m + d] - KnotVector[m]);
SecondTerm := (KnotVector[m + d + 1] - Parameter) / (KnotVector[m + d + 1] - KnotVector[m + 1]);
Temp[m] := FirstTerm * Temp[m] + SecondTerm * Temp[m + 1];
end;
Temp[k] := (Parameter - KnotVector[k]) * Temp[k] / (KnotVector[k + d] - KnotVector[k]);
end;
end;
Result := True;
end;
procedure TSample.FormBasisMatrix;
var
i, j: integer;
begin
SetLength(A, Length(FitPoints), Length(FitPoints));
for j := Low(A) to High(A) do
begin
for i := low(A[j]) to High(A[j]) do //j - row, i - column
begin
If GetBasis(KnotVector[j + SplineDegree]) then A[j, i] := Temp[i];
end;
end;
end;
var
i, j, iFitPoints: integer;
Test: TSample;
N: array of array of single;
begin
Test := TSample.Create;
//define degree
Test.SplineDegree := 3;
//random fit points
iFitPoints := 10;
SetLength(Test.FitPoints, iFitPoints);
For i := Low(Test.FitPoints) to High(Test.FitPoints) do
begin
Test.FitPoints[i].x := Random()*200;
Test.FitPoints[i].y := Random()*200;
end;
//get knot vector
Test.GetKnots;
//get B-Spline basis matrix
Test.FormBasisMatrix;
// print matrix
for j := Low(Test.A) to High(Test.A) do
begin
for i := Low(Test.A) to High(Test.A) do write(FloatToStrF(Test.A[j, i], ffFixed, 2, 2) + ', ');
writeln();
end;
readln();
Test.Free;
end.
This does not appear to be the complete answer, but it may help you on your way, and the result is closer to what you expect, but as I say, not completely there.
First of all the knots do not look right to me. The knots appear to form a 'ramp' function (clamped line), and though I can't work out if 'm' has any specific value, I would expect the function to be continuous, which yours is not. Making it continuous gives better results, e.g.
procedure TSample.GetKnots();
var
i, j: integer;
iL : integer;
begin
// KNOTS
//https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/INT-APP/PARA-knot-generation.html
iL := Length( FitPoints );
SetLength(KnotVector, iL + SplineDegree + 1);
// set outer knot values and sum used to geterate first internal value
for i := 0 to SplineDegree - 1 do
begin
KnotVector[ i ] := 0;
KnotVector[ High(KnotVector)-i] := 1;
end;
// and internal ones
for i := 0 to High(KnotVector) - 2* SplineDegree + 1 do
begin
KnotVector[ SplineDegree + i - 1] := i / (iL - 1);
end;
end;
I introduced iL = Length( Fitpoints ) for convenience - it is not important.
The second issue I spotted is more of a programming one. In the GetBasis routine, you evaluate k by breaking a for loop. The problem with that is that k is not guaranteed to persist outside the loop, so your use of it later is not guaranteed to succeed (although it may)
Finally, in the same place, your range determination is completely wrong in my opinion. You should be looking for parameter to lie in a half open line segment, but instead you are looking for it to lie close to an endpoint of that line.
Putting these two together
for k := Low(KnotVector) to High(KnotVector) do if Abs(KnotVector[k] - Parameter) < 1e-8 then break;
should be replaced by
k1 := 0;
for k1 := High(KnotVector) downto Low(KnotVector) do
begin
if Parameter >= KnotVector[k1] then
begin
k := k1;
break;
end;
end;
where k1 is an integer.
I can't help feeling that there is a plus 1 error somewhere, but I can't spot it.
Anyway, I hope that this helps you get a bit further.
To build recursive pyramid for coefficient calculation at intervals, you have to start top level of recursion (inner loop of calculations) from the first real (not duplicate) knot index:
For i := Test.Degree...
Also check the last loop index.
P.S. You can remove constructor and destructor from class description and implementation if they have nothing but inherited.
I slept over the answer to question Quicksort drama and wanted to recode it from scratch, implementing your tip with the call-by-reference var. And again: I cannot find any failure I made again. I compare the code to your program one by one and I cannot find the problem. The following code produces an Exception (External:SIGSEV at address 11602) during compilation/run
program quicksort;
var
iArray : array[0..8] of integer;
procedure fillArray(var iArray : array of integer);
begin;
iArray[0] := 3;
iArray[1] := 1;
iArray[2] := 8;
iArray[3] := 4;
iArray[4] := 9;
iArray[5] := 0;
iArray[6] := 8;
iArray[7] := 2;
iArray[8] := 5;
end;
procedure writeArray(iArray : array of integer);
var i:integer;
begin
for i:=low(iArray) to high(iArray) do begin
write(iArray[i]);
end;
writeln('');
end;
procedure quickSort(var iArray : array of integer; links : integer; rechts:integer);
var
l,r,pivot, temp: integer;
begin
if (rechts > links) then begin
l := links;
r := rechts;
pivot := iArray[(rechts+links) div 2];
while (l<r) do begin
while (iArray[l] < pivot) do l:=l+1;
while (iArray[r] > pivot) do r:=r-1;
if (l<=r) then begin
temp := iArray[l];
iArray[l] := iArray[r];
iArray[r] := temp;
end;
end;
if (links < r) then quickSort(iArray, links, r);
if (l < rechts) then quickSort(iArray, l, rechts);
end;
end;
begin
fillArray(iArray);
quickSort(iArray,low(iArray),high(iArray));
writeArray(iArray);
end.
The block of code that swaps, also needs to increment l and decrement r once the swap is complete:
if (l <= r) then
begin
temp := iArray[l];
iArray[l] := iArray[r];
iArray[r] := temp;
inc(l); // <-- this was missing
dec(r); // <-- as was this
end;
The complete program, with some other minor tidy ups:
program quicksort24340509;
var
iArray: array [0 .. 8] of integer;
Procedure fillArray(var iArray: array of integer);
begin;
iArray[0] := 3;
iArray[1] := 1;
iArray[2] := 8;
iArray[3] := 4;
iArray[4] := 9;
iArray[5] := 0;
iArray[6] := 8;
iArray[7] := 2;
iArray[8] := 5;
end;
Procedure writeArray(const iArray: array of integer);
var
i: integer;
begin
for i := low(iArray) to high(iArray) do
begin
write(iArray[i], ' ');
end;
writeln;
end;
Procedure quickSort(var iArray: array of integer; links, rechts: integer);
var
l, r, pivot, temp: integer;
begin
if (rechts > links) then
begin
l := links;
r := rechts;
pivot := iArray[(rechts + links) div 2];
while l < r do
begin
while iArray[l] < pivot do inc(l);
while iArray[r] > pivot do dec(r);
if l <= r then
begin
temp := iArray[l];
iArray[l] := iArray[r];
iArray[r] := temp;
inc(l);
dec(r);
end;
end;
if links < r then
quickSort(iArray, links, r);
if l < rechts then
quickSort(iArray, l, rechts);
end;
end;
begin
fillArray(iArray);
quickSort(iArray, low(iArray), high(iArray));
writeArray(iArray);
readln;
end.
Output
0 1 2 3 4 5 8 8 9
The reason that your version fails, without the missing lines, is that the recursive calls to quickSort operate on the wrong ranges.
For example, Given your input of
3 1 8 4 9 0 8 2 5
the partitioning step pivots on 9 and results in
3 1 8 4 5 0 8 2 9
Now, the recursive step should be to sort all the values to the left of the pivot, and all the values to the right. And we leave the pivot alone because partitioning ensured that it is in its final position.
There are no values to the right of the pivot so we should be making a recursive call for the range 0 to 7. But if you inspect what happens with your code you will find that it does not. Instead it makes a recursive call for the range 0 to 8. That in itself is a little benign, but once the ranges become small, at the stopping condition, it's different. Try asking your program to sort these values:
1 2
The code pivots on 1. At the end of partitioning we have:
links = 0
rechts = 1
l = 0
r = 0
So we recursively call quickSort passing l and rechts as the ranges. But that's exactly the same call as we initially made. And that therefore leads to a stack overflow.
So the point is that we must make sure that when we partition on a pivot, we exclude that pivot from all future recursive calls to quickSort. If we don't do that we don't sub-divide the problem, and the recursion does not terminate.
I have a very simple class definition for 3D Vectors, TVector3D, and a few methods used to implement the TVector3D.Normalise function. If I pass the Normalise function a vector that is already normalised, I want it to return the vector I passed it. Here I have used Result := Self but I am having some crazy returns.
The console application:
program Project1;
{$APPTYPE CONSOLE}
{$R *.res}
uses
System.SysUtils;
type
TVector3D = Class
public
x : Single;
y : Single;
z : Single;
constructor Create(x : Single;
y : Single;
z : Single);
function GetMagnitude() : Single;
function IsUnitVector() : Boolean;
function Normalise() : TVector3D;
end;
constructor TVector3D.Create(x : Single;
y : Single;
z : Single);
begin
Self.x := x;
Self.y := y;
Self.z := z;
end;
function TVector3D.GetMagnitude;
begin
Result := Sqrt(Sqr(Self.x) + Sqr(Self.y) + Sqr(Self.z));
end;
function TVector3D.IsUnitVector;
begin
if Self.GetMagnitude = 1 then
Result := True
else
Result := False;
end;
function TVector3D.Normalise;
var
x : Single;
y : Single;
z : Single;
MagnitudeFactor : Single;
begin
if IsUnitVector then
Result := Self
else
MagnitudeFactor := 1/(Self.GetMagnitude);
x := Self.x*MagnitudeFactor;
y := Self.y*MagnitudeFactor;
z := Self.z*MagnitudeFactor;
Result := TVector3D.Create(x,
y,
z);
end;
procedure TestNormalise;
var
nonUnitVector : TVector3D;
unitVector : TVector3D;
nUVNormed : TVector3D;
uVNormed : TVector3D;
begin
//Setup Vectors for Test
nonUnitVector := TVector3D.Create(1,
1,
1);
unitVector := TVector3D.Create(1,
0,
0);
//Normalise Vectors & Free Memory
nUVNormed := nonUnitVector.Normalise;
nonUnitVector.Free;
uVNormed := unitVector.Normalise;
unitVector.Free;
//Print Output & Free Memory
WriteLn('nUVNormed = (' + FloatToStr(nUVNormed.x) + ', ' + FloatToStr(nUVNormed.y) + ', ' + FloatToStr(nUVNormed.z) + ')');
nUVNormed.Free;
WriteLn('uVNormed = (' + FloatToStr(uVNormed.x) + ', ' + FloatToStr(uVNormed.y) + ', ' + FloatToStr(uVNormed.z) + ')');
uVNormed.Free;
end;
begin
try
TestNormalise;
Sleep(10000);
except
on E: Exception do
Writeln(E.ClassName, ': ', E.Message);
end;
end.
Normalise works fine for non-unit vecors, i.e. IsUnitVector returns false. But for unit vectors, such as (1,0,0), instead of returning itself I get a result with very low nonzero numbers wherever there was a nonzero previously, such as (8.47122...E-38,0,0).
If I run this through the debugger with a breakpoint on the line Result := Self set to evaluate Self, Self is (1,0,0) yet result becomes (Very Low Number,0,0). Where Very Low Number changes each time I run the programme but always seems to be around E-38/E-39.
I do not understand why this happens. Why does it happen and how is it best to alter my Normalise function to avoid it.
Your current TVector3D.Normalise implementation has some issues:
The last 4 lines are always executed, because you have not used a begin-end block after the else,
So the routine never returns Self, but always a new instance,
The returned instance's memory is propably leaked because you lost ownership of it after the function call,
When IsUnitVector returns True, then the assignment of MagnitudeFactor will be skipped, and it will be a random value (currently present at that memory's address), which explains why you get rubish. You are also warned by the compiler for this: Variable MagnitudeFactor might not have been initialized.
Instead, I would rewrite the routine as follows:
function TVector3D.Normalise: TVector3D;
begin
if not IsUnitVector then
begin
x := x / GetMagnitude;
y := y / GetMagnitude;
z := z / GetMagnitude;
end;
Result := Self;
end;
The root of all your problems is that you are using a class, which is a reference type. Instead you need to make your vector be a value type. That means use a record.
In your code, even when you fix the problem identified by #NGLN, you have still destroyed all instances of your class by the time you start calling WriteLn.
Unless you grasp this issue soon, I fear that you will continue having problems. Switching to using a value type will make your coding trivially easy in comparison to your current approach.
Here's something to get you started:
type
TVector3 = record
public
class operator Negative(const V: TVector3): TVector3;
class operator Equal(const V1, V2: TVector3): Boolean;
class operator NotEqual(const V1, V2: TVector3): Boolean;
class operator Add(const V1, V2: TVector3): TVector3;
class operator Subtract(const V1, V2: TVector3): TVector3;
class operator Multiply(const V: TVector3; const D: Double): TVector3;
class operator Multiply(const D: Double; const V: TVector3): TVector3;
class operator Divide(const V: TVector3; const D: Double): TVector3;
class function New(const X, Y, Z: Double): TVector3; static;
function IsZero: Boolean;
function IsNonZero: Boolean;
function IsUnit: Boolean;
function Mag: Double;
function SqrMag: Double;
function Normalised: TVector3;
function ToString: string;
public
X, Y, Z: Double;
end;
const
ZeroVector3: TVector3=();
class operator TVector3.Negative(const V: TVector3): TVector3;
begin
Result.X := -V.X;
Result.Y := -V.Y;
Result.Z := -V.Z;
end;
class operator TVector3.Equal(const V1, V2: TVector3): Boolean;
begin
Result := (V1.X=V2.X) and (V1.Y=V2.Y) and (V1.Z=V2.Z);
end;
class operator TVector3.NotEqual(const V1, V2: TVector3): Boolean;
begin
Result := not (V1=V2);
end;
class operator TVector3.Add(const V1, V2: TVector3): TVector3;
begin
Result.X := V1.X + V2.X;
Result.Y := V1.Y + V2.Y;
Result.Z := V1.Z + V2.Z;
end;
class operator TVector3.Subtract(const V1, V2: TVector3): TVector3;
begin
Result.X := V1.X - V2.X;
Result.Y := V1.Y - V2.Y;
Result.Z := V1.Z - V2.Z;
end;
class operator TVector3.Multiply(const V: TVector3; const D: Double): TVector3;
begin
Result.X := D*V.X;
Result.Y := D*V.Y;
Result.Z := D*V.Z;
end;
class operator TVector3.Multiply(const D: Double; const V: TVector3): TVector3;
begin
Result.X := D*V.X;
Result.Y := D*V.Y;
Result.Z := D*V.Z;
end;
class operator TVector3.Divide(const V: TVector3; const D: Double): TVector3;
begin
Result := (1.0/D)*V;
end;
class function TVector3.New(const X, Y, Z: Double): TVector3;
begin
Result.X := X;
Result.Y := Y;
Result.Z := Z;
end;
function TVector3.IsZero: Boolean;
begin
Result := Self=ZeroVector3;
end;
function TVector3.IsNonZero: Boolean;
begin
Result := Self<>ZeroVector3;
end;
function TVector3.IsUnit: Boolean;
begin
Result := abs(1.0-Mag)<1.0e-5;
end;
function TVector3.Mag: Double;
begin
Result := Sqrt(X*X + Y*Y + Z*Z);
end;
function TVector3.SqrMag: Double;
begin
Result := X*X + Y*Y + Z*Z;
end;
function TVector3.Normalised;
begin
Result := Self/Mag;
end;
function TVector3.ToString: string;
begin
Result := Format('(%g, %g, %g)', [X, Y, Z]);
end;
This is extracted from my own codebase. I'm using Double, but if you really prefer to use Single, then you can readily change it.
The use of operator overloading makes the code you write so much more readable. Now you can write V3 := V1 + V2 and so on.
Here's what your test code looks like with this record:
var
nonUnitVector: TVector3;
unitVector: TVector3;
nUVNormed: TVector3;
uVNormed: TVector3;
begin
//Setup Vectors for Test
nonUnitVector := TVector3.New(1, 1, 1);
unitVector := TVector3.New(1, 0, 0);
//Normalise Vectors
nUVNormed := nonUnitVector.Normalised;
uVNormed := unitVector.Normalised;
//Print Output
WriteLn('nUVNormed = ' + nUVNormed.ToString);
WriteLn('uVNormed = ' + uVNormed.ToString);
Readln;
end.
Or if you want to compress it somewhat:
WriteLn('nUVNormed = ' + TVector3.New(1, 1, 1).Normalised.ToString);
WriteLn('uVNormed = ' + TVector3.New(1, 0, 0).Normalised.ToString);
A few hints:
First, I'd actually make the vector a record instead of a class if I were you, but YMMV. That would simplify a lot, since the compiler will manage the lifetime of every vector (you never need to worry about freeing things). Second,
function TVector3D.IsUnitVector;
begin
if self.GetMagnitude = 1 then
result := True
else
result := False;
end;
is normally written, syntactically and exactly equivalently,
function TVector3D.IsUnitVector;
begin
result := GetMagnitude = 1
end;
But even so, it is incorrect. Since you are dealing with floating-point numbers, you cannot reliably test equality. Instead, you should see if the magnitude is within some interval of unity, so that 'fuzz' do not interfere. For instance, you could do (uses Math)
function TVector3D.IsUnitVector;
begin
result := IsZero(GetMagnitude - 1)
end;
Third, your Normalize function returns a new vector object if it needs to normalize, and returns the same object if not. That's very confusing. You'd never know how many instances you have! Instead, make this a procedure:
procedure TVector3D.Normalize;
var
norm: single;
begin
norm := GetMagnitude;
x := x / norm;
y := y / norm;
z := z / norm;
end;
Fourth, why use single instead of double or real?
Fifth, as NGLN pointed out (please upvote his answer!), you forgot the begin...end block in the else part of your Normalize function, so the four last lines are always executed! Hence, you always create a new vector instance! Still, my point is very important: your original function 'intends' (if you just add the begin...end block) to return self or create a new instance depending on a condition, which is rather terrible, since then you do not know how many instances you have! (And so, you'll probably begin to leak vectors...)
I need input sequence of Integer number and find the longest arithmetic and geometric progression sequence. I had wrote this code( I must use Delphi 7)
program arithmeticAndGeometricProgression;
{ 203. In specifeied sequence of integer numbers find the longest sequence, which is
arithmetic or geometric progression. }
{$APPTYPE CONSOLE}
uses
SysUtils;
var
sequence, longArithmSequ, longGeomSequ: Array of Integer;
curArithmSequ, curGeomSequ: Array of Integer; // Current progress
q, q1: Double;
d1, d: Double;
i, k: Integer;
begin
i := 0;
d := 0;
k := 0;
d1 := 0;
Repeat
SetLength(sequence, i + 1);
// Make room for another item in the array
try
read(sequence[i]);
except // If the input character is not an integer interrupt cycle
Break;
end;
inc(i);
Until False;
k := 0;
curArithmSequ := NIL;
curGeomSequ := NIL;
longArithmSequ := NIL;
longGeomSequ := NIL;
d1 := sequence[1] - sequence[0];
q1 := sequence[1] / sequence[0];
i := 1;
repeat
d := d1;
q := q1;
d1 := sequence[i] - sequence[i - 1];
q1 := sequence[i] / sequence[i - 1];
if d = d1 then
begin
SetLength(curArithmSequ, Length(curArithmSequ) + 1);
curArithmSequ[Length(curArithmSequ) - 1] := sequence[i];
end;
if q = q1 then
begin
SetLength(curGeomSequ, Length(curGeomSequ) + 1);
curGeomSequ[Length(curGeomSequ) - 1] := sequence[i];
end;
if Length(curArithmSequ) > Length(longArithmSequ) then
begin
longArithmSequ := NIL;
SetLength(longArithmSequ, Length(curArithmSequ));
for k := 0 to Length(curArithmSequ) - 1 do
longArithmSequ[k] := curArithmSequ[k];
end;
if Length(curGeomSequ) > Length(longGeomSequ) then
begin
longGeomSequ := NIL;
SetLength(longGeomSequ, Length(curGeomSequ));
for k := 0 to Length(curGeomSequ) - 1 do
longGeomSequ[k] := curGeomSequ[k];
end;
if d <> d1 then
curArithmSequ := NIL;
if q <> q1 then
curGeomSequ := NIL;
inc(i);
Until i >= Length(sequence) - 1;
writeLn('The Longest Arithmetic Progression');
for k := 0 to Length(longArithmSequ) - 1 do
Write(longArithmSequ[k], ' ');
writeLn('The Longest Geometric Progression');
for k := 0 to Length(longGeomSequ) - 1 do
Write(longGeomSequ[k], ' ');
Readln(k);
end.
I have such question:
Why it can't print first 1-2 members of arithmetic progression
Why it always print '2' as geometric progression
Is there monkey-style code in my programm?
Please mention to me where are my mistakes.
Updated:
You need to change the logic inside the repeat loop in this way:
if d = d1 then
begin
if (Length(curArithmSequ) = 0) then
begin
if (i > 1) then
SetLength(curArithmSequ,3)
else
SetLength(curArithmSequ,2);
end
else
SetLength(curArithmSequ,Length(curArithmSequ)+1);
for k := 0 to Length(curArithmSequ) - 1 do
curArithmSequ[k] := sequence[i - (Length(curArithmSequ) - k - 1)];
end
else
SetLength(curArithmSequ,0);
if q = q1 then
begin
if (Length(curGeomSequ) = 0) then
begin
if (i > 1) then
SetLength(curGeomSequ,3)
else
SetLength(curGeomSequ,2);
end
else
SetLength(curGeomSequ,Length(curGeomSequ)+1);
for k := 0 to Length(curGeomSequ) - 1 do
curGeomSequ[k] := sequence[i - (Length(curGeomSequ) - k - 1)];
end
else
SetLength(curGeomSequ,0);
An input sequence of:
2,6,18,54 gives LAP=2,6 and LGP=2,6,18,54
while an input sequence of:
1,3,5,7,9 gives: LAP=1,3,5,7,9 and LGP=1,3
And a sequence of
5,4,78,2,3,4,5,6,18,54,16 gives LAP=2,3,4,5,6 and LGP=6,18,54
Here is my complete test (see comments below):
program arithmeticAndGeometricProgression;
{ 203. In specified sequence of integer numbers find the longest sequence, which is
arithmetic or geometric progression. }
{$APPTYPE CONSOLE}
uses
SysUtils;
Type
TIntArr = array of integer;
TValidationProc = function( const sequence : array of integer) : Boolean;
function IsValidArithmeticSequence( const sequence : array of integer) : Boolean;
begin
Result :=
(Length(sequence) = 2) // Always true for a sequence of 2 values
or
// An arithmetic sequence is defined by: a,a+n,a+2*n, ...
// This gives: a+n - a = a+2*n - (a+n)
// s[1] - s[0] = s[2] - s[1] <=> 2*s[1] = s[2] + s[0]
(2*sequence[1] = (Sequence[2] + sequence[0]));
end;
function IsValidGeometricSequence( const sequence : array of integer) : Boolean;
var
i,zeroCnt : Integer;
begin
// If a zero exists in a sequence all members must be zero
zeroCnt := 0;
for i := 0 to High(sequence) do
if (sequence[i] = 0) then
Inc(zeroCnt);
if (Length(sequence) = 2) then
Result := (zeroCnt in [0,2])
else
// A geometric sequence is defined by: a*r^0,a*r^1,a*r^2 + ... ; r <> 0
// By comparing sequence[i]*sequence[i-2] with Sqr(sequence[i-1])
// i.e. a*(a*r^2) with Sqr(a*r) we can establish a valid geometric sequence
Result := (zeroCnt in [0,3]) and (Sqr(sequence[1]) = sequence[0]*Sequence[2]);
end;
procedure AddSequence( var arr : TIntArr; sequence : array of Integer);
var
i,len : Integer;
begin
len := Length(arr);
SetLength(arr,len + Length(sequence));
for i := 0 to High(sequence) do
arr[len+i] := sequence[i];
end;
function GetLongestSequence( IsValidSequence : TValidationProc;
const inputArr : array of integer) : TIntArr;
var
i : Integer;
currentSequence : TIntArr;
begin
SetLength(Result,0);
SetLength(currentSequence,0);
if (Length(inputArr) <= 1)
then Exit;
for i := 1 to Length(inputArr)-1 do begin
if (Length(Result) = 0) then // no valid sequence found so far
begin
if IsValidSequence([inputArr[i-1],inputArr[i]])
then AddSequence(currentSequence,[inputArr[i-1],inputArr[i]]);
end
else
begin
if IsValidSequence([inputArr[i-2],inputArr[i-1],inputArr[i]]) then
begin
if (Length(currentSequence) = 0) then
AddSequence(currentSequence,[inputArr[i-2],inputArr[i-1],inputArr[i]])
else
AddSequence(currentSequence,inputArr[i]);
end
else // Reset currentSequence
SetLength(currentSequence,0);
end;
// Longer sequence ?
if (Length(currentSequence) > Length(Result)) then
begin
SetLength(Result,0);
AddSequence(Result,currentSequence);
end;
end;
end;
procedure OutputSequence( const arr : TIntArr);
var
i : Integer;
begin
for i := 0 to High(arr) do begin
if i <> High(arr)
then Write(arr[i],',')
else WriteLn(arr[i]);
end;
end;
begin
WriteLn('Longest Arithmetic Sequence:');
OutputSequence(GetLongestSequence(IsValidArithmeticSequence,[0,1,2,3,4,5,6]));
OutputSequence(GetLongestSequence(IsValidArithmeticSequence,[1,0,1,2,3,4,5,6]));
OutputSequence(GetLongestSequence(IsValidArithmeticSequence,[0,0,0,0,0,0]));
OutputSequence(GetLongestSequence(IsValidArithmeticSequence,[0,0,1,2,4,8,16]));
OutputSequence(GetLongestSequence(IsValidArithmeticSequence,[0,0,6,9,12,4,8,16]));
OutputSequence(GetLongestSequence(IsValidArithmeticSequence,[9,12,16]));
OutputSequence(GetLongestSequence(IsValidArithmeticSequence,[1,0,1,-1,-3]));
OutputSequence(GetLongestSequence(IsValidArithmeticSequence,[5,4,78,2,3,4,5,6,18,54,16]));
WriteLn('Longest Geometric Sequence:');
OutputSequence(GetLongestSequence(IsValidGeometricSequence,[0,1,2,3,4,5,6]));
OutputSequence(GetLongestSequence(IsValidGeometricSequence,[1,0,1,2,3,4,5,6]));
OutputSequence(GetLongestSequence(IsValidGeometricSequence,[0,0,0,0,0,0]));
OutputSequence(GetLongestSequence(IsValidGeometricSequence,[0,0,1,2,4,8,16]));
OutputSequence(GetLongestSequence(IsValidGeometricSequence,[0,0,6,9,12,4,8,16]));
OutputSequence(GetLongestSequence(IsValidGeometricSequence,[9,12,16]));
OutputSequence(GetLongestSequence(IsValidGeometricSequence,[1,0,9,-12,16]));
OutputSequence(GetLongestSequence(IsValidGeometricSequence,[5,4,78,2,3,4,5,6,18,54,16]));
ReadLn;
end.
As commented by David, mixing floating point calculations with integers can cause unwanted behavior. Eg. input sequence 9,12,16 with a geometric factor of 4/3 will work here, but other similar non-integer geometric factors may fail. More extensive testing is required to verify this.
In order to remove the dependency of floating point operations, following change in the loop can be made:
// A geometric function is defined by a + n*a + n^2*a + ...
// By comparing sequence[i]*sequence[i-2] with Sqr(sequence[i-1])
// i.e. n^2*a*a with Sqr(n*a) we can establish a valid geometric sequence
q := Sqr(sequence[i-1]);
if (i < 2)
then q1 := q // Special case, always true
else q1 := sequence[i] * sequence[i - 2];
Change the declarations of d,d1,q,q1 to Integer and remove the assignment of q1 before the loop.
The test code is updated to reflect these changes.
There is a problem when a sequence has one or more zeroes for the geometric sequence calculations.
Zero is only considered a member of a geometric sequence if all values are zero.
Geometric sequence: a*r^0, a*r^1, a*r^2, etc; r <> 0.
With a = 0 the progression consists of zeroes only.
This also implies that a valid geometric sequence can not hold both non-zero and zero values.
To rectify this with current structure it became messy. So I updated my test above with a better structured program that handles all input sequences.
This is quite an interesting problem. LU RD has given you an answer that fixes your code. I offer as an alternative, the way I would address the problem:
program LongestSubsequence;
{$APPTYPE CONSOLE}
type
TSubsequence = record
Start: Integer;
Length: Integer;
end;
function Subsequence(Start, Length: Integer): TSubsequence;
begin
Result.Start := Start;
Result.Length := Length;
end;
type
TTestSubsequenceRule = function(a, b, c: Integer): Boolean;
function FindLongestSubsequence(
const seq: array of Integer;
const TestSubsequenceRule: TTestSubsequenceRule
): TSubsequence;
var
StartIndex, Index: Integer;
CurrentSubsequence, LongestSubsequence: TSubsequence;
begin
LongestSubsequence := Subsequence(-1, 0);
for StartIndex := low(seq) to high(seq) do
begin
CurrentSubsequence := Subsequence(StartIndex, 0);
for Index := CurrentSubsequence.Start to high(seq) do
begin
if (CurrentSubsequence.Length<2)
or TestSubsequenceRule(seq[Index-2], seq[Index-1], seq[Index]) then
begin
inc(CurrentSubsequence.Length);
if CurrentSubsequence.Length>LongestSubsequence.Length then
LongestSubsequence := CurrentSubsequence;
end
else
break;
end;
end;
Result := LongestSubsequence;
end;
function TestArithmeticSubsequence(a, b, c: Integer): Boolean;
begin
Result := (b-a)=(c-b);
end;
function FindLongestArithmeticSubsequence(const seq: array of Integer): TSubsequence;
begin
Result := FindLongestSubsequence(seq, TestArithmeticSubsequence);
end;
function TestGeometricSubsequence(a, b, c: Integer): Boolean;
begin
Result := (b*b)=(a*c);
end;
function FindLongestGeometricSubsequence(const seq: array of Integer): TSubsequence;
begin
Result := FindLongestSubsequence(seq, TestGeometricSubsequence);
end;
procedure OutputSubsequence(const seq: array of Integer; const Subsequence: TSubsequence);
var
Index: Integer;
begin
for Index := 0 to Subsequence.Length-1 do
begin
Write(seq[Subsequence.Start + Index]);
if Index<Subsequence.Length-1 then
Write(',');
end;
Writeln;
end;
procedure OutputLongestArithmeticSubsequence(const seq: array of Integer);
begin
OutputSubsequence(seq, FindLongestArithmeticSubsequence(seq));
end;
procedure OutputLongestGeometricSubsequence(const seq: array of Integer);
begin
OutputSubsequence(seq, FindLongestGeometricSubsequence(seq));
end;
begin
Writeln('Testing arithmetic sequences:');
OutputLongestArithmeticSubsequence([]);
OutputLongestArithmeticSubsequence([1]);
OutputLongestArithmeticSubsequence([1,2]);
OutputLongestArithmeticSubsequence([1,2,3]);
OutputLongestArithmeticSubsequence([1,2,4]);
OutputLongestArithmeticSubsequence([6,1,2,4,7]);
OutputLongestArithmeticSubsequence([6,1,2,4,6,7]);
Writeln('Testing geometric sequences:');
OutputLongestGeometricSubsequence([]);
OutputLongestGeometricSubsequence([1]);
OutputLongestGeometricSubsequence([1,2]);
OutputLongestGeometricSubsequence([1,2,4]);
OutputLongestGeometricSubsequence([7,1,2,4,-12]);
OutputLongestGeometricSubsequence([-16,-12,-9]);
OutputLongestGeometricSubsequence([4,-16,-12,-9]);
Readln;
end.
The key point to stress is that your code is hard to understand because all the different aspects are mixed in with each other. I have attempted here to break the algorithm down into smaller parts which can be understood in isolation.