📄 usaco 3_4_1 closed fences题解_leokan的blog.mht
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<DIV class=3Dmodbox id=3Dm_blog>
<DIV class=3Dtit>USACO 3.4.1 Closed Fences=CC=E2=BD=E2</DIV>
<DIV class=3Ddate>2008=C4=EA02=D4=C213=C8=D5 =D0=C7=C6=DA=C8=FD =
12:54</DIV>
<TABLE style=3D"TABLE-LAYOUT: fixed">
<TBODY>
<TR>
<TD>
<DIV class=3Dcnt>
<H2>USACO 3.4.1 Closed Fences</H2>
<P class=3Dt_msgfont>Closed Fences<BR><BR>A closed fence in the =
plane is a=20
set of non-crossing, connected line segments with N corners (3 =
< N <=20
200). The corners or vertices are each distinct and are listed in=20
counter-clockwise order in an array {xi, yi}, i in (1..N). =
<BR><BR>Every=20
pair of adjacent vertices defines a side of the fence. Thus {xi yi =
xi+1=20
yi+1} is a side of the fence for all i in (1..N). For our =
purposes, N+1 =3D=20
1, so that the first and last vertices making the fence closed.=20
<BR><BR>Here is a typical closed fence and a point x,y:=20
<BR><BR><BR> =20
* x3,y3<BR> =20
=20
x5,y5 / \<BR>x,y * * /=20
\<BR> =
/ \=20
/ \<BR> =20
/ * \<BR> =
x6,y6* x4,y4 =20
\<BR> | =
=20
\<BR> =20
| =
\<BR> =20
x1,y1*----------------* x2,y2<BR><BR>Write a =
program=20
which will do the following: <BR><BR>Test an ordered list of =
vertices=20
{xi,yi}, i in (1..N) to see if the array is a valid fence. =
<BR>Find the=20
set of fence sides that a person (with no height) who is standing =
in the=20
plane at position (x,y) can "see" when looking at the fence. The =
location=20
x,y may fall anywhere not on the fence. <BR>A fence side can be =
seen if=20
there exists a ray that connects (x,y) and any point on the side, =
and the=20
ray does not intersect any other side of the fence. A side that is =
parallel to the line of sight is not considered visible. In the =
figure,=20
above the segments x3,y3-x4,y4; x5,y5-x6,y6; and x6-y6-x1,y1 are =
visible=20
or partially visible from x,y. <BR><BR>PROGRAM NAME: =
fence4<BR>INPUT=20
FORMAT<BR>Line 1: N, the number of corners in the=20
fence <BR>Line 2: Two space-separated =
integers, x=20
and y, that are the location of the observer. Both integers will =
fit into=20
16 bits. <BR>Line 3-N+2: A pair of space-separated =
integers=20
denoting the X,Y location of the corner. The pairs are given in=20
counterclockwise order. Both integers are no larger than 1000 in=20
magnitude. <BR><BR>SAMPLE INPUT (file fence4.in) <BR>13<BR>5 =
5<BR>0 0<BR>7=20
0<BR>5 2<BR>7 5<BR>5 7<BR>3 5<BR>4 9<BR>1 8<BR>2 5<BR>0 9<BR>-2 =
7<BR>0=20
3<BR>-3 1 <BR><BR>OUTPUT FORMAT<BR>If the sequence is not a valid =
fence,=20
the output is a single line containing the word "NOFENCE".=20
<BR><BR>Otherwise, the output is a listing of visible fence =
segments, one=20
per line, shown as four space-separated integers that represent =
the two=20
corners. Express the points in the segment by showing first the =
point that=20
is earlier in the input, then the point that is later. Sort the =
segments=20
for output by examining the last point and showing first those =
points that=20
are earlier in the input. Use the same rule on the first of the =
two points=20
in case of ties. <BR><BR>SAMPLE OUTPUT (file fence4.out)<BR>7<BR>0 =
0 7=20
0<BR>5 2 7 5<BR>7 5 5 7<BR>5 7 3 5<BR>-2 7 0 3<BR>0 0 -3 1<BR>0 3 =
-3=20
1<BR><BR><BR><BR>Closed =
Fences<BR><BR>=B1=D5=BA=CF=B5=C4=D5=A4=C0=B8<BR><BR>=D2=EB by=20
=
Jeru<BR><BR><BR>=D2=BB=B8=F6=B1=D5=BA=CF=B5=C4=D5=A4=C0=B8=CA=C7=C6=BD=C3=
=E6=C9=CF=B5=C4=D2=BB=D0=A9=B2=BB=CF=E0=BD=BB=B5=C4=CA=D7=CE=B2=CF=E0=C1=AC=
=B5=C4=CF=DF=B6=CE=D0=CE=B3=C9=B5=C4=B6=E0=B1=DF=D0=CE=A3=AC=D3=D0N=B8=F6=
=BD=C7(=B6=A5=B5=E3) (3 < N <=20
200)=A1=A3 =
=B6=A5=B5=E3=B2=BB=D6=D8=BA=CF=A3=AC=CB=FC=D2=D4=C4=E6=CA=B1=D5=EB=B7=BD=CA=
=BD=D2=D4=CA=FD=D7=E9{xi, yi}=B8=F8=B3=F6(i=3D1,2,...,N)=A1=A3=20
=
<BR><BR>=C3=BF=D2=BB=B6=D4=CF=E0=C1=DA=B5=C4=B6=A5=B5=E3=B6=BC=CA=C7=D2=BB=
=CC=F5=D5=A4=C0=B8=A1=A3=D2=F2=B4=CB=B9=B2=D3=D0N=CC=F5=D5=A4=C0=B8 =
(=B6=A8=D2=E5xN+1=3Dx1, yN+1=3Dy1)=A1=A3=20
=
<BR><BR>=D5=E2=C0=EF=D3=D0=D2=BB=B8=F6=D5=A4=C0=B8=B5=C4=C0=FD=D7=D3=BA=CD=
=D2=BB=B8=F6=B5=E3x,y:<BR> =20
*=20
x3,y3<BR> =20
x5,y5 / \<BR>x,y * =20
* / \<BR> =
=20
/ \ / \<BR> =
=20
/ * =20
\<BR> x6,y6* x4,y4=20
\<BR> =20
| =
=20
\<BR> | =
=20
\<BR> =
=20
x1,y1*----------------*=20
=
x2,y2<BR><BR>=C7=EB=B1=E0=D0=B4=D2=BB=B8=F6=B3=CC=D0=F2=CA=B5=CF=D6=CF=C2=
=C3=E6=B5=C4=C8=CE=CE=F1:<BR><BR>=BC=EC=B2=E9=CA=E4=C8=EB=B5=C4=B6=A5=B5=E3=
=C1=D0=B1=ED{xi,yi}, i=3D1,2,...,N,=20
=
=C5=D0=B6=CF=CB=FC=CA=C7=B7=F1=CE=AA=D2=BB=B8=F6=BA=CF=B7=A8=B5=C4=B1=D5=BA=
=CF=D5=A4=C0=B8=A1=A3 =
<BR>=D5=D2=B3=F6=CB=F9=D3=D0=BF=C9=D2=D4=B1=BB=D5=BE=D4=DA=B5=E3(x,y)=B4=A6=
=B5=C4=C8=CB=CB=F9=C4=DC=BF=B4=B5=BD=B5=C4=D5=A4=C0=B8(=BA=F6=C2=D4=C8=CB=
=B5=C4=B8=DF=B6=C8)=A3=AC=D2=F2=CE=AA=D3=D0=B5=C4=D5=A4=C0=B8=BB=E1=B1=BB=
=C1=ED=CD=E2=B5=C4=D5=A4=C0=B8=CB=F9=B5=B2=D7=A1=A1=A3=20
=
<BR>=D6=BB=D3=D0=B5=B1=B4=E6=D4=DA=B4=D3(x,y)=B7=A2=C9=E4=B5=C4=D2=BB=CC=F5=
=C9=E4=CF=DF=B5=DA=D2=BB=B8=F6=B4=A9=B9=FD=D5=A4=C0=B8i=CA=B1=A3=AC=D5=A4=
=C0=B8i=CA=C7=BF=C9=D2=D4=B1=BB=BF=B4=BC=FB=B5=C4=A1=A3=C8=E7=B9=FB=D5=A4=
=C0=B8=CA=C7=C6=BD=D0=D0=D3=DA=C4=BF=B9=E2=B5=C4=A3=AC=CB=FC=B2=A2=B2=BB=C8=
=CF=CE=AA=CA=C7=BF=C9=D2=D4=BF=B4=BC=FB=B5=C4=A1=A3=D4=DA=C9=CF=C3=E6=B5=C4=
=C0=FD=D7=D3=C0=EF=A3=AC=CF=DF=B6=CE[x3,y3-x4,y4],=20
[x5,y5-x6,y6], =
[x6-y6-x1,y1]=CA=C7=BF=C9=D2=D4=B1=BB(x,y)=BF=B4=BC=FB=B5=C4=A1=A3 =
<BR><BR>PROGRAM NAME:=20
fence4<BR>INPUT FORMAT<BR>=B5=DA=D2=BB=D0=D0: N, =
=B1=ED=CA=BE=B1=D5=BA=CF=D5=A4=C0=B8=B5=C4=B6=A5=B5=E3=CA=FD=A1=A3 =
<BR>=B5=DA=B6=FE=D0=D0:=20
=
=C1=BD=B8=F6=D5=FB=CA=FDx=BA=CDy=A3=AC=B1=ED=CA=BE=B9=DB=B2=E2=D5=DF=B5=C4=
=CE=BB=D6=C3=A1=A3=C1=BD=B8=F6=D5=FB=CA=FD=B6=BC=CA=C716=CE=BB=B5=C4=A1=A3=
<BR>=B5=DA3=B5=BDN+2=D0=D0: =20
=
=C3=BF=D0=D0=D2=BB=B6=D4=D5=FB=CA=FD(x,y)=B1=ED=CA=BE=B6=D4=D3=A6=B1=D5=BA=
=CF=D5=A4=C0=B8=B5=C4=B5=DAk=B8=F6=B6=A5=B5=E3=B5=C4=D7=F8=B1=EA=A1=A3=D7=
=F8=B1=EA=D2=D4=C4=E6=CA=B1=D5=EB=CB=B3=D0=F2=B8=F8=B3=F6=A1=A3=D5=FB=CA=FD=
=BE=F8=B6=D4=D6=B5=B2=BB=B3=AC=B9=FD1000=A1=A3 <BR><BR>SAMPLE =
INPUT (file fence4.in)<BR>13<BR>5 5<BR>0 0<BR>7 0<BR>5 2<BR>7 =
5<BR>5=20
7<BR>3 5<BR>4 9<BR>1 8<BR>2 5<BR>0 9<BR>-2 7<BR>0 3<BR>-3 1 =
<BR><BR>OUTPUT=20
=
FORMAT<BR>=C8=E7=B9=FB=B8=F8=B3=F6=B5=C4=D0=F2=C1=D0=B2=BB=CA=C7=D2=BB=B8=
=F6=BA=CF=B7=A8=B5=C4=B1=D5=BA=CF=D5=A4=C0=B8=A3=AC=C4=C7=C3=B4=CA=E4=B3=F6=
=CE=C4=BC=FE=D6=BB=D3=D0=D2=BB=D0=D0=A3=AC=CE=AA"NOFENCE"(=B2=BB=B0=FC=C0=
=A8=D2=FD=BA=C5)=A1=A3=20
=
<BR><BR>=B7=F1=D4=F2=A3=AC=CA=E4=B3=F6=CA=C7=D2=BB=B8=F6=BF=C9=BC=FB=D5=A4=
=C0=B8=B5=C4=C1=D0=B1=ED=A1=A3=D5=A4=C0=B8=D3=C3=C1=BD=B6=CB=B5=C4=B6=A5=B5=
=E3=B1=ED=CA=BE=A3=AC=B6=A5=B5=E3=B5=C4=CA=E4=B3=F6=CB=B3=D0=F2=D2=D4=CA=E4=
=C8=EB=CE=C4=BC=FE=D6=D0=B5=C4=CB=B3=D0=F2=CE=AA=D7=BC=A1=A3=B0=D1=D5=A4=C0=
=B8=B0=B4=D5=D5=D7=EE=BA=F3=D2=BB=B8=F6=B5=E3=D4=DA=CA=E4=C8=EB=CE=C4=BC=FE=
=D6=D0=B5=C4=CB=B3=D0=F2<SPAN=20
class=3Dt_tag=20
=
href=3D"tag.php?name=3D%C5%C5%D0%F2">=C5=C5=D0=F2</SPAN>=A1=A3=C8=E7=B9=FB=
=C1=BD=CC=F5=D5=A4=C0=B8=B5=C4=D7=EE=BA=F3=D2=BB=B8=F6=B5=E3=CA=C7=D2=BB=D1=
=F9=B5=C4=A3=AC=BE=CD=D2=D4=CB=FC=C3=C7=B5=DA=D2=BB=B8=F6=B5=E3=B5=C4=CB=B3=
=D0=F2<SPAN=20
class=3Dt_tag =
href=3D"tag.php?name=3D%C5%C5%D0%F2">=C5=C5=D0=F2</SPAN>=A1=A3 =
<BR><BR>SAMPLE=20
OUTPUT (file fence4.out)<BR>7<BR>0 0 7 0<BR>5 2 7 5<BR>7 5 5 =
7<BR>5 7 3=20
5<BR>-2 7 0 3<BR>0 0 -3 1<BR>0 3 -3 1</P>
<DIV class=3Dt_msgfont>
<HR>
</DIV>
<P class=3Dt_msgfont><STRONG>USACO 3.4.1 Closed=20
Fences<BR>=CC=E1=BD=BB=B4=CE=CA=FD:25=B4=CE</STRONG></P>
<P=20
=
class=3Dt_msgfont><STRONG>=CC=E1=BD=BB=C1=CB=BA=DC=B6=E0=B4=CE...=CE=D2=D3=
=C3=B5=C4fp=CA=C7noi=B0=E6,=D2=BB=B8=F6=D0=A1=B5=C4=C8=B1=C2=A9=CA=B9=CE=D2=
=D5=E2=C0=EF=CA=E4=B3=F6=D5=FD=C8=B7=B6=F8USACO=B4=ED=CE=F3...=C3=A4=C4=BF=
=CC=E1=BD=BB=C1=CB=BA=C3=BE=C3<BR>=D4=DA=B4=CB=BC=C7=C2=BC=D2=BB=CF=C2=C4=
=C7=B8=F6=C8=B1=C2=A9,=D2=D4=C3=E2=D2=D4=BA=F3=D4=D9=B7=B8=D5=E2=D1=F9=B5=
=C4=B4=ED=CE=F3<BR>function=20
xx():<BR>begin <BR>if ...exit();<BR>if ...exit();<BR>if=20
...exit();<BR>end;</STRONG></P>
<P =
class=3Dt_msgfont><STRONG>=D4=DA=CA=B2=C3=B4=CC=F5=BC=FE=B6=BC=C3=BB=B4=EF=
=B5=BD=CA=B1=D3=A6=B8=C3=D4=D9=CA=E4=B3=F6=D2=BB=B8=F6<BR>function =
xx():<BR>begin=20
<BR>if ...exit();<BR>if ...exit();<BR>if=20
=
...exit();<BR>exit(xx)<BR>end;<BR>=B2=BB=C8=BB=B5=C4=BB=B0=BB=E1=CA=E4=B3=
=F6=D2=E2=C1=CF=D6=AE=CD=E2=B5=C4=B6=AB=CE=F7...<BR>noi=B0=E6=B5=C4fp=C4=AC=
=C8=CF=C1=CB=CA=E4=B3=F6#0=CB=F9=D2=D4=D4=DA=CE=D2=D5=E2=C0=EF=B9=FD,=B5=BD=
=CB=FC=C4=C7=C0=EF=B2=BB=B9=FD.</STRONG></P>
<P=20
=
class=3Dt_msgfont><STRONG>=CB=E3=B7=A8=D6=F7=D2=AA=CA=C7=D3=C3=C1=CB=CF=F2=
=C1=BF=B5=C4=D4=CB=CB=E3(=D6=AA=B5=C0=D3=D0=BC=C6=CB=E3=BC=B8=BA=CE=B5=C4=
=CC=E2=C4=BF=D4=A4=CF=C8=D7=BC=B1=B8=C1=CB=BC=B8=CC=EC=CA=FD=D1=A7,=B0=D1=
=CF=F2=C1=BF=BF=D5=BC=E4,=BE=D8=D5=F3=D6=AE=C0=E0=B5=C4=B6=BC=D4=A4=CF=B0=
=C1=CB...)</STRONG></P>
<P=20
=
class=3Dt_msgfont><STRONG>=CA=D7=CF=C8=CF=F2=C1=BF=BB=FD=B5=C4=CA=FD=D6=B5=
=CA=C7=B2=BB=CD=AC=D3=DA=CA=FD=C1=BF=BB=FD=B5=C4,=B5=AB=CA=C7=CE=D2=C3=C7=
=D4=DA=D4=CB=D3=C3=BC=C6=CB=E3=BC=B8=BA=CE=CA=B5=BC=CA=C9=CF=B6=D4=CF=F2=C1=
=BF=B5=C4=B7=BD=CF=F2=D5=E2=B8=F6=BD=C7=B6=C8=B2=A2=B2=BB=D4=DA=BA=F5,=CB=
=F9=D2=D4=BE=CD=C8=A1=CA=FD=D6=B5<BR>(=D2=D4=CF=C2=CC=E1=B5=BD=B5=C4ab=B6=
=BC=CA=C7=CF=F2=C1=BF)<BR>a=20
* b=3D|a|*|b|*sin=A6=C8 =
<BR>=D5=E2=BA=CD=CA=FD=C1=BF=BB=FD=B5=C4<BR>a * b=3D|a|*|b|*cos=A6=C8=20
=
=BA=DC=CF=E0=CB=C6<BR>=CA=B5=BC=CA=C9=CF=CF=F2=C1=BF=BB=FD=BE=CD=CA=C7=D2=
=BB=B8=F6=BE=D8=D5=F3=B5=C4=D0=D0=C1=D0=CA=BD=B7=FB=BA=C5=B5=C4=D4=CB=CB=E3=
,=BD=AB=CF=F2=C1=BF=B7=D6=BD=E2,=C6=F0=B5=E3=D2=C6=B5=BD=D4=AD=B5=E3=B5=C3=
=B7=D6=C1=BFa1i,b1j,a2i,a2j<BR>a *=20
b=BE=CD=CA=C7<BR>|i j |<BR>|a1 b1|<BR>|a2=20
b2|<BR>a1*b2-b1*a2</STRONG></P>
<P =
class=3Dt_msgfont><STRONG>=B2=BB=B1=D8=D2=C6=B5=BD=D4=AD=B5=E3=B5=C4=CD=A8=
=CA=BD:(p1 - p0) =A1=C1 (p2 - p0) =3D (x1 - x0)(y2=20
- y0) - (x2 - x0)(y1 - y0).</STRONG></P>
<P =
class=3Dt_msgfont><STRONG>=D7=F3=D3=D2=CA=D6=C2=DD=D0=FD:<BR>=CD=BC=C6=AC=
:</STRONG></P><STRONG>
<DIV class=3Dt_msgfont align=3Dcenter forimg=3D"1"><IMG =
class=3Dblogimg=20
=
src=3D"http://hiphotos.baidu.com/leokan/pic/item/a2a09a2b2793d7f5e7cd4038=
.jpg"=20
border=3D0 small=3D"0"></DIV></STRONG>
<P class=3Dt_msgfont></P>
<P=20
=
class=3Dt_msgfont><STRONG>=D7=F3=D3=D2=CA=D6=C2=DD=D0=FD=B2=BB=CA=C7=BF=B4=
=D2=BB=CC=F5=CF=DF=D4=DA=C1=ED=D2=BB=CC=F5=CF=DF=B5=C4=D7=F3=B1=DF=BB=B9=CA=
=C7=D3=D2=B1=DF,=CA=C2=CA=B5=C9=CF=C7=A1=C7=A1=CF=E0=B7=B4,a=D4=DAb=B5=C4=
=D7=F3=B1=DF=CB=FC=CA=C7=CD=A8=B9=FD=D3=D2=CA=D6=C2=DD=D0=FD=B5=C3=B5=BD=B5=
=C4.<BR>=BD=E1=BA=CF=C7=B0=C3=E6=CB=B5=B5=C4=CF=F2=C1=BF=BB=FD,a*b,=C8=E7=
=B9=FBa,b=B3=C9=D7=F3=CA=D6=CF=B5=CA=B1=A6=C8=BD=C7=CA=C7=B8=BA=CA=FD,=CB=
=F9=D2=D4a*b=CA=C7=D2=BB=B8=F6=B8=BA=CA=FD,=B6=F8=CB=FC=B3=C9=D3=D2=CA=D6=
=CF=B5=CA=B1a*b=CA=C7=D2=BB=B8=F6=D5=FD=CA=FD.<BR>=CD=A8=B9=FD=D5=E2=B8=F6=
=BE=CD=BF=C9=D2=D4=C5=D0=B6=CF=D2=BB=B8=F6=B5=E3=D4=DA=C1=ED=D2=BB=B8=F6=CF=
=F2=C1=BF=B5=C4=D7=F3=B1=DF=BB=B9=CA=C7=D3=D2=B1=DF.=A6=C8=3D0=CA=B1=C1=BD=
=CF=F2=C1=BF=C6=BD=D0=D0,=CB=F9=D2=D4=CB=FB=C3=C7=B5=C4=BB=FD=CE=AA0.</ST=
RONG></P>
<P =
class=3Dt_msgfont><STRONG>=C1=BD=CF=DF=B6=CE=CF=E0=BD=BB:<BR>=BF=EC=CB=D9=
=C5=C5=B3=E2=CA=B5=D1=E9<BR>=CD=BC=C6=AC</STRONG></P>
<P class=3Dt_msgfont></P>
<DIV class=3Dt_msgfont align=3Dcenter forimg=3D"1"><IMG =
class=3Dblogimg=20
=
src=3D"http://hiphotos.baidu.com/leokan/pic/item/de7276cb5fd01010bf09e63a=
.jpg"=20
border=3D0 small=3D"0"></DIV>
<P =
class=3Dt_msgfont><BR>=D2=D4=C1=BD=B8=F6=CF=DF=B6=CE=CE=AA=B6=D4=BD=C7=CF=
=DF=D7=F6=C1=BD=B8=F6=BE=D8=D0=CE,=C1=BD=B8=F6=BE=D8=D0=CE=D3=D0=CF=E0=BD=
=BB=B2=C5=CD=A8=B9=FD=BF=EC=CB=D9=C5=C5=B3=E2=CA=B5=D1=E9</P>
<P =
class=3Dt_msgfont><STRONG>=BF=E7=C1=A2=CA=B5=D1=E9:<BR></STRONG><STRONG><=
IMG class=3Dblogimg=20
=
src=3D"http://hiphotos.baidu.com/leokan/pic/item/058b8a44b66ff843500ffe3b=
.jpg"=20
border=3D0 small=3D"0"></STRONG></P>
<P =
class=3Dt_msgfont><STRONG>=BD=E9=C9=DC=CE=C4=D7=D6=BC=FB=CD=BC=C6=AC=C4=DA=
=C8=DD</STRONG></P>
<P class=3Dt_msgfont><STRONG>=B4=FA=C2=EB:<BR>function=20
=
multi(p1,p2,p0:xy):real;{=BC=C6=CB=E3=CF=F2=C1=BF=BB=FD}<BR>begin<BR>&nbs=
p; =20
=
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