. - 3GL   - 4GL   5GL  

3GL

() , . :

n! = n*(n-1)!

, " " , . :

if n < 2 then fact:=l else fact:=n*fact(n-1);

, :

-> -> -> -> ...

, , , forward:

{ }

procedure (< >);

forward; { }

procedure (< >);

begin

(...); { }

end; { }

procedure A; { } begin

(...); { } end;

, . . , . , , n!, :

= =1;

for i:=l to n do p:=p*i;

fact:=p;

, , , (., , quicksort " ").

,

5.01.

XIII ., . - , , . . , k . :

, :

fk = fk-2 + fk-1

, :

1,1,2,3,5,8,13,21,34,55,...

0,1,1,2,3,5,8,13,21,34,.....

, 0. : fit>(22)=17711, fib(23) =28657 24- . , fib :

f ib (k) = ( ( (1+sqrt (5) ) /2)*k- ( (1-sqrt (5) ) /2} ^k) /sqrt (5)

. , . . k .

5_01.bas

DECLARE FUNCTION FIB%(N%)

INPUT " - ",N%

PRINT " ";N%;" ";FIB%(N%)

END

FUNCTION FIB%(N%)

IF N% < 2 THEN

FIB%=N% ELSE

FIB%=FIB%(N%-2)+FIB%(N%-1)

END IF

END FUNCTION

5_01.

#include <stdio.h>

#include <conio.h>

1 ()

() . :

H(kl,k2) = HO(k2,kl) // , kl < k2

H(0,k) = k // , ..

H(kl,k2) = H(k3,kl) // k3 - k2 kl. , : k1*m + k3 = k2 // m - k2 k1

kl k2 , k3 . :

  1. kl , .
  2. kl=0, .
  3. k2 kl .
  4. , .

2 ()

. :

(120,84)=(84,120)=(36,84)=(12,36)=(0,12)==12 .

5_02.bas

DECLARE FUNCTION NOD&(NlS,N2&)

PRINT " 2 , "

INPUT "",M&,N&

PRINT " ";NOD&(M&,N&)

END

FUNCTION NOD&(N1&,N2&) IF Nl&=0 THEN

NODS=N2& ELSE

NOD&=NOD&(N2& MOD N1&,N1&)

END IF

END FUNCTION

5_02.

#include <stdio.h>

#include <conio.h>

long nod(long nl,long n2);

main() {

long m,n;

printf("\n 2 , \n");

scanf("%ld %ld",&n,&m);

printf(" %ld",nod(m,n));

getch(); }

long nod(long n1,long n2) {

if(nl==0) return n2;

return nod(n2%nl,nl); }

5_02.pas

program Euclid;

var

n,m:longint;

function nod(nl,n2:longint):longint;

begin

if nl=0 then nod:=n2

else nod:=nod(n2 mod n1,n1);

end;

begin

writeln(' ');

readln(n,m);

writeln{'x ',nod(n,m));

readln; end.

5.03.

" " . XIX . ,

, . k , "" ( , , , , ). . , , .

, , , 2k-i. k=1 k=2 . : k-1, k. , k-1 2k-1-1 . k :

, , k , :

2k-1 - 1 + 1 + 2k-1 -1 = 2k-l

1 ()

, . :

MoveAll(k,from,to,tmp) MoveOne(from,to)

k from to, tmp. from to.

2 (QBasic)

% . MoveOne STATIC.

3 ()

to, . . for.

5_03.bas

DECLARE SUB MoveAll(k%,from$,to$,tmp$)

DECLARE SUB MoveOne(from$,to$)

CLS

INPUT " ",k%

MoveAll k%,"A","C","B"

END

SUB MoveAll (k%, from$, to$,tmp$)

IF k%=0 THEN EXIT SUB

MoveAll k%-l,from$,tmp$,to$

MoveOne from$,to$

MoveAll k%-l,trap$,to$,from$ END SUB

SUB MoveOne(from$,to$) STATIC

m%=m%+l

PRINT USING "#### : &--> & ";m%;from$;to$ END SUB

5_03.

#include <stdio.h>

#include <conio.h>

void MoveAll(int k,char from,char to,char trap);

void MoveOne(char from,char to);

int m=0;

main () {

int k;

clrscr () ;

printf("\n - ");

scanf("Id",&k);

MoveAll(k,'A','C','B');

getch(); }

void MoveAll(int k,char from,char to,char tmp)

{

if(k==0) return; MoveAll(k-1,from,tmp,to);

MoveOne(from,to); MoveAll(k-1,tmp,to,from); }

void MoveOne(char from,char to) {

m++;

printf("\n%4d : %c --> %c",m,from,to); }

5_03.pas

program Hanoi; uses Crt; var

k:integer; const

m: integer=0;

procedure MoveOne(from,tol:char);

begin

inc (m) ;

writeln(m:4,from:2, ' > ',tol);

end;

procedure MoveAll(k:integer;from,tol,tmp:char);

begin

if k = 0 then exit;

MoveAll(k-1,from,tmp,tol);

MoveOne(from,tol);

MoveAll(k-1,tmp,tol,from);

end;

begin

clrscr;

write(' - ') ;

readln(k);

MoveAll(k, '', '', '');

readln;

end.

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