. , . , . , . .

9.1. .

, . , . . , , , , . , () .

. S - IS, P Q - () . {P}S{Q} , P , Q - S. , ( , ) S {P}S{Q}, , S P, S Q.

:

(9.1) {n=0} n:= n+1{n=1},
(9.2) {n<m} n:= n + k {n<m+k},
(9.3) {n<m+k} n:=3* n {n<3* (m + k)},
(9.4) {n>0} p:=1; m:=1;
 m <> n 
m:=m+1; p:= p* m
 
{p= n!}.

S ( ) (), ( , . 8). .

9.2.

9.1. P - . {P}{P}.

: ( ), .

9.2. IS X RIS:

IS = (X, RIS).

{Q(F(X, RIS), RIS)} X:= F(X, RIS) {Q(X, RIS)} ,

F(X, RIS) - , Q - .

. (X0, RIS0) - IS, Q(F(X0, RIS0), RIS0) . Q(X, RIS), X F(X0, RIS0), RIS , , ,

Q(X, RIS)=Q(F(X0, RIS0), RIS0).

.

9.1.

: , .

9.3. P, Q R - , S1 S2 - ,

{P}S{Q} {Q}S2{R}.

S1; S2

{P} S1; S2 {R} .

. S1 P. S1 Q. S1 S2, Q S2. , S2 R, S2 ( ), R , .

, (9.2) (9.3),

{n<m} n:= n + k; n:= 3* n {n<3* (m + k)}.

9.4. P, Q R - , S1 S2 - ,

{P,Q} S1{R}  { P,Q} S2 {R}.

 P  S1 S2  

{Q}  P  S1 S2   {R} .

. Q. P, S1. S1 ( - ) R. P ( Q, -, ), S2. S2 ( - ) R. .

9.5. P, Q, P1 Q1 - ,

P1 P Q Q1,

S {P}S{Q}. {P1}S{Q1} .

.

. S P1. P ( P1 P). , S Q, Q1 ( Q Q1). .

9.6. I, P, Q R - ,

P I (I, Q) R ,

S - , {I}S{I}.

Q S

{P} Q S {R} .

I .

.

{I} Q S {I, Q}

( 9.5 ). I. Q , ( ) 9.1 (I, Q). Q ,

S; Q S

S I, : I , () ( Q ). , , , , (I, Q). , , . .

, (9.4)

{n>0, p=1, m=1} m <> n

m:=m+1; p:= p* m

{p= n!}.

9.6, p= m!

(n>0, p=1, m=1) p= m! (p= m!, m= n) p= n!

9.4.

, , , , .. . . .

9.7. F - , :

  1. Q, ;
  2. S.

Q S

.

. IS - F(IS)= k. Q(IS) , . Q(IS) , k>0. S . S F , S Q ( ), F ( ). F S k . .

,

9.7 f(n, m)= n- m. m=1, (n- 1) , .. .

9.5.

, . , - , . .

(9.4). .

( 1). n>0 (n>0, p - , m - ).

( 2).

{n>0, p - , m - } p:=1 {n>0, p=1, m - }.

- - 9.2.

( 3).

{n>0, p=1, m - } m:=1 {n>0, p=1, m=1}.

- - 9.2.

( 4).

{n>0, p - , m - } p:=1; m:=1 {n>0, p=1, m=1}.

- - 9.3 2 3.

, p= m! , .. {p=m!} m:=m+1; p:=p* m {p=m!}.

( 5). {p= m!} m:= m+1 {p= (m- 1)!}.

- - 9.2, {p= ((m+1)- 1)!}.

( 6). {p= (m- 1)!} p:= p* m {p= m!}.

- - 9.2, {p* m= m!}.

( 7).

{p= m!} m:= m+1; p:= p* m {p= m!}.

- - 9.3 5 6.

( 8).

{n>0, p=1, m=1} m <> n

m:= m+1; p:= p* m

{p= n!}.

- - 9.6 7 , (n>0, p=1, m= 1) p= m!; (p= m!, m= n) p= n!.

( 9).

{n>0, p - , m - } p:=1; m:=1;

m <> n

m:= m+1; p:= p* m

{p= n!}.

- - 9.3 3 8.

( 10). (9.4) 9.5 1 9.

9

9.1. ?

9.2. ?

9.3.

const n= < >;

var k, m: integer;

x: array[1..n] of integer;

 

:

{n>0}

m:= x[1]

k:=1;

k<n

k:= k+1;

x[k]<m

m:= x[k]

;

{n>0 & m<= x[i] i, 1<=i<= n}

9

9.1. .. . . - .: , 1982. . 85-94.

9.2. . , . , . . . - .: , 1982. . 98-105.


, , Class diagram - - , - .




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