📄 usaco 2_4_3 cow tours 题解_leokan的blog.mht
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<DIV class=3Dtit>USACO 2.4.3 Cow Tours =CC=E2=BD=E2</DIV>
<DIV class=3Ddate>2008=C4=EA01=D4=C231=C8=D5 =D0=C7=C6=DA=CB=C4 =
00:34</DIV>
<TABLE style=3D"TABLE-LAYOUT: fixed">
<TBODY>
<TR>
<TD>
<DIV class=3Dcnt>
<H2>USACO 2.4.3 Cow Tours</H2>
<DIV class=3Dt_msgfont>
<P>Cow Tours<BR><BR>Farmer John has a number of pastures on his =
farm. Cow=20
paths connect some pastures with certain other pastures, forming a =
field.=20
But,at the present time, you can find at least two pastures that =
cannot be=20
connected by any sequence of cow paths, thus partitioning Farmer =
John's=20
farm into multiple fields. <BR><BR>Farmer John would like add a =
single a=20
cow path between one pair of pastures using the constraints below. =
<BR><BR>A field's `diameter' is defined to be the largest distance =
of all=20
the shortest walks between any pair of pastures in the field. =
Consider the=20
field below with five pastures, located at the points shown, and =
cow paths=20
marked by lines: <BR><BR> =20
15,15 20,15<BR> =
D E<BR> =
=20
*-------*<BR> =20
| =
=20
_/|<BR> =
|=20
_/ |<BR> =
=20
| _/ |<BR> =
=20
|/ |<BR> =20
*--------*-------*<BR> A =20
B C<BR> =
10,10=20
15,10 20,10<BR><BR>The `diameter' of this field is approximately =
12.07106,=20
since the longest of the set of shortest paths between pairs of =
pastures=20
is the path from A to E (which includes the point set {A,B,E}). No =
other=20
pair of pastures in this field is farther apart when connected by =
an=20
optimal sequence of cow paths. <BR><BR>Suppose another field on =
the same=20
plane is connected by cow paths as follows: <BR><BR> =20
=20
*F 30,15<BR> =20
/ =
<BR> =20
=20
_/ <BR> =20
_/ =
<BR> =20
=
/=20
<BR> =
=20
*------ <BR> =20
G H<BR> =
=20
25,10 30,10<BR><BR>In the =
scenario=20
of just two fields on his farm, Farmer John would add a cow path =
between a=20
point in each of these two fields (namely point sets {A,B,C,D,E} =
and=20
{F,G,H}) so that the joined set of pastures {A,B,C,D,E,F,G,H} has =
the=20
smallest possible diameter. <BR><BR>Note that cow paths do not =
connect=20
just because they cross each other; they only connect at listed =
points.=20
<BR><BR>The input contains the pastures, their locations, and a =
symmetric=20
"adjacency" matrix that tells whether pastures are connected by =
cow paths.=20
Pastures are not considered to be connected to themselves. Here's =
one=20
annotated adjacency list for the pasture {A,B,C,D,E,F,G,H} as =
shown above:=20
<BR><BR> A B C =
D E F G=20
H<BR> A 0 =
1 0 0 0=20
0 0 0<BR> =
B 1 0 1=20
1 1 0 0 0<BR> =
C 0=20
1 0 0 1 0 0 0<BR> =
=20
D 0 1 0 0 1 0 0 0<BR> =20
E 0 1 1 1 0 0 0 0<BR> =20
F 0 0 0 0 0 0 1 0<BR> =20
G 0 0 0 0 0 1 0=20
1<BR> H 0 =
0 0 0 0=20
0 1 0<BR><BR>Other equivalent adjacency lists might permute the =
rows and=20
columns by using some order other than alphabetical to show the =
point=20
connections. The input data contains no names for the points. =
<BR><BR>The=20
input will contain at least two pastures that are not connected by =
any=20
sequence of cow paths. <BR><BR>Find a way to connect exactly two =
pastures=20
in the input with a cow path so that the new combined field has =
the=20
smallest possible diameter of any possible pair of connected =
pastures.=20
Output that smallest possible diameter. <BR><BR>PROGRAM NAME:=20
cowtour<BR>INPUT FORMAT<BR>Line 1: An integer, N (1 =
<=3D N=20
<=3D 150), the number of pastures <BR>Line =
2-N+1: =20
Two integers, X and Y (0 <=3D X ,Y<=3D 100000), that denote =
that X,Y=20
grid location of the pastures; all input pastures are=20
unique. <BR>Line N+2-2*N+1: lines, each =
containing=20
N digits (0 or 1) that represent the adjacency matrix as described =
above,=20
where the rows' and columns' indices are in order of the points =
just=20
listed. <BR><BR>SAMPLE INPUT (file cowtour.in) =
<BR>8<BR>10=20
10<BR>15 10<BR>20 10<BR>15 15<BR>20 15<BR>30 15<BR>25 10<BR>30=20
=
10<BR>01000000<BR>10111000<BR>01001000<BR>01001000<BR>01110000<BR>0000001=
0<BR>00000101<BR>00000010<BR><BR>OUTPUT=20
FORMAT<BR>The output consists of a single line with the diameter =
of the=20
newly joined pastures. Print the answer to exactly six decimal =
places. Do=20
not perform any special rounding on your output. <BR><BR>SAMPLE =
OUTPUT=20
(file cowtour.out)<BR>22.071068<BR><BR><BR><BR>Cow=20
Tours<BR><BR>=C5=A3=B5=C4=C2=C3=D0=D0<BR><BR>=D2=EB by=20
=
Jeru<BR><BR><BR>=A1=A1=A1=A1=C5=A9=C3=F1John=B5=C4=C5=A9=B3=A1=C0=EF=D3=D0=
=BA=DC=B6=E0=C4=C1=C7=F8=A1=A3=D3=D0=B5=C4=C2=B7=BE=B6=C1=AC=BD=D3=D2=BB=D0=
=A9=CC=D8=B6=A8=B5=C4=C4=C1=C7=F8=A1=A3=D2=BB=C6=AC=CB=F9=D3=D0=C1=AC=CD=A8=
=B5=C4=C4=C1=C7=F8=B3=C6=CE=AA=D2=BB=B8=F6=C4=C1=B3=A1=A1=A3=B5=AB=CA=C7=BE=
=CD=C4=BF=C7=B0=B6=F8=D1=D4=A3=AC=C4=E3=C4=DC=BF=B4=B5=BD=D6=C1=C9=D9=D3=D0=
=C1=BD=B8=F6=C4=C1=C7=F8=B2=BB=C1=AC=CD=A8=A1=A3=D5=E2=D1=F9=A3=AC=C5=A9=C3=
=F1John=BE=CD=D3=D0=B6=E0=B8=F6=C4=C1=C7=F8=C1=CB=A1=A3=20
=
<BR><BR>=A1=A1=A1=A1John=CF=EB=D4=DA=C5=A9=B3=A1=C0=EF=CC=ED=BC=D3=D2=BB=CC=
=F5=C2=B7=BE=B6(=D7=A2=D2=E2=A3=AC=C7=A1=BA=C3=D2=BB=CC=F5)=A1=A3=B6=D4=D5=
=E2=CC=F5=C2=B7=BE=B6=D3=D0=D2=D4=CF=C2=CF=DE=D6=C6=A3=BA=20
=
<BR><BR>=A1=A1=A1=A1=D2=BB=B8=F6=C4=C1=B3=A1=B5=C4=D6=B1=BE=B6=BE=CD=CA=C7=
=C4=C1=B3=A1=D6=D0=D7=EE=D4=B6=B5=C4=C1=BD=B8=F6=C4=C1=C7=F8=B5=C4=BE=E0=C0=
=EB(=B1=BE=CC=E2=D6=D0=CB=F9=CC=E1=B5=BD=B5=C4=CB=F9=D3=D0=BE=E0=C0=EB=D6=
=B8=B5=C4=B6=BC=CA=C7=D7=EE=B6=CC=B5=C4=BE=E0=C0=EB)=A1=A3=BF=BC=C2=C7=C8=
=E7=CF=C2=B5=C4=D3=D05=B8=F6=C4=C1=C7=F8=B5=C4=C4=C1=B3=A1=A3=AC=C4=C1=C7=
=F8=D3=C3=A1=B0*=A1=B1=B1=ED=CA=BE=A3=AC=C2=B7=BE=B6=D3=C3=D6=B1=CF=DF=B1=
=ED=CA=BE=A1=A3=C3=BF=D2=BB=B8=F6=C4=C1=C7=F8=B6=BC=D3=D0=D7=D4=BC=BA=B5=C4=
=D7=F8=B1=EA=A3=BA=20
<BR><BR> 15,15=20
20,15<BR> =
=20
D E<BR> =
=20
*-------*<BR> =20
| _/|<BR> =
| =
_/ =20
|<BR> =
| _/=20
|<BR> =
|/=20
|<BR> =20
*--------*-------*<BR> A =20
B C<BR> =
10,10=20
15,10 =
20,10<BR><BR>=A1=A1=A1=A1=D5=E2=B8=F6=C4=C1=B3=A1=B5=C4=D6=B1=BE=B6=B4=F3=
=D4=BC=CA=C712.07106, =
=D7=EE=D4=B6=B5=C4=C1=BD=B8=F6=C4=C1=C7=F8=CA=C7A=BA=CDE=A3=AC=CB=FC=C3=C7=
=D6=AE=BC=E4=B5=C4=D7=EE=B6=CC=C2=B7=BE=B6=CA=C7A-B-E=A1=A3=20
=
<BR><BR>=A1=A1=A1=A1=D5=E2=C0=EF=CA=C7=C1=ED=D2=BB=B8=F6=C4=C1=B3=A1=A3=BA=
<BR><BR> =20
*F=20
30,15<BR> =
=20
/ <BR> =
=20
=20
_/ <BR> =
=20
_/ <BR> =
=20
/ =20
<BR> =
=20
*------ <BR> =20
G H<BR> =
=20
25,10=20
=
30,10<BR><BR><BR>=A1=A1=A1=A1=D5=E2=C1=BD=B8=F6=C4=C1=B3=A1=B6=BC=D4=DAJo=
hn=B5=C4=C5=A9=B3=A1=C9=CF=A1=A3John=BD=AB=BB=E1=D4=DA=C1=BD=B8=F6=C4=C1=B3=
=A1=D6=D0=B8=F7=D1=A1=D2=BB=B8=F6=C4=C1=C7=F8=A3=AC=C8=BB=BA=F3=D3=C3=D2=BB=
=CC=F5=C2=B7=BE=B6=C1=AC=C6=F0=C0=B4=A3=AC=CA=B9=B5=C3=C1=AC=CD=A8=BA=F3=D5=
=E2=B8=F6=D0=C2=B5=C4=B8=FC=B4=F3=B5=C4=C4=C1=B3=A1=D3=D0=D7=EE=D0=A1=B5=C4=
=D6=B1=BE=B6=A1=A3=20
=
<BR><BR>=A1=A1=A1=A1=D7=A2=D2=E2=A3=AC=C8=E7=B9=FB=C1=BD=CC=F5=C2=B7=BE=B6=
=D6=D0=CD=BE=CF=E0=BD=BB=A3=AC=CE=D2=C3=C7=B2=BB=C8=CF=CE=AA=CB=FC=C3=C7=CA=
=C7=C1=AC=CD=A8=B5=C4=A1=A3=D6=BB=D3=D0=C1=BD=CC=F5=C2=B7=BE=B6=D4=DA=CD=AC=
=D2=BB=B8=F6=C4=C1=C7=F8=CF=E0=BD=BB=A3=AC=CE=D2=C3=C7=B2=C5=C8=CF=CE=AA=CB=
=FC=C3=C7=CA=C7=C1=AC=CD=A8=B5=C4=A1=A3=20
=
<BR><BR>=A1=A1=A1=A1=CA=E4=C8=EB=CE=C4=BC=FE=B0=FC=C0=A8=C4=C1=C7=F8=A1=A2=
=CB=FC=C3=C7=B8=F7=D7=D4=B5=C4=D7=F8=B1=EA=A3=AC=BB=B9=D3=D0=D2=BB=B8=F6=C8=
=E7=CF=C2=B5=C4=B6=D4=B3=C6=C1=DA=BD=D3=BE=D8=D5=F3=A3=BA <BR><BR>A B C =
D E F G H<BR>A 0 1=20
0 0 0 0 0 0<BR>B 1 0 1 1 1 0 0 0<BR>C 0 1 0 0 1 0 0 0<BR>D 0 1 0 0 =
1 0 0=20
0<BR>E 0 1 1 1 0 0 0 0<BR>F 0 0 0 0 0 0 1 0<BR>G 0 0 0 0 0 1 0 =
1<BR>H 0 0=20
0 0 0 0 1 =
0<BR><BR>=A1=A1=A1=A1=CA=E4=C8=EB=CE=C4=BC=FE=D6=C1=C9=D9=B0=FC=C0=A8=C1=BD=
=B8=F6=B2=BB=C1=AC=CD=A8=B5=C4=C4=C1=C7=F8=A1=A3=20
=
<BR><BR>=A1=A1=A1=A1=C7=EB=B1=E0=B3=CC=D5=D2=B3=F6=D2=BB=CC=F5=C1=AC=BD=D3=
=C1=BD=B8=F6=B2=BB=CD=AC=C4=C1=B3=A1=B5=C4=C2=B7=BE=B6=A3=AC=CA=B9=B5=C3=C1=
=AC=C9=CF=D5=E2=CC=F5=C2=B7=BE=B6=BA=F3=A3=AC=D5=E2=B8=F6=B8=FC=B4=F3=B5=C4=
=D0=C2=C4=C1=B3=A1=D3=D0=D7=EE=D0=A1=B5=C4=D6=B1=BE=B6=A1=A3=20
<BR><BR>=A1=A1<BR><BR>PROGRAM NAME: cowtour<BR>INPUT =
FORMAT<BR>=B5=DA1=D0=D0: =20
=D2=BB=B8=F6=D5=FB=CA=FDN (1 <=3D N <=3D 150), =
=B1=ED=CA=BE=C4=C1=C7=F8=CA=FD <BR>=B5=DA2=B5=BDN+1=D0=D0: =
=C3=BF=D0=D0=C1=BD=B8=F6=D5=FB=CA=FDX,Y (0=20
<=3D X ,Y<=3D 100000), =
=B1=ED=CA=BEN=B8=F6=C4=C1=C7=F8=B5=C4=D7=F8=B1=EA=A1=A3=D7=A2=D2=E2=C3=BF=
=B8=F6=20
=
=C4=C1=C7=F8=B5=C4=D7=F8=B1=EA=B6=BC=CA=C7=B2=BB=D2=BB=D1=F9=B5=C4=A1=A3&=
nbsp; <BR>=B5=DAN+2=D0=D0=B5=BD=B5=DA2*N+1=D0=D0: =
=C3=BF=D0=D0=B0=FC=C0=A8N=B8=F6=CA=FD=D7=D6(0=BB=F21)=20
=
=B1=ED=CA=BE=C8=E7=C9=CF=CE=C4=C3=E8=CA=F6=B5=C4=B6=D4=B3=C6=C1=DA=BD=D3=BE=
=D8=D5=F3=A1=A3 <BR><BR>SAMPLE INPUT (file=20
cowtour.in)<BR>8<BR>10 10<BR>15 10<BR>20 10<BR>15 15<BR>20 =
15<BR>30=20
15<BR>25 10<BR>30=20
=
10<BR>01000000<BR>10111000<BR>01001000<BR>01001000<BR>01110000<BR>0000001=
0<BR>00000101<BR>00000010<BR><BR>OUTPUT=20
=
FORMAT<BR>=A1=A1=A1=A1=D6=BB=D3=D0=D2=BB=D0=D0=A3=AC=B0=FC=C0=A8=D2=BB=B8=
=F6=CA=B5=CA=FD=A3=AC=B1=ED=CA=BE=CB=F9=C7=F3=B4=F0=B0=B8=A1=A3=CA=FD=D7=D6=
=B1=A3=C1=F4=C1=F9=CE=BB=D0=A1=CA=FD=A1=A3 <BR><BR>SAMPLE OUTPUT (file=20
cowtour.out)<BR>22.071068</P></DIV>
<P></P>
<HR>
<P></P>
<P><STRONG>USACO 2.4.3 Cow Tours =
<BR>=CC=E1=BD=BB=B4=CE=CA=FD:3=B4=CE</STRONG></P>
=
<P><STRONG>=D7=F6=B9=FD=B5=C4=CC=E2=BB=B9=CC=E1=BD=BB=C1=CB3=B4=CE,=B6=F8=
=C7=D2=BB=A8=C1=CB=BD=FC3=B8=F6=D0=A1=CA=B1=B5=C4=B5=F7=CA=D4=CA=B1=BC=E4=
!!=D5=E6=CA=A7=B0=DC.<BR>=B4=ED=CE=F3=D0=C4=B5=C3:<BR>floyd=B5=C4=D1=AD=BB=
=B7=CB=B3=D0=F2=CA=C7=D5=E2=D1=F9=B5=C4</STRONG></P>
<P><STRONG>for k:=3D1 to n do<BR>for i:=3D1 to n =
do<BR> for=20
j:=3D1 to n do<BR> if ...then =
...</STRONG></P>
<P><STRONG>=B6=F8=CE=D2=D3=C3=B5=C4<BR>for i:=3D1 to n do<BR>for =
j:=3D1 to n=20
do<BR> for k:=3D1 to n=20
do<BR> if ...then=20
=
...<BR>=B2=BB=D6=AA=CE=AA=BA=CE=BE=CD=B4=ED=C1=CB,=CB=FC=C3=BF=D6=D6=C7=E9=
=BF=F6=B6=BC=D1=AD=BB=B7=B9=FD=D2=BB=B4=CE=B0=A1,=C4=D1=B5=C0=C2=A9=C1=CB=
=CA=B2=C3=B4?=B6=F8=C7=D2=CB=FC=B4=F3=B2=BF=B7=D6=CA=FD=BE=DD=B6=BC=C4=DC=
=B9=FD,=BF=A8=D4=DA=C4=B3=B8=F6=B5=E3=B9=FD=B2=BB=C1=CB,=B2=E9=C1=CB=BA=C3=
=BE=C3=B5=F7=BB=BB=C1=CB=D2=BB=CF=C2floyd=B5=C4=CB=B3=D0=F2=B2=C5=B9=FD=B5=
=C4.</STRONG></P>
=
<P><STRONG>=A1=BE=B2=B9=B3=E4=A1=BF=CE=D2=C3=F7=B0=D7=C1=CB,=B7=AD=D4=C4=C1=
=CB=B4=F3=D1=A7=BD=CC=B2=C4=D4=CB=B3=EF=D1=A7,=B4=D3=CA=FD=D1=A7=B5=C4=BD=
=C7=B6=C8=C0=ED=BD=E2floyd,=D6=AA=B5=C0=CE=D2=C4=C7=D1=F9=CA=C7=B4=ED=CE=F3=
=B5=C4=C1=CB.floyd=B5=C4=D4=AD=C0=ED=CA=C7=CD=A8=B9=FD=D1=AD=BB=B7k,=C0=B4=
=B5=C3=B5=BD=C4=DC=CD=A8=B9=FD=C7=B0k=B8=F6=B5=E3=C0=B4=B5=C3=B5=BD=B5=C4=
=D7=EE=B6=CC=C2=B7=B5=C4=BE=D8=D5=F3Dk,=B2=BB=B6=CF=B8=FC=D0=C2=D5=E2=B8=F6=
=D0=C2=B5=C4=D7=EE=B6=CC=C2=B7=B5=C4=BE=D8=D5=F3,=B8=FC=D0=C2=CD=EA=B1=CF=
=BA=F3=B5=C4=BE=D8=D5=F3=BE=CD=CA=C7=D7=EE=B6=CC=C2=B7=B5=C4=BE=D8=D5=F3=C1=
=CB.=B6=F8=CE=D2=CF=C8=D1=AD=BB=B7ij=D4=D9=D1=AD=BB=B7k=CA=C7=C3=BB=D3=D0=
=C8=CE=BA=CE=B5=C0=C0=ED=BF=C9=D2=D4=BD=B2=B5=C4.</STRONG></P>
=
<P><STRONG>=CE=D2=D2=D4=C7=B0=B5=C4=CC=E2=BD=E2:http://hi.baidu.com/leoka=
n/blog/item/004f9d520cd4ec0d0df3e3d6.html</STRONG></P>
<P><STRONG><FONT=20
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<P><STRONG>{<BR>TASK:cowtour<BR>LANG:PASCAL<BR>}<BR>program=20
cowtour;<BR>const<BR> =20
maxlen=3D100001;<BR> =20
maxn=3D150;<BR>var<BR> =
map:array[1..maxn,1..maxn] of=20
real;<BR> maxdis:array[1..maxn] of=20
real;<BR> maxmaxdis:real;<BR> =20
xy:array[1..maxn,1..2] of integer;<BR> =20
n:integer;<BR>procedure init;<BR>var<BR> =20
i,j:integer;<BR> =
ch:char;<BR>begin<BR> =20
assign(input,'cowtour.in');reset(input);<BR> =20
readln(n);<BR> for i:=3D1 to n=20
do<BR> =20
readln(xy[i,1],xy[i,2]);<BR> for i:=3D1 to n=20
do<BR> =20
=
begin<BR> &nbs=
p;=20
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