ࡱ> Root Entry1^PageMaker  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~b 08Root Entry`:^PageMaker <  Q3@@@q=2'@MP2ԗP88 88 hL  ; kZ 4&@ } @ Pd 0  @@ L  & ^U N &   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~12345679:;<=>?@ABCDEFGHIcdefghijklmnopqb 08  Q@9@93@@@q=2'@MP2ԗPx88 88 hL  ; kZ 4&@ } @ Pd 0  @@ L  & ^U N & &4    $7< MS  B@ & >  ; G3Ld 26 kZ 3L  1 @ @  @   @} .+@RTFC:\INSTALL\NEW\cd-pasico\BOOKS\SHEN\druk\ 9p-Y-5 (pnmcxO~xh|dlpn,OกLonky?@!ABCDEF!GHIJKL!MNOPQR!STUVWX!YZ[\]^!!;Times New Roman$Arial Cyr"$Arial"$(xKdddxGMMdBody text(xKddddGMMdCaption(xKdddxGMMdHanging indentU(xKddd,GMMdHeadlineU(xKdddGMMdSubhead 1U(xKdddxGMMdSubhead 2(xKdddxGMMdNormalNoneRegistrationPaperBlackRedGreenBlueCyanMagentaYellowdDAdobe Compatibility CMSAdobe Compatibility CMSPageMaker 5.0 RGB DAdobe Compatibility CMS Adobe Compatibility CMSPageMaker 5.0 CMYKDefaultETIsBLDB#Document MasterpnmcxO~xh|dlpn,OกLonky@"@"A@"A@"2@X"@"A@P"A@",@4"@"A@"A@X"@"@"A@("6@"@"A@ ")@ "@"A@"A@\"@"@"9@"5@d "@"A@" @,"@" @d"4@ "'@ "@" @\"@""@"-@ "@&"#@"@ " @"!@"5@ " @d"@" @"@"A@",@ "@"A@"A@"A@"@"@"%@ "*@ "@"A@"A@"A@"A@\"A@\"@"A@P"@"@"A@"A@L">@L"@"@"@X"8@L "@"A@"A@"@"/@L"@"A@X"A@4" @4"@"A@"A@p"@"@"@"A@$"A@8"1@d"A@|"A@"@"@"A@"A@ "A@"A@"A@ "A@h"@8"A@"A@"A@"A@"2@"A@<"A@<"'@$ "1@"@"A@ "A@"A@"A@"A@"=@"@"A@d"A@"%@ "@"A@"@"@"A@"A@"A@"A@ "@`"@"A@"@0 "@"A@T"A@"@"A@"A@"A@" @"@"@"@"A@"@0"@"A@"A@"A@"A@"A@("A@"A@"@"@"A@,"A@"@"A@"A@"A@ "A@"A@"A@"!@ "@"7@"@"A@"A@p"A@"A@"A@"3@"@"A@"A@"A@<"A@"A@X"A@"=@L"@"A@"A@"@"A@D"@t "@"A@"A@X" @"@"A@"A@T"A@"A@h"@"@"$@ ":@X"@8"@"@"@@"@"@"@X"@,":@"3@"@"6@"8@l"@"+@p "%@"@(")@ "@"@8"@ " @" @4" @"@"@"A@p"A@T"A@T"A@<"$@ "@"A@<"A@X" @"@&"@"=@"@"A@"A@L"'@ "@"4@"+@ "@"A@L"A@"A@"A@H"A@"A@"A@p"3@"@"@"@"A@<"A@x"A@`"A@h"A@"A@8"A@("A@x"A@"A@"A@"A@"A@"@T"A@@"A@P"A@"A@":@4"@"A@ "A@X"A@"A@"A@"A@"A@$"A@"@"@&"@"A@"A@<"A@"A@l"A@"A@t"@"@"1@ "A@8"A@l"A@"A@X"A@"A@"A@|"@,"@"A@"A@"A@"A@"A@"A@"A@<"A@"@h"@"A@(")@ "@"A@"A@("A@"A@0"@p"@"A@"A@"=@"@"A@"@"@"A@("A@0"@L"@"A@"@&"A@"A@"A@"A@h"A@H"A@P"=@"A@"A@`"3@"@"A@L"A@"A@"A@4"A@"!@ " @" @|"-@d "A@p"+@@ ""@ "@"A@L"A@$"A@x"@p"@"?@"?@\")@ "@"@"@"&@"5@p "/@< "<@\"9@""@4"@"(@"@"8@ "@x"<@ "/@H "#@"@<"@&"6@ "@h"@" @"<@"*@ "@"A@"@x"@"A@h"A@"A@"A@p"A@p"<@t"@"@" 9. 9.1. - . n , 1 n. i, j a[i][j] - - i j. , , a[i,i] = 0 i, a[i][j] a[j,i]. i j ( ), i j. ( a[i][j], .) - - a . 9.1.1. , , . , . . n , - n, . , ( ) . 9.1.2. 1- O(n 3). . (1,s,) 1 s k . : (1,s,k+1) = (1,s,k) (1,i,k) + a[i][s] (i=1..n) , (1,i,n) i=1..n. k:= 1; for i := 1 to n do begin x[i] := a[1][i]; end; {: x[i] := (1,i,k)} while k <> n do begin | for s := 1 to n do begin | | y[s] := x[s]; | | for i := 1 to n do begin | | | if y[s] > x[i]+a[i][s] then begin | | | | y[s] := x[i]+a[i][s]; | | | end; | | end | | {y[s] = (1,s,k+1)} | | for i := 1 to n do begin x[s] := y[s]; end; | end; | k := k + 1; end; - , - . 9.1.3. , , y, x ( y x ). . : (1,i,n) <= x[i] <= M(1,i,k) : O(n 3) - i->j i,j ( i=1), - O(n 2). , - , a[i][j] . 9.1.4. i->j i,j O(n 3). . k = 0..n (i,j,k) i j, - k. A(i,j,0) = a[i][j], A(i,j,k+1) = min (A(i,j,k), A(i,k+1,k)+A(k+1,j,k)) ( k+1 ; , ). . 9.1.5. , . - 1->i i=1..n O(n 2). . ( - 1, - ). : i - 1->i; , , ; i - 1->i, - . - : , , - . , . - ! ( - .) , - , . , - , , - . - ( ) O(n). . . A - , B - . ( , 0.) , - A, - B. , i j? 9.1.6. , , , - . 9.1.7. , - . 9.1.8. , A: - A, A*A, A*A*A,... , , . ( - !) 9.1.9. - ? ( ) , . ( ), , a[i,j] 1, , 0, . a ( ) k i-j- . 9.1.10. ? . i j k . , , , ( ) . . n*n, - , . : , . 9.1.11. , - , n k C*(n+k log n) . . ? - , . - , , C*(n+k) . , (. 6.4.1 ) log n. 9.2. , - 0 . , - i j, ( ). : ( , - ) , . - . , 7 (), - 6 ( ). : , , . - . : - , , . ( , 1 .) 9.2.1. C*( , ). . 6 ( - ), 6.3.7 - 6.3.8. . num[i] - , i, out[i][1],..., out[i][num[i]] - , . , - : procedure (i: integer); | { , i, i} | var X: 1..n; | P: 1..n; | q, v, w: 1..n; | k: integer; begin | ... X, P ; | writeln (i); | ... i X, P; | {(1) P = ; P i; | (2) i ; | (3) X - P; | (4) , | , X} | while X do begin | | ... - X v; | | for k := 1 to num [v] do begin | | | w := out [v][k]; | | | if w P then begin | | | | writeln (w); | | | | w P; | | | | w X | | | end; | | end; | end; end; , X - . X ( - - ), , i, i ( i). . V(k) , - i ( ) k. - : V(k+1) = ( V(k))-V(0)-V(1)-...-V(k) ( - ). , - k=0,1,2... ( while), V(k) V(1),...,V(k) ( k=0 - .) , , V(k). - , ( , ). , , - - V(k+1). - , V(k+1). . , - . , - , . - , . , - . . , - . , . - , , , . : - , . - , . , , . ( ). - , . ( ) - - . , (, ). - . : , - ( ). . . - , , - . : , , : ; , , . - , . - . 9.2.2. . . ( - - ) - . : - . , . ( , - ). . . ( ). , _, . , . - , - . , . 9.2.3. , , - . , ( C*( + ). . () . () - , . . , . 9.2.4. - . (. 7.4.2 .) . , 1..n, i num[i] dest[i][1],..., dest[i][num[i]], - . , - : , . , - . , - . 0, - 1,...,n. , . , - . l - . vert[1],..., vert[l] , edge[1]...edge[l]. edge[s] - , vert[s]. s edge[s] <= num[vert[s]] vert[s+1] = dest [vert[s]] [edge[s]] , , , .. edge[l] num[vert[l]]+1. , , . , - : () , (.. vert[1]..vert[l]) , , : l:=1; vert[1]:=0; edge[1]:=1; while not( (l=1) and (edge[1]=n+1)) do begin | if edge[l]=num[vert[l]]+1 then begin | | { , , | | vert[l], - | | vert[l]} | | writeln (vert[l]); | | l:=l-1; edge[l]:=egde[l]+1; | end else begin | | {edge[l] <= num[vert[l]], | | } | | lastvert:= dest[vert[l]][edge[l]]; {} | | if lastvert then begin | | | edge[l]:=edge[l]+1; | | end else begin | | | l:=l+1; vert[l]:=lastvert; edge[l]:=1; | | end; | end; end; { , , 1..n, } 9.2.4. , , - . . . , - . 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