D, w) Voi m6i lu~ tr mftta co th€ ap d1,lngtre nH de suy ra nhung thuQctinh
Ope n~ {H}; IIdanhsach dInhmd ban dilu chIco dInh xu[{tphat
Close ~ {}; II danh sach dInh dong
g(R) ~ 0; II dQ dai lQ trlnh de"nH la 0
f(R) ~ h(R);11 dQ dai lQ trlnh u'oc tinh tU H de"n m1;lctieu la h(R)
found ~ false; II bie"n ki€m tra qua trlnh Hm Wi giai
Bu'6c 2: Th1;l'chi<$nqua trlnh l~p d€ tlm Wi giai t6i uu.
While (Open :1={}) do Begin
Bu'oc 2.1: ChQn ffiQt dInh N trong Open voi u'oc tinh du'ong di f nha nh[{t.
Bu'oc 2.2: Chuy€n N tu danh sach Open sang danh sach Close. Bu'oc 2.3: if (N la ffiQtm\lc tieu) then
,. Begin
Found ~ true; Break; II Ke"t thuc qua trlnh l~p End
Bu'oc 2.4: else II N kh6ng la ffiQtm1;lctieu Begin
Duy<$t qua cac dinh ke" S cua N (Wc la co cling r n6i N va S) ma S ~ Close, ling voi m6i S ta xet cac tru'ong hQp sail:
1. S ~ Open: Tinh
B6 sung S vao Open; 2. S E Open:
If g(N) + WeT)< g(S) then Begin
g(S) +- g(N) + WeT); f(S) +- g(S) + h(S);
C~p nh~t thong tin v~ dinh ke' tntoc cua S tren 19 tdnh; end
End
End II Ke't thuc vong l~p while Bu'oc 3: Ki§m ITake't qua vi~c tlm kie'm.
If Found then Ke't qua la tlm duQCWi giai t6i u'u va thie't l~p loi giai Else Ke't qua la bai tmln khong co Wi giai.
Menh d~ 2.7 Thu~t tmln 2.5 cho loi giai la dung va co d9 phuc t~p
O(1A12.IDI2).
Vi du 2.12: Gia sa ta co m~ng suy di€n co trQng sO'(A, D, w) nhu sail: A = {A, B, C, a, b, c, p, S, ha, hb, hc}. D ={ fl: A + B + C=180; B: b/sin(B) =c/sin(C); ~ f2: a/sin(A) =b/sin(B); f4: a/sin(A) =c/sin(C); f5: 2*p =a + b + c; f6: S=a*ha/2; f8: S=c*hc/2; n: S =b * hb/2; f9: S = sqrt(p*(p-a)*(p-b)*(p-c)); fl1: hb =a *sin(C); flO: ha =b*sin(C); fl2: hc =b*sin(A). }. w(fl) =2; w(f5) =3; w(f2) =wen) =w(f4) =2*c2 + 2; w(f6) =wen) =w(f8) =2; w(f9) =c1 + 6; w(flO) =w(fl1) =w(fl2) = c2 + 1. '"
Trang do c1 va c2 la cac h~ng s6 dudng voi c1 » 1 va c2 » 1.
Xet bai roan H -+ G voi H ={a, b, B} va G ={S}. Tren m~ng suy di€n (A,
D), n€u ap d\lng thu~t roan 2.4 ta co th@tlm duQc mQt Wi giai 5 ={f2, fl, n,
f5, f9}. Tren m~ng suy di€n co trQng s6 (A, D, w) Wi giai 5 co trQng s61a
w(S) =4*c2 + c1 + 15. Ap d\lng thu~t roan 2.5 d@tlm Wi giai tren m~ng (A,
D, w) ta co th@ tlm duQc mQt Wi giiii t6i u'u 5' ={f2, fl, flO, f6} vdi trQng s6
la w(5') =3*c2 + 7.
,.. , ,.. '" '" ?,..~
2.5T~P H<)P SINH VA VI~C KIEM DfNH, BO SUNG GIA THIET
Trong ml,lcn~y se xem xet v6 sv thua hay thi€u d6i vdi gia thi€t cua bai roan
H -+ G tren mQt m~ng suy di€n (A, D) va trong truong hQp c~n thi€t thl tlm cach di6u chinh gia thi€t H. Trudc h€t ta dn xet xem bai roan co giai duQc hay
khong. Truong hQp bai roan giai duQcthl gia thi€t la duoTuy nhien co th@xay ra tlnh tr~ng thua gia thi€t. f)@bi€t duQc bai roan co th~t sv thua gia thi€t hay khong, ta co th@dva vao thu~t roan tlm ffiQtsv thu gQn gia thi€t sail day:
Thuat toan: TIm mQt sVthu gQngia thie't cua bai roan.
Nhap : M~ng suy di€n (A,D), Bai roan H-+ G giai duQc,
Xua't: t~p gia thi€t ffidi H' c H t6i ti@uIDeo thli tv C.
~ '
Thua t roan :
Repeat
H'+-H;
for x E H do
if H - {x} -+ G giai duQc then H +- H - {x};
Trang thu~t to(ln tren ne'u t~p gia thie't moi H' th~t st;tbaa ham tfong H thl bai roan bi thita gia thie't va ta co th§ bot ra tit gia thie't H t~p hQp cac bie'n kh6ng thuQc H' , coi nhuIa gia thie't cho thita.