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( ) : . , - , . ? : ( , , , RISC-), - . : - . , - . 8.1. ( ) 8.1.1. - ( ). - . function C(n,k: integer):integer; | {n,k >=0; k <=n} begin | if (k = 0) or (k = n) then begin | | C:=1; | end else begin {0 2. 8.1.3. n- ( ). - , n-2 ( n). . . n. (- , - .) . , 1 n . k, l - , l>k. A(k,l) , kl. ( 2, 1n; A(k,l) - .) A(1,n). l=k+1 . a(k,l) A(k,l) . a(k,l). l=k+1 , a(k,l)=0. l=k+2 , - a(k,l)=0. l > k+2. kl - A(k,l) , , - , . i k+1,...,l-1, - min {( ki)+( il)+a(k,i)+a(i,l)} i=k+1,..., i=l-1. , i=k+1 ki - , , 0 ( ). a(k,l) - ( l-k+2), , - n*n n*n*n ( n ). 8.1.4. m*n - m n , . m*n n*k ( - ), m*k. m*n*k ( , - - ). - , n - . - . - , . . . 2*3, 3*4, 4*5 . 2*3*4 + 2*4*5 = 24 + 40 = 64, 3*4*5 + 2*3*5 = 90. . , [0,1], - [1,2],..., s- - [s-1,s]. [i-1,i] [i,i+1] - , . d[i]. , d[0]..d[s]. a(i,j) - [i,j] ( 0<=i, n); | end else begin | | s:=6-m-n; {s - : 6} | | move (i-1, m, s); | | writeln ( , m, ->, n); | | move (i-1, s, n); | end; end; , i m- n- : i-1 . - , , . , . - i m- n-. : - . - : procedure move(i,m,n: integer); begin | | | {: } | while do begin | | , | | if j = 1 then begin | | | writeln ( , p, ->, q); | | end else begin | | | s:=6-p-q; | | | {s - : 6} | | | , <1,p,q>, | | end; | end; end; (, , - .) . ( , , , .) 8.2.2. ( .. - .) . : ( , , , ) . : , - . 8.2.3. - - . . , . 8.2.4. , . . - : ( ) ( nil ). , : < , >. , ( ) - . 8.2.5. , , ? . . , : ( ) = () + ( , ). 8.2.6. , - . . . : , , , , - . , , . , (- ) : x, x (.. x). - , . , , , - . . , - . . l r - , . C . 8.2.7. . , C*log n, n - ? . , - . , - n. - , : - . f(n) - - , n . f(n) : ( ) , f(n/2)+1, - , f(n) <= max (f(n/2)+1, f(n-1)), f(n) = O(log n). 8.3. . f - f(0) = a, f(x) = h(x, f(l(x))), a - , h l - . , f x f l(x). , x - x, l(x), l(l(x)),... 0. , l(x) < x x, f : f(0), f(1), f(2),... 8.3.1. f . . f(x) l(x), l(l(x)), l(l(l(x))),... , f , . - ( , , ). : f - f(0) = a, f(x) = h(x, f(l(x)), f(r(x))), a - , l, r h - . - , l r , 0. 8.3.2. f. . , x, i l(i) r(i) - i , , . . ( ) - , , . : f(2) 2 f f(g(2)) 2 g f s(2,t(7)) 2 7 t s s(2, u(2, s(5,3)) 2 2 5 3 s u s . , ( ). . - . , 2 3 4 5 6 s, , 2 3 4 s(5,6) . f , - f, l, r, h, - . : , , . , , f(100). 100, - f. 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