Vizual dasturlash tili yordamida matematik masalalarni yechish. Vektor masalasi
![Men ushbu kurs ishimda matematik masalalarni, yani vetorlarga oid
masalalarni vizuallashtirish jaryonini o’rganib chiqdim.
Dastur kodi:
Procedure Mul(Const A: TLong;Const К : LongInt;Var
С : TLong);
Var i: Integer;{*Natija - C o’zgaruvchisi qiymati.*}
Begin
FillChar(C, SizeOf(C), 0);
If K=0 Then Inc(C[0]){*Nolga ko’paytirish*}
Else Begin
For i:=1 To A[0] Do Begin
C[i+1]:=(LongInt (A[i] )*K+C[i] ) DivOsn;
С [i]:=(LongInt(A[i])*K+C[i]) Mod Osn;
End;
If C[A[0]+1]>0 Then C[0]:=A[0]+1
Else С [0]:=A[0];{*Natija uzunligini aniqlaymiz .*}
End;
End;
Ikki sonni ko’paytirish prosedurasi, mumkin bo’lgan variant teksti
quyidagicha:
Procedure MulLong(Const А , В : TLong; Var С : TLong);
{*”Uzun soni “uzun” songa ko’paytirish .*}
Var i, j : Word;
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![dv: Longlnt;
Begin
FillChar(Cr SizeOf(C), 0) ;
For i:=1 To A[0] Do
For j : = 1 То B[0] Do Begin
dv:=LongInt (A[i])*B[j]+C[i+j-1];
Inc (C[i+j], dv Div Osn);
C[i+j-1] :=dv Mod Osn;
End;
C[0] :=A[0]+B[0] ;
While (C[0]>1) And (C[C[0]]=0) Do Dec(C[0]);
End;
Ko’paytirish. Ko’paytirish qo’shish va ayirishga qaraganda yanada
murakkab amaldek tuyiladi. Rimliklardek rivojlangan sivilizatsiya rim sonlar
binolarning burchaklari va super kublarda yarmani bajaradigan bo’lsalar ham,
ko’paytirish amali bilan muammoga ega bo’lgan.
Rimliklar muamosi shu bo’lganki ular hisoblash sistemalarining asosini
ishlatmaganlar. Albatta biz ko’paytirishni ko’p martali qo’shishdek ko’rib chiqib,
masalani yechsak bo’ladi, lekin jarayon juda sekin bo’ladi.
999 999 ni kvadratga ko’tarish milliongacha operatsiyalarni talab qiladi,
lekin buni qo’l bilan qildanda juda oson, bunda ustma ust ko’paytirish metodi
qo’llaniladi, biz uni maktablik davridan bilamiz.
multiply_bignum(bignum * а , bignum *b)
{
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![bignum row; /*siljigan qator */
bignum tmp; /*soni to’ldirish */
int i/j; /*schotchiklar */
initialize_bignum(c);
row = *a;
for (i=0; i<=b->lastdigit; i++) {
for (j=l; j<=b->digits[i];
add_bignum(c,&row,&tmp);
*c = tmp;
}
digit_shift(&row,l);
c->signbit = a->signbit * b->signbit;
zero_justify(c);
procedure mul(var nl. n2. n3 : number);
var
il. i2, i3. lenl. len2. carry : integer;
begin
lenl := len(nl):
len2 := len(n2):
setO(n3):
for il := 1 to lenl do begin
for i2 := 1 to len2 do begin
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![carry := пГ[И] * n2[i2]:
i3 := il + i2 - 1;
while carry > 0 do begin
carry := carry + n3[i3];
n3[i3] := carry mod 10;
carry := carry div 10;
inc(i3);
end;
end;
end;
end;
Har bir razryadni bir biriga ko’paytiramiz va mos natija joyiga qo’shmiz.
Uzun sonlarni ko’paytirishda butkul voz kechib faqatgina qo’shishdan
foydalansak bo’ladi.
nl va n2 sonlarni ko’paytirish talab qilinsin.nlx ko’rinishidagi massivni
to’ldiramiz
nlx : array [0..9. 1..2502] of byte;
nlx[i] i ga ko’paytirilgan nl raqamni saqlaydi. Uni nlx[0]=0,
nlx[i]=nlx[i-1]+ nl formula bo’yicha topish mumkin.
Ikkita uzun sonni ko’paytmasi endi nlx[n2[i]] yig’indisida yotadi. O’nliklar
darajasida ko’paytirish, sonni mos razryadga siljitish orqali qilinadi.
Algoritmlarni solishtirish.
3 variatning afzalligi tezligi. U 1 variantdan 1,5 marta tezroq ishlaydi.
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![3 variant qanchiligi 10 lik sanoq sistemasidan tashqari boshqa 10N(N=
2,4,9) hisoblash sistemalarda olib borish imkoniyatining yo’qligi, ayni avqda esa, 1
– variant bemallol bu sanoq sistelarga o’ta oladi va bazilarida 0,5 o’nlik matra
tezlik oshilishini ko’tish mumkin.
Qisqa songa ko’paytirish.
procedure mulShort(var n : number; short : integer);
var
i, carry : integer;
begin
carry : = 0;
for i : = 1 to numlen do begin
carry := carry + n[i] * short;
n[i] := carry mod 10;
carry := carry div 10;
end;
if carry <> 0 then {to’lilib qolish diagnostikasi
halt(l);
end;
Uzun sonlarni ko’paytirish.
procedure mul(nl. n2 : number; var n3 : number):
var
il. i2. i3. lenl. len2. саггу : integer;
begin
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![setO(n3);
lenl := len(nl);
len2 := len(n2);
for il := 1 to lenl do
for i2 := 1 to len2 do begin
i3 := il + i2 - 1;
саггу := nl[il] * n2[i2];
while саггу > 0 do begin
саггу := саггу + n3[i3]:
n3[i3] := саггу mod 10;
саггу := саггу div 10;
inc(i3);
end;
end;
end;
Prosedurani ko’rsatish vaqti keldi. Ishlatilayotgan “blokchlar”: siljishni
inobatga olgan holda solishtirish funksiyasi ( More ) va uzun sonni qisqasiga
ko’paytish ( Mul ) funksiyasi yuqorida keltirilgan.
Function FindBin(Var Ost : Tlong; Const В : TLong; Const sp : Integer) :
Longint;
Var Down, Up : Word; C : TLong;
Begin
Down := 0;Up := 0sn;
{sanoq sistemasi asosi }
While Up - l > Down Do
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![Label3: TLabel;
GroupBox1: TGroupBox;
RadioButton1: TRadioButton;
RadioButton2: TRadioButton;
RadioButton3: TRadioButton;
Button2: TButton;
Button3: TButton;
Button4: TButton;
procedure Button1Click(Sender: TObject);
procedure Button2Click(Sender: TObject);
procedure Button3Click(Sender: TObject);
procedure Button4Click(Sender: TObject);
private
{ Private declarations }
public
{ Public declarations }
end ;
Const NMax = 2000 ;
Type Digit = 0. . 9 ; DlChislo = Array [ 1. .Nmax] Of Digit;
var
Form1: TForm1;
S : String ;
M, N, R, F : DlChislo;
I, MaxF : Word;
Logic : Boolean;
implementation
uses Unit2, Unit3;
{$R *.dfm}
{uzun sonni nolga yalantirish protsedurasi, massivni bo'shatish.}
Procedure Zero( Var A : DlChislo);
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![Var I : Integer;
Begin
For I := 1 To NMax Do A[I] := 0 ;
End ;
{uzun sonni yozishda uning raqamlar sonini aniqlaydigan funksiya}
Function Dlina(C : DlChislo) : Integer;
Var I : Integer;
Begin
I := NMax;
While (I > 1 ) And (C[I] = 0 ) Do I := I - 1 ;
Dlina := I
End ;
17. {Uzun soni chop etish protsedurasi}
Procedure Print(A : DlChislo);
Var I : Integer;
Begin
For I := Dlina(A) DownTo 1 Do Write (A[I] : 1 );
WriteLn
End ;
{Uzun sonni massivga aylantiruvchi protsedura}
Procedure Translate(S : String ; Var A : DlChislo; Var OK : Boolean);
Var I : Word;
Begin
Zero(A); I := Length(S); OK := True;
While (I >= 1 ) And OK Do
Begin
If S[I] In [ '0' .. '9' ]
Then A[Length(S) - I+ 1 ] := Ord(S[I]) - 48
Else OK := False;
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Vizual dasturlash tili yordamida matematik masalalarni yechish. Vektor masalasi