function [nc] = ncutf(g)3 H5 ^' n+ @- A3 w5 k# Z
%求割点的算法 g为邻接矩阵 nc为割点的集合 1 w7 ^, H# V, Gn=size(g,1);, x! { e, a$ V
if n>=3 8 {* x# g" E" l; J) k$ U a=sum(g); ! I! ]( I* D; n, a b=sum(a==2); f5 O' J# C2 H+ {3 Z2 W if b==n1 w/ w8 h1 y7 r; l1 t' E
fprintf('本图为圈,无割点。n')0 W: H* C J8 h% ~" \7 ?
nc=0; 2 @- w. }7 T) t1 u end! J9 q+ y f# o8 b3 d: w/ P
else( x q3 X* G) d0 M1 A
[w,k]=dfs3(g); " C" Z3 G7 ^6 o %nc=[]; . T7 Q: P4 P1 A4 @ nc=isncf(w,k);& }9 u6 |3 I8 y$ J+ V. y* h
n=size(g,1); @* L) E. U3 L5 t* ^$ B for i=1:n/ V7 m5 u7 [0 m! Q2 g r
for j=1:n" E( D# G! I3 t- d6 a5 f
if w(i,j)>1 & k- l H- U6 `; L, }- N/ } if k(i)>k(j) 9 i3 d4 I$ X) J; ~) F# b5 l g(i,j)=2;# A" u+ }$ M5 |/ j5 A# L
else 3 h/ N, c- y2 i" d g(i,j)=3;( i% s- H; ^! ?3 t) o$ b+ W! `4 ^0 ?
end3 @0 ?! h& Q, n) H; O
end( O9 w) w1 C0 v8 S1 d
end , r/ G2 D- @% |4 y end / A0 t7 _0 o" j 0 O2 c) B7 Q7 s/ w& t
for i=1:n 2 m9 R; X% n' h r f1=find(g(i,==2);! ]3 e/ @- C5 N5 @( i4 m
f2=find(g(i,==3);$ F/ X- B5 r% }4 w
f=union(f1,f2); * H0 m* G- O, I- ~8 _# U8 f l(i)=min([k(f) k(i)]); ! a& t4 Z1 b6 O9 g+ T; N end( K2 p: J5 x/ t4 ?3 a" d
- @3 y# Z5 \8 o for i=1:n5 g1 O% P4 U. w
for j=1:n+ l; C! |/ F( T) K
if g(i,j)==3 & k(i)>1&l(j)>=k(i)9 G: v ?" s5 y& r9 g5 d3 I$ U
nc=union(i,nc); 2 P* [5 k8 t, g" M4 M- o! f! z end 5 b/ k* n% Z0 ], V/ I end T: V( Q: \/ e5 B B9 D
end' D8 R* b6 y% S
end# c8 q% @2 w, `
end 3 O3 G3 I5 M) x8 @% n 7 F, |- j) A+ |' ?7 B% x: K! e ]" r2 O4 m
function nc=isncf(w,k); h. ]( }! ]$ U' v) M z4 B
nc=[]; & R* W3 M, A9 ~8 D: N2 K7 g t=zeros(size(w)); # O2 J& ^! a! F$ R" a n=size(w,1); " v1 f6 w8 ]/ _ a=find(w~=0);6 Y3 O' u3 U9 |* ~$ b" C# G
for i=1:length(a) . c# N- E' N% H5 p* t d(i)=w(a(i));' D" F5 N5 I! U
if a(i)/n>floor(a(i)/n) - F& ~2 H/ @' ?0 e! `5 e t(i)=floor(a(i)/n)+1;- S/ [/ O X- s+ q I
else, |4 Y% z" e9 S" [& m2 P8 |! V
t(i)=floor(a(i)/n);/ z2 x+ l4 W+ T/ J- d0 L
end2 W# L5 v5 j% Z
t1(i)=mod(a(i),n); . p; S$ D/ C# [1 x if t1(i)==0 5 N! u/ ^& D- g' l8 o) \! a t1(i)=n; ( ]- \6 u! I7 ]8 x! \ end 0 t0 [. G+ k- y J end p+ M) [5 t. H0 o1 J1 S- I [b,c]=sort(d); . h$ u! g) A+ k' D Y p=[1];pc=0; 9 B/ g! c" h2 R% \7 Q6 w for i=1:length(a)" z Z. j; H+ _# e) A
if k(t1(c(i)))<k(t(c(i)))( t8 Z/ n# z1 _. T: m4 a
p=union(p,t(c(i)));% l0 b. r z1 v3 r
t(t1(c(i)),t(c(i)))=3;7 ?1 Y2 n( s3 K; e
end ! L W q* _4 d# H9 {6 O if pc==00 G; @7 U+ i a) [- ]9 l
tc=isempty(setdiff([1:n],p));$ y+ t* ~6 b3 e. J# d4 m: c
if tc & X, f+ w5 n; \7 c t0=sum(t(1,==3);3 B7 H- g$ V) h; p" [7 O
if t0>=2- _3 p \2 f' ~( N
nc=union(nc,1); . I& e: _/ G) a/ g- H end 9 b/ S# Y: G0 s) w: t/ } break;& Y8 Z" [) x- C+ L; r2 Q2 t
end / R P; Y$ k1 [0 J3 M end: }, a* t' K( n8 d- Q0 R
end# G) Q5 W$ [& Q2 j- k
2 C+ \* d# w* k. c: }