0\0\ 500 @ ???@@ ???@ 0′?U?4???Y?? l ?,XFEen `,|4§X l ` ??,XFEen?,|4§X l ` ??,X ??01k"? l ? `` ??,XE@6 l ??D? ?Jh*ü E??E?? 5.1 ? 5.2 ` ?? 5.3 ??D? ?Jh*ü 5.1 ?? 5.1.1 ?,Xn ` ?E¤1k 1. n ??/? *ü,XM24??4§X??à ?1E- n ? ?  n? n1 0?t4§&?,XYL$L? ü?81 n=0èí/?  0N? × úíèYè?Y?t(Mn,X4§&?>/?  è ' n>1êèJ-4§&?>ú? m? m>0?tfá,ìx,X$ L? T1è T2è ...è Tmè!￡t$L? ??é??+!8 ?1 ,??è?,XnE?&? ò 5-1 K L M E F G H I J B C D AA? (a) (b) (c) 4§&? DB2?,XY? ?J? ?J$? ,Xú43 /?4§&?? 4§&?,Xz 4§&?,XúD? 4?0?4§&?? ê$? z 0,X4§&?? M24?0?4§&? zá 0,X4§&?? 4§&?,X ? ? 4§&?,X ? 1è 4§&?$? ,X 1 2è1!82O|? ?,Xz ?Y4§&?z,X??? ?,X#?z ?Y4§&? ?,X??? Yc??′c? Vp?!￡é$?￠o ? ?,Xf ?1Y?n,XNNcèákf6èí/?Yc?è úí /?′c?? ?k  m? m1 0?éfá,ìx,X?,XL? ü? ü?4§Xè4§&?Kè,XG2? ? ?1*ü?￡G2? ￡E?ènV?? =$? ?? 4§&?$?,X /?E-t4§&?,X= $è5àE-t4§&? ?>/?=$,X ??? $- 1¤4§&? ,X$?,XY4§&?F?>/? A14§&?,X$-? /* ￠ 4§&?A14§&?C?XT,XY4§&?? ó à?t ??,X=$Kèfó? ?ó ?? ü à?,X4§&?f ?ó? 2. ?,X ?E¤1k  *ü?0? ? 1?XE??t? CreateTree (T) ? 2?#ù0N1 T ,X? ClearTree(T) ? 3???? ú0N TreeEmpty(T) ? 4?9? a4-n4§&?,X1 it=$ Child(T,node,i) ? 5?9? a4-n4§&?,X ?? Parent(T,node) ? 6?F! Z? Traverse(T) í?F! Z,X?U,?,XúM24??4§XE?E?F! ZE?/? 4??êè G9?k?t4??c???,XF! ZNNcY? /?è?/?cF! Zè GA?K? 4§&?è' aaq ? *ü à ,X?"?A?K?!￡é$?× o?/? acF! Zè G q 5.1.2 ?,X,|4§X 1. ??></"? ?,X ??></"??U￡E?,X4§&?,X ??G2?? ò 5-3 ?? info paren t 0 A -1 1B0 2C0 3D0 4E1 5F1 6G3 7H6 8I6 9J6 H I J E F G B C D A A B DC EF G HIJ 2O _n? #define MAX_TREE_NODE_SIZE 100 typedef struct { TEntryType info; int parent; } ParentNode; typedef struct { ParentNode item[MAX_TREE_NODE_SIZE]; int n; //?'!,X4§&?D,? }ParentTree; E-/?,|?"?,X(M&??R4§&?,X ??\??è ?R4§&?,X=$!¨EW ?L?? 1k"?r)?_? int Parent(ParentTree T,int node) { if (node<0||node>=T.n) return -2; else return T.item[node].parent; } 2. =$></"? =$></"??U￡E?,X4§&?,X=$G2??+b !￡t4§&?,X=$tDánè1y*üJò?,|4§Xè tE?p?_? ò 5-4 root 0 A 2 1 4 ^ 1 C ^ 2 B 3 5 ^ 3 E ^ 4 D 6 ^ 5 F ^ 6 G 7 8 9 ^ 7 H ^ 8 I ^ 9 J ^ ü CAá??èE-/?,|6?nV?? #define MAX_TREE_NODE_SIZE 10 typedef struct ChildNode{ int child; //A1=$4§&? ü?4èD4?,X?? struct ChileNode *next; //? ???t=$4§&? }CNode; typedef struct{ TEntryType info; //4§&?μC CNode *firstchild; //? ?1?t=$4§&?,X?J}TNode; typedef struct { TNode item[MAX_TREE_NODE_SIZE]; int n,root; //n?'!4§&?,XD,?è root 4§&? ü?4è D4?,X!5B }ChildTree; E-/?,|4§X,X(M&??R¤t4§&?,X=$!¨EW ??è?R ??!¨EWT?&oè1è ü??U,Xêíè ?1ú ??></"? `=$></"?4§ üCK9è Gú?4è D4?2?rt?t></ ??4§&?,X 3 parentè*ü9? /4§&?,X ?? ü?4èD4?,X!5B? 9? a4-n4§&?1 it=$,X?01k"?r)?? int Child(ChildTree T, int node, int i) { if (node<0||node>=T.n) return -2× p=T.item[node].firstchild; j=1; while (p&&j!=i) { p=p->next; j++;} if (!p) return -2; else return p->child; } 3. =$ó></"? =$ó></"?3?/?Jò?,|4§X?WE?E? ￡E?!￡t4§&?,X?t=$ `óμC9 ??4§&?Kè ,X ?G2?èJ4§&?4§X? firstchild item nextsibli ng Jè firstchild? ?A14§&?1?t=$,X?J\è nextsibling? ?A14§&?,X??tóè itemDB2? Y??_? ò 5-5 ^ H ^ I ^ J ^ ^ E ^ F ^ G ^ B ^ C D ^ A ^ T ü CAá??èE-/?,|6?nV?? typedef struct CSNode{ EntryType item; struct CSNode *firstchild,*nextsibling; }CSNode,*CSTree; void AllChild(CSTree T, CSTree p) //Eg?? p?J\?4§&?,XY=$μC { q=p->fisrtchild; while (q) { printf(3%c′,q->item); q=q->nextsibling; } } 5.2 ` ??` ?? 5.2.1 ` ??,Xn ` ?E¤1k 1. n n? ` ??  o?/??64§X?Wa?64§X ,X ?? ? 1?!￡t4§&???Y?é$?× ? 2?$?Yo ?ú? ` ??3 ?1*üE?&,X6?n? G?` ?? n ? n1 0?t4§&?,XYL$L? ü?' n=0êè/?0N` ? ?×' n>0êèYè?Y?t4§&?` ??,X èJ- 4§&?>ú??tfá,ìx,X$L?è?t0o$L?è o?t0 ?$L?è!￡t$L? ??t` ??? ò 5-6 G H D E F B C A ` ??,X 5/?6 ?? ? ò 5-7 (a) (b) (c) (d) (e) 2. ` ??,X ?E¤1k ? 1?XE??é` ?? CreateBTree ( BT) ? 2?#ù0N1 BT ,X` ?? ClearBTree(BT) ? 3???` ?? ú0N BTreeEmpty(BT) ? 4?9? a4-n4§&?,Xo=$ ` ?=$ LeftChild(BT,node)è RightChild(BT,node) ? 5?9? a4-n4§&?,X ?? Parent(BT,node) ? 6?F! Z` ?? Traverse(BT) ê` ??,X?Bü ` ??KY?? 5tG??U,X?Bü? ??Bü 1D ü` ??,X1 iT??Y 2i-1t4§&? ? i1 1?? ??,X1 1 ?Y?t 4§&?è1è i=1êè 2i- 1=21-1=20=1?0?? A?íY,X jè 10 j<i?0?è G1 jT??Y 2j-1 t4§&??0??81 j=i-1èí1 jT??Y 2j-1=2i-2t4§ &??+b ü` ??è!￡t4§&?,Xz?? 2è1 ? 1|D?1 i??,X4§&?tD1 i-1??4§&?t D,X 2áè G 2i-2*2=2i-1? ??Bü 2D#?z K,X` ????Y 2K-1t4§&? ? K1 1?? +?Bü 1 ?1k?è 17? K ???,X4§&?tDú ?? 20,21,22,23,...,2K-1?E-?t1 2!¨,X1!¨D ?è! nNM `,XAu1k@?? q qaaS n n ? ?= 1 *1 J a11?NMè an1 nNMè q!¨? ?1k èA1D?! KNM `? 12 21 2*1202 ?= ? ?? KK ??Bü 3D íb???é` ?? BTèVpz 0,X 4§&?tD n0èz 2,X4§&?tD n2èí n0=n2+1? A?a?A?z 1,X4§&?tD n1è4§&?D nè B` ??,XúD? ′ ü` ??èY4§&?,Xz ?bê1b 2è 14§&?D? n=n0+n1+n2 ? 1? a1,???úD? ü` ??èL8 4§&? êè!￡t4§&?F?Y?t￠T ??,Xú? ?è1è ,X4§&?tD naúD BKè,XG2?? n=B+1? ? ′ ü` ??èz 1,X4§&?{*ó 1túè z 2,X4§&?{*ó 2túè1úD B ?1></? B=n1+2n2? ú!8?·9T?èk? n=n1+2n2+1 ? 2? *ü? 1??￡ ?? 2??èJ4￡E?A×H ak? n0=n2+1? $μ` ??? Vp?t#?z K,X` ??1Y 2K-1t4§&?èíú W/? $μ` ?? ? ò 5-8 8 9 10 11 12 13 14 15 4 5 6 7 2 3 1 `<` ???Y?é#?z hèKY nt4§&?,X` ??è81úWa?é à#?z,X$μ` ??,XY4§&? Y￠T?è￠o ?,XNNcú?Eˉ> 4ê ?èèA1` ??,X!￡t4§&?ú?a$μ` ??4ê ? 1~n,X4§&? !5B??íhèí/?E-é` ?? `<` ?? ? ??Bü 4D KY nt4§&?,X`<` ??,X#?z ?log2n?+1?Jè ?log2n?,X4§pá?b log2n,X?? HD? A?a?A?KY nt4§&?,X`<` ??,X#?z Kèí B?Bü 2 ?1k?? 2K-1-1<n0 2K-1 úá1??0?t 1k? 2K-10 n<2K úá1?,XYNM à a1 2i,XíDèJ4￡E?ê 1T ak? K-10 log2n<K +!8 ?1k? ?log2n? =K-1?H)ú ak? K= ?log2n?+1? ??Bü 5D íbY nt4§&?,X`<` ??,XY 4§&?Y￠T?è￠o ?,XNNcEˉ> 4ê ?èíí? ??t4§&? i? 10 i0 n?èF?Y? ? 1?Vp i=1èí4§&? iE-é`<` ??,X è"u Y ??× úíJ ??4§&?,X4ê ? ?i/2?? ? 2?Vp 2i>nèí4§&? i"uYo=$× úíJo= $4§&?,X4ê ? 2i? ? 3?Vp 2i+1>nèí4§&? i"uY ?=$× úíJ ? =$4§&?,X4ê ? 2i+1? ?M6?ày*üD:&4?"?A?aE-t?Bü? ?àOjA?a? 2? `? 3?? ' i=1êè81 n1 3èí ,Xo? ?=$,X4ê ?ú?  2è 3×81 n<3èí "uY ?=$×81 n<2èí ú"u Yo? ?=$×1Tíb? 2? `? 3? ?0?? A??íbY,X 10 j0 i4§A??0?? G?4§&? j,X o=$4ê ? 2j× ?=$4ê ? 2j+1? ò 5-10 2i +2 2i 2i+1 2i+2 2i+3 i+1 2i 2i+1 ii i+1 +`<` ??,X4§X ?1,???4§&? i+1ê5ùa4§ &? i àè2?F? i4§&?,X ?{èê5ù i!b¤,X? ? 0?è i+1!b??,X?o0?? ?1,??è i+1,Xo? ?=$2?F? ü4§&? i,X=$ a M6è+b4§&? i,Xo? ?=$4ê ?ú? 2i ` 2i+1è 1è4§&? i+1,Xo? ?=$4ê ?ú? 2i+2 ` 2i+3è4￡ ¤ a@ ′? ?1k? 2(i+1) ` 2(i+1)+1è G4§&? i+1,X o=$4ê ? 2(i+1)× ?=$4ê ? 2(i+1)+1? ? ′` ??+ nt4§&?4??è1è' 2(i+1)+1>nèè 2(i+1)=nêè4§&? i+1 ?Yo=$è5à"u Y ?=$×' 2(i+1)>nè4§&? i+1?"uYo=$3"uY ?=$? 1TA?ak? 2? `? 3??0?? ?M6y*üTM6,X4§A?A?a? 1?? íb???t4§&? iè81 2i0 nèío=$,X4ê ? 2iè ?E?94§&? 2i,X ?? iè5à ?2i/2?=i×81 2i+10 nèí ?=$,X4ê ? 2i+1è ?E?94§&? 2i+1,X ?? iè5à ?(2i+1)/2? =iè+!8 ?1k?? 1?? 0?? 5.2.3 ` ??,X,|4§X ` ??3 ?1G?*ü?/?,|???NNc,|4§X `Jò?,|4§X? 1. NNc,|4§X E-/?,|4§XE?*üb`<` ???J,|6? ?*ü?4?E24á,X,| )Y';`<` ??,X!￡t4§ &?4ê ?,XNNc,4§&?Y???M6?é` ?? ?J ,ìh,X,|4§X? ò 5-11 012345678 12345678 8 4 5 6 7 2 3 1 ? 1?XE??é`<` ?? void CreateBTree(QBTree *BT,EntryType item[ ],int n) { if (n>=MAX_TREE_NODE_SIZE) n=MAX_TREE_NODE_SIZE-1; for (i=1; i<=n;i++) BT->item[i]=item[i]; BT->n=n; } ? 2?9? a4-n4§&?,Xo=$ int LeftCHild(QBTree BT,int node) { if (2*node>BT.n) return 0; else return 2*node; } RightChild(BT,node)aE-t?02OèA?5ù ?A?-7?> `?? ? 3?9? a4-n4§&?,X ?? int Parent(QBTree BT,int node) { if (1<=node&&node<=BT.n) return i/2; else return -1; } ê Jò?,|4§X üNNc,|4§Xèy*ü4ê ?></2?,X!5B ? 2?Kè=$ê ??,XG2?è ′!8íbM2`<` ??è L??Uú0N5,X!5B*ü(Mn,X0ú ??>9è810N54§&?EW ?è??E??0NKèy*ü)[,X?L!? üE-/????è hA15×<%S*üJò?,|4§X?  ??,X` ??4§&?4§XV?/? Lc hild item Rc hild ò 5-12 Jè Lchild ` Rchildú?? ?A14§&?o=$ ` ?=$,X?J\è itemDB2?,XY?? ü CAá??,X 2O _n? typedef struct BTNode{ EntryType item; struct BTNode *Lchild,*Rchlid; }BTNode,*BTree; ?M6?é` ?? ?,ìh,XJò?,|4§X? ò 5-13 G H D E F B C A ^ G ^ ^ H ^ ^ D ^ E ^ F ^ B ^ C A BT E-/?,|4§X,X(M&??R=$4§&???è ??!¨ EW ?L?? ′!8è81L??UNe4 ?R ??è ?14-!￡t 4§&?#?t?t? ? ??4§&?,X?J\ 3èJ4§&?4§XV ?/? Lchild item Rchil d Parent ò 5-14 YG` ?? üJò?,|4§X?,X?01k"?ú üLc a?4?? 5.2.4 F! Z` ?? ` ???/?M24??,XDB4§Xè üíWEˉ> ? 0êèL??UE??í!￡tDB2?r??0èE- , ü?t?0NNcK?Nlè+!8¤?Z` ??,XF! Z ?0?A?F! Z` ??Y¤/?NNcA?K?` ?? ,X!￡t4§&?? ?è?? ?,XE?/??E-G?,XA?K? ?1 Eg??!¨EW?è??1,?2?Y?11 ?/??0? ` ??,XF! Z??ú??2O??2OY ?o$ ? ` ?$?YtF?úEˉ> A?K?× o?2OY ?A?K?? ?M6?àúú?Eˉ> A|A?? 1. Y ?o$? ` ?$?YF?úEˉ> F! Z F! Z` ??,XNNc, ü?M6 6/? ?6?? TLR? o ?? , TRL? ?o? LTR?o ?? , RTL? ? o? LRT?o ? ? , RLT? ?o ? Jè TRL? RTL ` RLTY/?NNc üo ?$? Kè  ?$? ao$?èE-a?ào a ?,X4? á àè ′!8èTTá\G?*ü?-?,XY/?NNc TLR? LTR ` LRT B A?K?,X!5Bá àú?>/?cF! Z?cF! Z ` acF! Z? ? 1?cF! Z 81` ??0Nèí4§3F! Z?0× úí A?K? 4§&?× cF! Zo$?× cF! Z ?$?? ? 2?cF! Z 81` ??0Nèí4§3F! Z?0× úí cF! Zo$?× A?K? 4§&?× cF! Z ?$?? ? 3? acF! Z 81` ??0Nèí4§3F! Z?0× úí acF! Zo$?× acF! Z ?$?× A?K? 4§&?? ?M6?é` ?? ?J4￡E?Y/?F! Zk,X,ìhc?? G H D E F B C A cc?? ABDGCEFH cc?? DGBAECHF acc?? GDBEHFCA ò 5-15 ?M6?àa4-??/?F! Z` ??,X?"?? ? 1?í?é` ??cF! Zêè81?àú` ?? ù Yo$?,XY4§&?!b 4§&?,Xo{è ?$ ?,XY4§&?!b ?{,X6?4? è ?1í!￡t 4§&?.?5 V4?è???M6,X"G4?Tè+!8k ,XNNcA1` ??,XcF! Zc?? D G B A E C H F G H D E F B C A ò 5-16 ? 2??)?é` ??F? ?1úW,XêF?EB§*ü? 54?4? ?9è?àúW/?` ??,Xù4?èE-5ù 4?íb)ú?·` ??,XF! ZE?/?\Y*ü? G H D E F B C A ò 5-17 +!8 ?1,???? 1?F! Z?0rLTúM24?? 4§X4??ê,XE?/?èJ4§p4??c?èJ BG?*ü ,XF! ZNNcú?/?cc??cc?ê acc ?×? 2?F! Z?0?tE?&,XE?/?è ′!8èE-Y/? F! Z?0,X1k"? ?1*üE?&?Dr)?? ? 1?cF! ZE?&1k"? void PreOrder(BTree BT) { if (BT) { Visit(BT); PreOrder(BT->Lchild); PreOrder(BT->Rchild); } } ? 2?cF! ZE?&1k"? void InOrder(BTree BT) { if (BT) { InOrder(BT->Lchild); Visit(BT); InOrder(BT->Rchild); } } ? 3? acF! ZE?&1k"? void PostOrder(BTree BT) { if (BT) { PostOrder(BT->Lchild); PostOrder(BT->Rchild); Visit(BT); } } 2. Y ?F! Z` ?? r)??"?￠T?è!￡￠o{ ?{ q ?A?K?!￡t4§&???M6?àú4-??é` ?? ?J Y ?NNcA?K?J!￡t4§&?,XF! Zc?? G H D E F B C A ò 5-19 Y ?F! ZA1` ??,Xc?? ABCDEFGH ` ??*üNNc,|4§X></êèYF! Z,X1k"?r)? A 1 B 3 4 C D 5 6 E F 7 8 G 01234567 ABCDEFG (a) A 1 B 2 3 C D 4 E 6 7 F (b) 01234567 ABC#DEF ò 5-20 void LevelOreder(QBTree BT) { for (i=1;i<=BT.n;i++) if (BT.item[i]!=??) Visite(BT.item[i]); } ` ??*üJò?,|4§X></êèYF! Z,X1k"?r)? A?K?E?/?￡E?V?? lA?K? 4§&?èJúA14§&?A?)?9× l81A?),XY4§&?F???)ú`!?èí4§3F! Z? 0× úíG?á???0? l a?A?)1?tE?"uYA?K?=$,X4§&?è81W Yo=$èíA?K?o=$èJúA?)?9×81W Y ?=$èíA?K? ?=$èJA?)?9? üE-t1k"?èhS*ü?tKó?4§X`?E-NM? 0?A?A?)A?K?4§&?9Kó?0×5à a?A?),X 4§&??Kó?0?E- ?9è?à,X1k"? ?1￡ E????6?? ? 1?A?K? 4§&?èJú 4§&?9Kó× ? 2?'Kó?á0NêèG?á???0? l ￠Kó?E???t4§&?× l 81JYo=$èíA?K?o=$èJúJo=$9Kó× l 81JY ?=$èíA?K? ?=$èJúJ ?=$9Kó× void LevelOrder(BTree *BT) { if (!BT) exit; InitQueue(Q); p=BT; //??ê Visite(p); EnQueue(&Q,p); //A?K?? 4§&?èJú 4§&?9Kó while (!QueueEmpty(Q)) { //'KóM20NêG?á;> ???0 DeQueue(&Q,&p); //?Kó if (!p->Lchild) {Visite(p->Lchild);EnQueue(&Q,p- >Lchild); //?)úo=$ if (!p->Rchild) {Visite(p->Rchild);EnQueue(&Q,p- >Rchild); //?)ú ?=$ } } 5.2.5 L _` ??,X?01k"? 1. Eg9?t` ??,Xcc?èXE?E-é` ?? Z±A? ? XE??à?,X` ??è üK9 E-é?,Xcc?êèL??U üY0N` ??,X!5BT ?>9?t(M!^,X+0úè!¨Vè μ?? ü1k"?èL??Uí !?tEg9,X+0úEˉ> ??èVpíh,X+0ú μ?èí ü,ìh,X!5BTXE??é0N` ??× úíè???t ?4§&??Ht1k"?4§X1cF! ZE?&1k"? ?.è ` ??4§&?Kè,X?J\E2yE?E??J\ ?D üE?& A×*üE¨ 2ê`?? ?1k"? 5-12D BTree Pre_Create_BT( ) { getch(ch); if (ch==μ?) return NULL; //XE?0N? else { BT=(BTree)malloc(sizeof(BTNode)); //XE??4§&? BT->data=ch; BT->lchild =Pre_Create_BT( ); //XE?o$? BT->rchild =Pre_Create_BT( ); //XE? ?$? return BT; } } 2. Au1k?é` ??,X ê$4§&?D,? E-t?0 ?1S*üY/?F! ZNNc,X?)?/?è ? L??UúA?K??0 ????A14§&? ú ê$4§&?è Vp ê$4§&?ú3t <t 1 G ???M6E-t1k"?y *ücF! Zr)?,X? ?1k"? 5-13D void Leaf(BTree BT,int *count) { if (BT) { Leaf(BT->child,&count); //Au1ko$?,X ê$4§&?tD if (BT->lchild==NULL&&BT->rchild==NULL) (*count)++; Leaf(BT->rchild,&count); //Au1k ?$?,X ê$4§&?tD } } ê x6` ??,Xo ?$? A???0 ?1y*üY/?F! ZNNc,X?)?/?è ? ¤/?F! ZNNcr)?CK9èt???o?5àYo?0 íá' èW ?6?S*üJ,X?/?ê?/?F! ZNNc?ú ` ??Y4§&?,Xo ?$?Eˉ> x6E-t?02 bE-2O??? void change_left_right(BTree BT) { if (BT) { change_left_right(BT->lchild); change_left_right(BT->rchild); BT->lchild<->BT->rchild; } } ê 4 "` ??,XP?z E-t?0S*ü acF! Z!¨EW0ú ü?à"?·` ?? P?z,X?4è???Ojú?"?o ?$?,XP?zè ü !8 ?.Tk?A1é?,XP?zè Go ?$?EW?,XP?z t 1? int hight(BTree BT) {//h1 ` h2ú?1 BT ,Xo ?$?,XP?z if (BT==NULL) return 0; else { h1=hight(BT->lchild); h2=hight(BT->right); return max{h1,h2}+1; } } 5.2.6 ???ka` ??,XE@6 1. ???kE@6?` ?? ú?é?E@6?` ??,X?"?? ú?é?E@6?` ??rLTúE-é?*ü= $ó></"?,| G ?è!8êè?,X!￡t4§&??? Y?t?J\??t?J\? ?1?t=$è o?t? ? ? ?{1?tó?'4úE-?t?J\,?0` ? ?,Xo=$? `=$ ??J\êè?é` ??? Z? (M&???é?E@6?` ?? aè 4§&?"uY ?= $? ú?kE@6?` ??,X?"?a?é?E@6?` ? ?,X?"?2Oè ?^?kY?,X 4§&?,?0 óG2?èJíJ,X!￡é?qq Eˉ> E@6? 2. ` ??E? s??ê?k E-tE?/?rLT???kE@6?` ??,XEúE? /?è GúA1` ??,?0?ê?k,X=$ó></ "??!¨Vè81` ??0Nè?30N× úíè+` ? ?,X 4§&???èê ??J\ ??CDè,è0NèEè4￡ ,X4§&?tD,ìh?k ??,XéD×81¤t4§&?,X o?J\M20NèAèa-t4§&? ü??Y=$èJè￠ ` ??A14§&?o?J\?4§&???èê ??J\ ?? CDè,è0NèEè4￡,X4§&?tDE-t4§&?,X=$ D,?? 5.3 ??D? ?Jh*ü ??D? ?Jh*ü 1ê ??D?,Xn ò 5-26 G H D E F B C A ü` ??è?t4§&? o?t4§&?Kè,Xú X?E-?t4§&?Kè,X C?X ? üC?XT,XúD,?>/? C?XKSz ?*ü@? ? ></? ∑ = = n k kklwWPL 1 ú,XC?XKSz??,X` ??/? ??D` ?? ê ?ì` ?? ? 54 8 ò 5-27 ê$4§&?ú,X` ?? ?M6?àA|A?????6aú,XC?XKSz Kè,XG2??A?Y 6tú? {3è 6è 9è 10è 7è 11}è1E- 6t0 ê$4§&?,X ?1XE?? ?M6Yé` ??? 3 6 7 9 10 11 (a) ò 5-28 11 10 9 7 6 3 11 10 3 6 7 9 (b) (c) E-Yé` ??,XúC?XKSzú?? WPL1=10*2+11*2+3*3+6*3+7*3+9*3=117 WPL2=3*1+6*2+7*3+9*4+10*5+11*5=177 WPL3=9*1+7*2+6*3+3*4+10*5+11*5=158 XE? ??D?,XE?/?? ? 1?ú4-n,X nt {w1,w2,...,wn}0 nt 4§&? ,XXE??tKY né` ??,X?k {T1,T2,...,Tn}è J!￡é` ?? ?Y?t 4§&?× ? 2? ü?kEY a?é 4§&???,X` ?? 0o ?$?XE??é?` ??è?` ??,X 4§&? E-?é? ,X `× ? 3? ü?kèúTM6EY?,XE-?é ?? ,X` ??￠?k?L8èJú???XE?,X` ??t 9?k× ? 4?G?áTM6? 2? `? 3?è,è?k ?Y? é` ??!6?E-é` ?? ??D?? A?Y?4? {5,29,7,8,14,23,3,11}è?M6?àú y*üE-4?$è/XE? ??D?,XE?/?? 1?!9?1E- 8t0 4§&?,XXE?KY 8é?,X?k 5 29 7 8 14 23 3 11 1`!9?￠EY??t ,X??,X? 3è 50 o ?$?XE??é??èJúE-?é?￠?k? L8èJú??#?tEˉ ? 3 5 29 7 8 14 23 11 8 1Y!9?G?á1`!9E?/?è,è?k ?Y?é?!6 EY? 7è?8 29 14 23 11 7 8 15 3 5 8 29 14 23 7 8 15 8 3 5 19 11 EY? 8è 11 EY? 14è 15 EY? 19è 23 3 5 29 15 7 8 29 14 8 42 23 19 11 EY? 29è 29 7 8 15 58 29 29 14 3 5 8 42 23 19 11 EY? 42è 58 100 7 8 15 58 29 29 14 3 5 8 42 23 19 11 E-1TE? 8t ê$4§&?X? ,X ??D?èW,Xú,XC?XKSz? WPL=(2329)*2+(11+14)*3+(3+5+7+8)*4=271 5.3.2 ?n? ü\?K?Nl,X?)úE?/?èL??UEˉ> ?G￡,X5ê ??èE-o??4§X,XA?Au,èyE ?-/?c,X;>  )[?_Vè4ê ?t/?cèú,Rú E@6?ht14{ Eg???? ?6?AxE-t/?c\1T )èJè\? ? 1*ü??6?4êm?9? if (socre<60) printf(3bad′); else if (socre<70) printf(3pass′); else if (score<80) printf(3general′); else if (score<90) printf(3good′); esle printf(3very good′); ürLh*üèTT ?túD!?,Xú×Já  ?,X??M6 ü? ?5×A?¤K?Aò/?,X ?úD!?,X ú×??? ?M6?ày*ü ??D??R?é?G?n?è G,X!¨EW ?D??,X?n?? úD 0~59 60~69 70~79 80~89 90~100 !¨_ 0.05 0.15 0.40 0.30 0.10 ò 5-29 very good bad pass general good <80 <90 <70 <60 Ojèú ?úD!?,X!¨_D0XE??é ??D?? very goodbad pass general good 600 ...0 69 ...<59 800 ...0 89 700 ...0 79 ò 5-30 ò 5-31 <70 <90 <80 general good very good bad pass <60 5.3.3 !4?4ê-? ü+ [?EgèL??Uú+ [?)?,X!￡t+0úEˉ > `Eˉ 4ê-?? üA?Au4ê-?êL??UFI\?t sí? ? 1? ￥E???Eg,X`Eˉ 4ê-?èy ??·-? a?NO KY ??è G?·-?4§pa ￥E?? ￥E?,X+ [`<?  ×? 2? ￥E?,X`Eˉ 4ê-? ?6? -á??M6?à? 4??/?4ê-?,X??? 1.1KS4ê-? E-/?4ê-???,X(M&?!￡t+0ú,X4ê-?KSz,ì à ?4ê-?KSz!￡t4ê-? ?,X`Eˉ !D??A? +0úL? ? ?Y 4t+0ú Aè Bè Cè Dè*ü`Eˉ ?!>< /,X4ê-?ú? 00è 01è 10è 11?81)? üY?!?+ [ ? ABACCDAèíh ￥E?`Eˉ c?? 00010010101100èKSz 14!?'y ?y E- !?+ [ aèúY?!?!?Eˉ> A￥-??E-/?4ê-?,X(M&? A￥-?1T )èKY ??è4ê-?KSzJá?-á ,X? 2.á1KS4ê-? ü?E?+ [êèZSJ`Eˉ !D ?6?  ?è ?1ú!￡t+0ú,X4ê-?A?Auá1KS,XèS*üNe zEWP?,X+0úúG!?t,ìí!¨EW-á,X4ê-?èS*üNez EW",X+0úúG!?t!¨EWKS,X4ê-??_Vè ?1 Aè Bè Cè D ˉt+0úú?úG! 0è 00è 1è 01èJ ?úT E?+ [*ü`Eˉ c?? 000011010 ￥E?èJKSz ?Y 9 t`Eˉ !èLcú9Z?tK?Nlèy ?yE- !?+ [ a′"?Eˉ> A￥-?è ′′"??n!M6 4t 0 4t Aè 1t B? 2t AèE? 2t Bè GA￥-?á ?è ′!8E- /?4ê-??"?á ?S*ü? ? 1?y*ü+0úL?!￡t+0ú,XS*üNe)[0 XE??t ??D?× ? 2?￠ 4§&???è!￡t ê$4§&?C?XT,X oúC\ 0è ?úC\ 1èJ￠  ê$? ?6? A1 ê$4§&?,X4ê-?? A?Y?t+ [+0úL?Y 8t+0úè!￡t+0ú,X S*üNe)[ú? {0.05,0.29,0.07,0.08,0.14,0.23,0.03,0.11}è)?1!8_A? Au ??D4ê-?? ??D4ê-?A?AuE?/?? ? 1???Au1kèúY+0ú,XNez,1 100èS JE@6?H _DL? üèk {5,29,7,8,14,23,3,11}× ? 2?1!8L? ü,XD0 ê$4§&?,XXE? ?é ??D?èV ò 5-27/× ? 3?+!8 ??D?*ó? ??D4ê-?èV ò 5-28 /? ? ak?!￡t+0ú,X4ê-?? +0ú +0ú,XS*üNe)[ 4ê-? 7 0.05 0111 8 0.29 10 9 0.07 1110 : 0.08 1111 ; 0.14 110 < 0.23 00 = 0.03 0110 > 0.11 010 1T,X 7 ～> ú?·>< 8 t+0ú ? !¨Vè ￥E??!?4ê-?? 0000011011010010è y ? ?1?.B E?E?A￥-?k?<<=;8>?