³£ÓÃÅÅÐòËã·¨

Ò»¡¢²åÈëÅÅÐò(Insertion Sort)
1. »ù±¾Ë¼Ï룺
??ÿ´Î½«Ò»¸ö´ýÅÅÐòµÄÊý¾ÝÔªËØ£¬²åÈ뵽ǰÃæÒѾ­ÅźÃÐòµÄÊýÁÐÖеÄÊʵ±Î»Öã¬Ê¹ÊýÁÐÒÀÈ»ÓÐÐò£»Ö±µ½´ýÅÅÐòÊý¾ÝÔªËØÈ«²¿²åÈëÍêΪֹ¡£
2. ÅÅÐò¹ý³Ì£º¡¡
¡¾Ê¾Àý¡¿£º
[³õʼ¹Ø¼ü×Ö] [49] 38 65 97 76 13 27 49
????J=2(38) [38 49] 65 97 76 13 27 49
????J=3(65) [38 49 65] 97 76 13 27 49
????J=4(97) [38 49 65 97] 76 13 27 49
????J=5(76) [38 49 65 76 97] 13 27 49
????J=6(13) [13 38 49 65 76 97] 27 49
????J=7(27) [13 27 38 49 65 76 97] 49
????J=8(49) [13 27 38 49 49 65 76 97]

Procedure InsertSort(Var R : FileType);
//¶ÔR[1..N]°´µÝÔöÐò½øÐвåÈëÅÅÐò, R[0]ÊǼàÊÓÉÚ//
??Begin
????for I := 2 To N Do //ÒÀ´Î²åÈëR[2],...,R[n]//
????begin
??????R[0] := R[I]; J := I - 1;
??????While R[0] < R[J] Do //²éÕÒR[I]µÄ²åÈëλÖÃ//
???????begin
????????R[J+1] := R[J]; //½«´óÓÚR[I]µÄÔªËغóÒÆ//
????????J := J - 1
???????end
??????R[J + 1] := R[0] ; //²åÈëR[I] //
????end
??End; //InsertSort //

¶þ¡¢Ñ¡ÔñÅÅÐò
1. »ù±¾Ë¼Ï룺
¡¡¡¡Ã¿Ò»ÌË´Ó´ýÅÅÐòµÄÊý¾ÝÔªËØÖÐÑ¡³ö×îС£¨»ò×î´ó£©µÄÒ»¸öÔªËØ£¬Ë³Ðò·ÅÔÚÒÑÅźÃÐòµÄÊýÁеÄ×îºó£¬Ö±µ½È«²¿´ýÅÅÐòµÄÊý¾ÝÔªËØÅÅÍê¡£
2. ÅÅÐò¹ý³Ì£º
¡¾Ê¾Àý¡¿£º
??³õʼ¹Ø¼ü×Ö [49 38 65 97 76 13 27 49]
µÚÒ»ÌËÅÅÐòºó 13 £Û38 65 97 76 49 27 49]
µÚ¶þÌËÅÅÐòºó 13 27 £Û65 97 76 49 38 49]
µÚÈýÌËÅÅÐòºó 13 27 38 [97 76 49 65 49]
µÚËÄÌËÅÅÐòºó 13 27 38 49 [49 97 65 76]
µÚÎåÌËÅÅÐòºó 13 27 38 49 49 [97 97 76]
µÚÁùÌËÅÅÐòºó 13 27 38 49 49 76 [76 97]
µÚÆßÌËÅÅÐòºó 13 27 38 49 49 76 76 [ 97]
×îºóÅÅÐò½á¹û 13 27 38 49 49 76 76 97

Procedure SelectSort(Var R : FileType); //¶ÔR[1..N]½øÐÐÖ±½ÓÑ¡ÔñÅÅÐò //
??Begin
????for I := 1 To N - 1 Do //×öN - 1ÌËÑ¡ÔñÅÅÐò//
?????begin
??????K := I;
??????For J := I + 1 To N Do //ÔÚµ±Ç°ÎÞÐòÇøR[I..N]ÖÐÑ¡×îСµÄÔªËØR[K]//
???????begin
????????If R[J] < R[K] Then K := J
???????end;
??????If K <> I Then //½»»»R[I]ºÍR[K] //
????????begin Temp := R[I]; R[I] := R[K]; R[K] := Temp; end;
?????end
??End; //SelectSort //

Èý¡¢Ã°ÅÝÅÅÐò(BubbleSort)
1. »ù±¾Ë¼Ï룺
¡¡¡¡Á½Á½±È½Ï´ýÅÅÐòÊý¾ÝÔªËصĴóС£¬·¢ÏÖÁ½¸öÊý¾ÝÔªËصĴÎÐòÏ෴ʱ¼´½øÐн»»»£¬Ö±µ½Ã»Óз´ÐòµÄÊý¾ÝÔªËØΪֹ¡£
2. ÅÅÐò¹ý³Ì£º
¡¡¡¡ÉèÏë±»ÅÅÐòµÄÊý×éR£Û1..N£Ý´¹Ö±ÊúÁ¢£¬½«Ã¿¸öÊý¾ÝÔªËØ¿´×÷ÓÐÖØÁ¿µÄÆøÅÝ£¬¸ù¾ÝÇáÆøÅݲ»ÄÜÔÚÖØÆøÅÝ֮ϵÄÔ­Ôò£¬´ÓÏÂÍùÉÏɨÃèÊý×éR£¬·²É¨Ã赽Υ·´±¾Ô­ÔòµÄÇáÆøÅÝ£¬¾ÍʹÆäÏòÉÏ"Ư¸¡"£¬Èç´Ë·´¸´½øÐУ¬Ö±ÖÁ×îºóÈκÎÁ½¸öÆøÅݶ¼ÊÇÇáÕßÔÚÉÏ£¬ÖØÕßÔÚÏÂΪֹ¡£
¡¾Ê¾Àý¡¿£º
49 13 13 13 13 13 13 13
38 49 27 27 27 27 27 27
65 38 49 38 38 38 38 38
97 65 38 49 49 49 49 49
76 97 65 49 49 49 49 49
13 76 97 65 65 65 65 65
27 27 76 97 76 76 76 76
49 49 49 76 97 97 97 97

Procedure BubbleSort(Var R : FileType) //´ÓÏÂÍùÉÏɨÃèµÄÆðÅÝÅÅÐò//
Begin
??For I := 1 To N-1 Do //×öN-1ÌËÅÅÐò//
???begin
?????NoSwap := True; //ÖÃδÅÅÐòµÄ±êÖ¾//
?????For J := N - 1 DownTo 1 Do //´Óµ×²¿ÍùÉÏɨÃè//
??????begin
???????If R[J+1]< R[J] Then //½»»»ÔªËØ//
????????begin
?????????Temp := R[J+1]; R[J+1 := R[J]; R[J] := Temp;
?????????NoSwap := False
????????end;
??????end;
?????If NoSwap Then Return//±¾ÌËÅÅÐòÖÐδ·¢Éú½»»»£¬ÔòÖÕÖ¹Ëã·¨//
????end
End; //BubbleSort//

ËÄ¡¢¿ìËÙÅÅÐò£¨Quick Sort£©
1. »ù±¾Ë¼Ï룺
¡¡¡¡ÔÚµ±Ç°ÎÞÐòÇøR[1..H]ÖÐÈÎÈ¡Ò»¸öÊý¾ÝÔªËØ×÷Ϊ±È½ÏµÄ"»ù×¼"(²»·Á¼ÇΪX)£¬Óô˻ù×¼½«µ±Ç°ÎÞÐòÇø»®·ÖΪ×óÓÒÁ½¸ö½ÏСµÄÎÞÐòÇø£ºR[1..I-1]ºÍR[I+1..H]£¬ÇÒ×ó±ßµÄÎÞÐò×ÓÇøÖÐÊý¾ÝÔªËؾùСÓÚµÈÓÚ»ù×¼ÔªËØ£¬ÓұߵÄÎÞÐò×ÓÇøÖÐÊý¾ÝÔªËؾù´óÓÚµÈÓÚ»ù×¼ÔªËØ£¬¶ø»ù×¼XÔòλÓÚ×îÖÕÅÅÐòµÄλÖÃÉÏ£¬¼´R[1..I-1]¡ÜX.Key¡ÜR[I+1..H](1¡ÜI¡ÜH)£¬µ±R[1..I-1]ºÍR[I+1..H]¾ù·Ç¿Õʱ£¬·Ö±ð¶ÔËüÃǽøÐÐÉÏÊöµÄ»®·Ö¹ý³Ì£¬Ö±ÖÁËùÓÐÎÞÐò×ÓÇøÖеÄÊý¾ÝÔªËؾùÒÑÅÅÐòΪֹ¡£
2. ÅÅÐò¹ý³Ì£º
¡¾Ê¾Àý¡¿£º
³õʼ¹Ø¼ü×Ö [49 38 65 97 76 13 27 49£Ý
µÚÒ»´Î½»»»ºó £Û27 38 65 97 76 13 49 49£Ý
µÚ¶þ´Î½»»»ºó £Û27 38 49 97 76 13 65 49£Ý
JÏò×óɨÃ裬λÖò»±ä£¬µÚÈý´Î½»»»ºó £Û27 38 13 97 76 49 65 49£Ý
IÏòÓÒɨÃ裬λÖò»±ä£¬µÚËĴν»»»ºó £Û27 38 13 49 76 97 65 49£Ý
JÏò×óɨÃè £Û27 38 13 49 76 97 65 49£Ý
£¨Ò»´Î»®·Ö¹ý³Ì£©

³õʼ¹Ø¼ü×Ö £Û49 38 65 97 76 13 27 49£Ý
Ò»ÌËÅÅÐòÖ®ºó £Û27 38 13£Ý 49 £Û76 97 65 49£Ý
¶þÌËÅÅÐòÖ®ºó £Û13£Ý 27 £Û38£Ý 49 £Û49 65£Ý76 £Û97£Ý
ÈýÌËÅÅÐòÖ®ºó 13 27 38 49 49 £Û65£Ý76 97
×îºóµÄÅÅÐò½á¹û 13 27 38 49 49 65 76 97
¸÷ÌËÅÅÐòÖ®ºóµÄ״̬

Procedure Parttion(Var R : FileType; L, H : Integer; Var I : Integer);
//¶ÔÎÞÐòÇøR[1,H]×ö»®·Ö£¬I¸øÒÔ³ö±¾´Î»®·ÖºóÒѱ»¶¨Î»µÄ»ù×¼ÔªËصÄλÖà //
Begin
??I := 1; J := H; X := R[I] ;//³õʼ»¯£¬XΪ»ù×¼//
??Repeat
????While (R[J] >= X) And (I < J) Do
??????begin
???????J := J - 1 //´ÓÓÒÏò×óɨÃ裬²éÕÒµÚ1¸öСÓÚ XµÄÔªËØ//
???????If I < J Then //ÒÑÕÒµ½R[J] ¡´X//
?????????begin
??????????R[I] := R[J]; //Ï൱ÓÚ½»»»R[I]ºÍR[J]//
??????????I := I + 1
?????????end;
???????While (R[I] <= X) And (I < J) Do
??????????I := I + 1 //´Ó×óÏòÓÒɨÃ裬²éÕÒµÚ1¸ö´óÓÚ XµÄÔªËØ///
??????end;
?????If I < J Then //ÒÑÕÒµ½R[I] > X //
???????begin ????????R[J] := R[I]; //Ï൱ÓÚ½»»»R[I]ºÍR[J]//
????????J := J - 1
???????end
??Until I = J;
??R[I] := X //»ù×¼XÒѱ»×îÖÕ¶¨Î»//
End; //Parttion //

Procedure QuickSort(Var R :FileType; S,T: Integer); //¶ÔR[S..T]¿ìËÙÅÅÐò//
Begin
??If S < T Then //µ±R[S..T]Ϊ¿Õ»òÖ»ÓÐÒ»¸öÔªËØÊÇÎÞÐèÅÅÐò//
????begin
??????Partion(R, S, T, I); //¶ÔR[S..T]×ö»®·Ö//
??????QuickSort(R, S, I-1);//µÝ¹é´¦Àí×óÇø¼äR[S,I-1]//
??????QuickSort(R, I+1,T);//µÝ¹é´¦ÀíÓÒÇø¼äR[I+1..T] //
????end;
End; //QuickSort//

Îå¡¢¶ÑÅÅÐò(Heap Sort)
1. »ù±¾Ë¼Ï룺
??¶ÑÅÅÐòÊÇÒ»Ê÷ÐÎÑ¡ÔñÅÅÐò£¬ÔÚÅÅÐò¹ý³ÌÖУ¬½«R[1..N]¿´³ÉÊÇÒ»¿ÅÍêÈ«¶þ²æÊ÷µÄ˳Ðò´æ´¢½á¹¹£¬ÀûÓÃÍêÈ«¶þ²æÊ÷ÖÐË«Ç×½áµãºÍº¢×Ó½áµãÖ®¼äµÄÄÚÔÚ¹ØϵÀ´Ñ¡Ôñ×îСµÄÔªËØ¡£
2. ¶ÑµÄ¶¨Òå: N¸öÔªËصÄÐòÁÐK1,K2,K3,...,Kn.³ÆΪ¶Ñ£¬µ±ÇÒ½öµ±¸ÃÐòÁÐÂú×ãÌØÐÔ£º
?????? Ki¡ÜK2i Ki ¡ÜK2i+1(1¡Ü I¡Ü [N/2])

??¶ÑʵÖÊÉÏÊÇÂú×ãÈçÏÂÐÔÖʵÄÍêÈ«¶þ²æÊ÷£ºÊ÷ÖÐÈÎÒ»·ÇÒ¶×Ó½áµãµÄ¹Ø¼ü×Ö¾ù´óÓÚµÈÓÚÆ亢×Ó½áµãµÄ¹Ø¼ü×Ö¡£ÀýÈçÐòÁÐ10,15,56,25,30,70¾ÍÊÇÒ»¸ö¶Ñ£¬Ëü¶ÔÓ¦µÄÍêÈ«¶þ²æÊ÷ÈçÉÏͼËùʾ¡£ÕâÖÖ¶ÑÖиù½áµã£¨³ÆΪ¶Ñ¶¥£©µÄ¹Ø¼ü×Ö×îС£¬ÎÒÃÇ°ÑËü³ÆΪС¸ù¶Ñ¡£·´Ö®£¬ÈôÍêÈ«¶þ²æÊ÷ÖÐÈÎÒ»·ÇÒ¶×Ó½áµãµÄ¹Ø¼ü×Ö¾ù´óÓÚµÈÓÚÆ亢×ӵĹؼü×Ö£¬Ôò³Æ֮Ϊ´ó¸ù¶Ñ¡£
3. ÅÅÐò¹ý³Ì£º
¶ÑÅÅÐòÕýÊÇÀûÓÃС¸ù¶Ñ£¨»ò´ó¸ù¶Ñ£©À´Ñ¡È¡µ±Ç°ÎÞÐòÇøÖйؼü×ÖС£¨»ò×î´ó£©µÄ¼Ç¼ʵÏÖÅÅÐòµÄ¡£ÎÒÃDz»·ÁÀûÓôó¸ù¶ÑÀ´ÅÅÐò¡£Ã¿Ò»ÌËÅÅÐòµÄ»ù±¾²Ù×÷ÊÇ£º½«µ±Ç°ÎÞÐòÇøµ÷ÕûΪһ¸ö´ó¸ù¶Ñ£¬Ñ¡È¡¹Ø¼ü×Ö×î´óµÄ¶Ñ¶¥¼Ç¼£¬½«ËüºÍÎÞÐòÇøÖеÄ×îºóÒ»¸ö¼Ç¼½»»»¡£ÕâÑù£¬ÕýºÃºÍÖ±½ÓÑ¡ÔñÅÅÐòÏà·´£¬ÓÐÐòÇøÊÇÔÚÔ­¼Ç¼ÇøµÄβ²¿Ðγɲ¢Öð²½ÏòÇ°À©´óµ½Õû¸ö¼Ç¼Çø¡£
¡¾Ê¾Àý¡¿£º¶Ô¹Ø¼ü×ÖÐòÁÐ42£¬13£¬91£¬23£¬24£¬16£¬05£¬88½¨¶Ñ

Procedure Sift(Var R :FileType; I, M : Integer);
//ÔÚÊý×éR[I..M]Öе÷ÓÃR[I]£¬Ê¹µÃÒÔËüΪÍêÈ«¶þ²æÊ÷¹¹³É¶Ñ¡£ÊÂÏÈÒÑÖªÆä×ó¡¢ÓÒ×ÓÊ÷(2I+1 <=Mʱ)¾ùÊǶÑ//
Begin
??X := R[I]; J := 2*I; //ÈôJ <=M, R[J]ÊÇR[I]µÄ×óº¢×Ó//
??While J <= M Do //Èôµ±Ç°±»µ÷Õû½áµãR[I]ÓÐ×óº¢×ÓR[J]//
???begin
????If (J < M) And R[J].Key < R[J+1].Key Then
??????J := J + 1 //ÁîJÖ¸Ïò¹Ø¼ü×ֽϴóµÄÓÒº¢×Ó//
????????//JÖ¸ÏòR[I]µÄ×ó¡¢ÓÒº¢×ÓÖйؼü×ֽϴóÕß//
????If X.Key < R[J].Key Then //º¢×Ó½áµã¹Ø¼ü×ֽϴó//
??????begin
????????R[I] := R[J]; //½«R[J]»»µ½Ë«Ç×λÖÃÉÏ//
????????I := J ; J := 2*I //¼ÌÐøÒÔR[J]Ϊµ±Ç°±»µ÷Õû½áµãÍùϲãµ÷Õû//
??????end;
?????Else
??????Exit//µ÷ÕûÍê±Ï£¬Í˳öÑ­»·//
???end
??R[I] := X;//½«×î³õ±»µ÷ÕûµÄ½áµã·ÅÈëÕýȷλÖÃ//
End;//Sift//

Procedure HeapSort(Var R : FileType); //¶ÔR[1..N]½øÐжÑÅÅÐò//
¡¡Begin
¡¡¡¡For I := N Div Downto 1 Do //½¨Á¢³õʼ¶Ñ//
¡¡¡¡¡¡Sift(R, I , N)
¡¡¡¡For I := N Downto 2 do //½øÐÐN-1ÌËÅÅÐò//
¡¡¡¡¡¡begin
¡¡¡¡¡¡¡¡T := R[1]; R[1] := R[I]; R[I] := T;//½«µ±Ç°¶Ñ¶¥¼Ç¼ºÍ¶ÑÖÐ×îºóÒ»¸ö¼Ç¼½»»»//
¡¡¡¡¡¡¡¡Sift(R, 1, I-1) //½«R[1..I-1]ÖسɶÑ//
¡¡¡¡¡¡end
¡¡End; //HeapSort//

Áù¡¢¼¸ÖÖÅÅÐòËã·¨µÄ±È½ÏºÍÑ¡Ôñ
1. Ñ¡È¡ÅÅÐò·½·¨ÐèÒª¿¼ÂǵÄÒòËØ£º
(1) ´ýÅÅÐòµÄÔªËØÊýÄ¿n£»
(2) ÔªËر¾ÉíÐÅÏ¢Á¿µÄ´óС£»
(3) ¹Ø¼ü×ֵĽṹ¼°Æä·Ö²¼Çé¿ö£»
(4) ÓïÑÔ¹¤¾ßµÄÌõ¼þ£¬¸¨Öú¿Õ¼äµÄ´óСµÈ¡£
2. С½á£º
(1) Èôn½ÏС(n <= 50)£¬Ôò¿ÉÒÔ²ÉÓÃÖ±½Ó²åÈëÅÅÐò»òÖ±½ÓÑ¡ÔñÅÅÐò¡£ÓÉÓÚÖ±½Ó²åÈëÅÅÐòËùÐèµÄ¼Ç¼Òƶ¯²Ù×÷½ÏÖ±½ÓÑ¡ÔñÅÅÐò¶à£¬Òò¶øµ±¼Ç¼±¾ÉíÐÅÏ¢Á¿½Ï´óʱ£¬ÓÃÖ±½ÓÑ¡ÔñÅÅÐò½ÏºÃ¡£
(2) ÈôÎļþµÄ³õʼ״̬ÒÑ°´¹Ø¼ü×Ö»ù±¾ÓÐÐò£¬ÔòÑ¡ÓÃÖ±½Ó²åÈë»òðÅÝÅÅÐòΪÒË¡£
(3) Èôn½Ï´ó£¬ÔòÓ¦²ÉÓÃʱ¼ä¸´ÔÓ¶ÈΪO(nlog2n)µÄÅÅÐò·½·¨£º¿ìËÙÅÅÐò¡¢¶ÑÅÅÐò»ò¹é²¢ÅÅÐò¡£ ¿ìËÙÅÅÐòÊÇÄ¿Ç°»ùÓڱȽϵÄÄÚ²¿ÅÅÐò·¨Öб»ÈÏΪÊÇ×îºÃµÄ·½·¨¡£
(4) ÔÚ»ùÓڱȽÏÅÅÐò·½·¨ÖУ¬Ã¿´Î±È½ÏÁ½¸ö¹Ø¼ü×ֵĴóС֮ºó£¬½ö½ö³öÏÖÁ½ÖÖ¿ÉÄܵÄתÒÆ£¬Òò´Ë¿ÉÒÔÓÃÒ»¿Ã¶þ²æÊ÷À´ÃèÊö±È½ÏÅж¨¹ý³Ì£¬ÓÉ´Ë¿ÉÒÔÖ¤Ã÷£ºµ±ÎļþµÄn¸ö¹Ø¼ü×ÖËæ»ú·Ö²¼Ê±£¬ÈκνèÖúÓÚ"±È½Ï"µÄÅÅÐòËã·¨£¬ÖÁÉÙÐèÒªO(nlog2n)µÄʱ¼ä¡£
(5) µ±¼Ç¼±¾ÉíÐÅÏ¢Á¿½Ï´óʱ£¬Îª±ÜÃâºÄ·Ñ´óÁ¿Ê±¼äÒƶ¯¼Ç¼£¬¿ÉÒÔÓÃÁ´±í×÷Ϊ´æ´¢½á¹¹¡£