📄 usaco 1_5_1 number triangles 题解_leokan的blog.mht
字号:
<TD class=3Dmodtl width=3D7> </TD>
<TD class=3Dmodtc noWrap>
<DIV class=3Dmodhead><SPAN =
class=3Dmodtit>=B2=E9=BF=B4=CE=C4=D5=C2</SPAN></DIV></TD>
<TD class=3Dmodtc noWrap align=3Dright>
<DIV class=3Dmodopt><A class=3Dmodact=20
href=3D"http://hi.baidu.com/leokan/creat/blog/"><IMG=20
src=3D"http://img.baidu.com/hi/img/ico_postnew.gif" =
align=3DabsMiddle=20
border=3D0>=D0=B4=D0=C2=CE=C4=D5=C2</A></DIV></TD>
<TD class=3Dmodtr width=3D7> </TD></TR></TBODY></TABLE>
<DIV class=3Dmodbox id=3Dm_blog>
<DIV class=3Dtit>USACO 1.5.1 Number Triangles =CC=E2=BD=E2</DIV>
<DIV class=3Ddate>2008=C4=EA01=D4=C226=C8=D5 =D0=C7=C6=DA=C1=F9 =
12:26</DIV>
<TABLE style=3D"TABLE-LAYOUT: fixed">
<TBODY>
<TR>
<TD>
<DIV class=3Dcnt>
<H2>USACO 1.5.1 Number Triangles</H2>
<DIV class=3Dt_msgfont>
<P>Number Triangles<BR>Consider the number triangle shown below. =
Write a=20
program that calculates the highest sum of numbers that can be =
passed on a=20
route that starts at the top and ends somewhere on the base. Each =
step can=20
go either diagonally down to the left or diagonally down to the =
right.=20
<BR><BR> =20
7<BR><BR> 3 =20
8<BR><BR> 8 =
1 =20
0<BR><BR> 2 7 =
4 =20
4<BR><BR>4 5 2 6 =20
5<BR><BR><BR>In the sample above, the route from 7 to 3 to 8 to 7 =
to 5=20
produces the highest sum: 30. <BR><BR>PROGRAM NAME: =
numtri<BR>INPUT=20
FORMAT<BR>The first line contains R (1 <=3D R <=3D 1000), =
the number of=20
rows. Each subsequent line contains the integers for that =
particular row=20
of the triangle. All the supplied integers are non-negative and no =
larger=20
than 100. <BR>SAMPLE INPUT (file numtri.in) <BR>5<BR>7<BR>3 8<BR>8 =
1=20
0<BR>2 7 4 4<BR>4 5 2 6 5<BR><BR>OUTPUT FORMAT<BR>A single line =
containing=20
the largest sum using the traversal specified. <BR>SAMPLE OUTPUT =
(file=20
numtri.out)<BR>30<BR><BR><BR><BR>Number =
Triangles<BR><BR>=CA=FD=D7=D6=BD=F0=D7=D6=CB=FE<BR><BR>=D2=EB by=20
tim=20
=
green<BR>=A1=A1<BR><BR><BR>=BF=BC=C2=C7=D4=DA=CF=C2=C3=E6=B1=BB=CF=D4=CA=BE=
=B5=C4=CA=FD=D7=D6=BD=F0=D7=D6=CB=FE=A1=A3<BR>=D0=B4=D2=BB=B8=F6=B3=CC=D0=
=F2=C0=B4=BC=C6=CB=E3=B4=D3=D7=EE=B8=DF=B5=E3=BF=AA=CA=BC=D4=DA=B5=D7=B2=BF=
=C8=CE=D2=E2=B4=A6=BD=E1=CA=F8=B5=C4=C2=B7=BE=B6=BE=AD=B9=FD=CA=FD=D7=D6=B5=
=C4=BA=CD=B5=C4=D7=EE=B4=F3=A1=A3<BR>=C3=BF=D2=BB=B2=BD=BF=C9=D2=D4=D7=DF=
=B5=BD=D7=F3=CF=C2=B7=BD=B5=C4=B5=E3=D2=B2=BF=C9=D2=D4=B5=BD=B4=EF=D3=D2=CF=
=C2=B7=BD=B5=C4=B5=E3=A1=A3<BR>7<BR><BR>3=20
8<BR><BR>8 1 0<BR><BR>2 7 4 4<BR><BR>4 5 2 6 =
5<BR>=D4=DA=C9=CF=C3=E6=B5=C4=D1=F9=C0=FD=D6=D0,=B4=D37 =B5=BD 3 =B5=BD =
8 =B5=BD 7 =B5=BD=20
5 =
=B5=C4=C2=B7=BE=B6=B2=FA=C9=FA=C1=CB=D7=EE=B4=F3=BA=CD:30<BR><BR>PROGRAM =
NAME: numtri<BR><BR>INPUT FORMAT<BR>=B5=DA=D2=BB=B8=F6=D0=D0=B0=FC=BA=AC =
R(1<=3D R<=3D1000)=20
=
,=B1=ED=CA=BE=D0=D0=B5=C4=CA=FD=C4=BF=A1=A3<BR>=BA=F3=C3=E6=C3=BF=D0=D0=CE=
=AA=D5=E2=B8=F6=CA=FD=D7=D6=BD=F0=D7=D6=CB=FE=CC=D8=B6=A8=D0=D0=B0=FC=BA=AC=
=B5=C4=D5=FB=CA=FD=A1=A3<BR>=CB=F9=D3=D0=B5=C4=B1=BB=B9=A9=D3=A6=B5=C4=D5=
=FB=CA=FD=CA=C7=B7=C7=B8=BA=B5=C4=C7=D2=B2=BB=B4=F3=D3=DA100=A1=A3<BR><BR=
>SAMPLE=20
INPUT (file numtri.in) <BR>5<BR>7<BR>3 8<BR>8 1 0<BR>2 7 4 4<BR>4 =
5 2 6=20
5<BR><BR>OUTPUT =
FORMAT<BR>=B5=A5=B6=C0=B5=C4=D2=BB=D0=D0=B0=FC=BA=AC=C4=C7=B8=F6=BF=C9=C4=
=DC=B5=C3=B5=BD=B5=C4=D7=EE=B4=F3=B5=C4=BA=CD=A1=A3<BR><BR>SAMPLE OUTPUT =
(file=20
numtri.out)<BR>30</P>
<HR>
<P><STRONG>USACO 1.5.1 Number Triangles =
<BR>=CC=E1=BD=BB=B4=CE=CA=FD=A3=BA1=B4=CE</STRONG></P>
=
<P><STRONG>=D5=E2=B5=C0=CC=E2=B6=AF=CC=AC=B9=E6=BB=AE=A3=AC=D3=C9=B5=D7=CF=
=F2=C9=CF=CD=C6=A3=ACf(i,j)=3Dmax{f(i+1,j),f(i+1,j+1)}+f(i,j);=D2=BB=BF=AA=
=CA=BC=CF=EB=B5=BD=B5=C4=CA=C7=D3=C9=B6=A5=CF=F2=CF=C2=CD=C6=A3=AC=D5=E2=D1=
=F9=B1=C8=BD=CF=C2=E9=B7=B3=A1=A3</STRONG></P>
<P><STRONG>{<BR>TASK:numtri<BR>LANG:PASCAL<BR>}<BR>program=20
numtri;<BR>var<BR> f:array[1..1000,1..1000] of=20
longint;<BR> r:integer;<BR>function=20
max(a,b:longint):longint;<BR>begin<BR> if =
a>=3Db then=20
exit(a)<BR> else exit(b);<BR>end;</STRONG></P>
<P><STRONG>procedure init;<BR>var<BR> =20
i,j:integer;<BR>begin<BR> =20
assign(input,'numtri.in');reset(input);<BR> =20
readln(r);<BR> for i:=3D1 to r=20
do<BR> =20
=
begin<BR> &nbs=
p;=20
for j:=3D1 to i=20
=
do<BR> &=
nbsp; =20
=
read(f[i,j]);<BR> &n=
bsp; =20
readln;<BR> =20
end;<BR> close(input);<BR>end;<BR>procedure=20
work;<BR>var<BR> =20
i,j:integer;<BR>begin<BR> for i:=3Dr-1 downto 1=20
do<BR> for j:=3D1 to i=20
=
do<BR> =
f[i,j]:=3Dmax(f[i+1,j],f[i+1,j+1])+f[i,j];<BR> =20
assign(output,'numtri.out');rewrite(output);<BR> =
writeln(f[1,1]);<BR> =20
close(output);<BR>end;<BR>begin<BR> =20
init;<BR> work;<BR>end.</STRONG></P><STRONG>
<HR>
</STRONG>
<P><STRONG>usaco=B5=C4=B7=D6=CE=F6</STRONG></P>
<P><STRONG>We keep track (in the "best" array) of total for the =
best path=20
ending in a given column of the triangle. Viewing the input, a =
path=20
through the triangle always goes down or down and to the right. To =
process=20
a new row, the best path total ending at a given column is the =
maximum of=20
the best path total ending at that column or the one to its left, =
plus the=20
number in the new row at that column. We keep only the best totals =
for the=20
current row (in "best") and the previous row (in "oldbest"). =
</STRONG></P><PRE><STRONG>#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#define MAXR 1000
int
max(int a, int b)
{
return a > b ? a : b;
}
void
main(void)
{
int best[MAXR], oldbest[MAXR];
int i, j, r, n, m;
FILE *fin, *fout;
fin =3D fopen("numtri.in", "r");
assert(fin !=3D NULL);
fout =3D fopen("numtri.out", "w");
assert(fout !=3D NULL);
fscanf(fin, "%d", &r);
for(i=3D0; i<MAXR; i++)
best[i] =3D 0;
for(i=3D1; i<=3Dr; i++) {
memmove(oldbest, best, sizeof oldbest);
for(j=3D0; j<i; j++) {
fscanf(fin, "%d", &n);
if(j =3D=3D 0)
best[j] =3D oldbest[j] + n;
else
best[j] =3D max(oldbest[j], oldbest[j-1]) + n;
}
}
m =3D 0;
for(i=3D0; i<r; i++)
if(best[i] > m)
m =3D best[i];
fprintf(fout, "%d\n", m);
exit(0);
}</STRONG></PRE></DIV></DIV></TD></TR></TBODY></TABLE><BR>
<DIV class=3Dopt><A =
title=3D=B2=E9=BF=B4=B8=C3=B7=D6=C0=E0=D6=D0=CB=F9=D3=D0=CE=C4=D5=C2=20
href=3D"http://hi.baidu.com/leokan/blog/category/Oi">=C0=E0=B1=F0=A3=BAOi=
</A> | <A=20
href=3D"http://hi.baidu.com/leokan/modify/blog/060b0224c1d08037c9955957">=
=B1=E0=BC=AD</A> |=20
<A onclick=3D"return blogdel('blogdelform')"=20
href=3D"http://hi.baidu.com/leokan/blog/item/060b0224c1d08037c9955957.htm=
l#">=C9=BE=B3=FD</A>=20
<FORM id=3Dblogdelform style=3D"DISPLAY: none" name=3Dblogdelform=20
action=3D/leokan/commit method=3Dpost><INPUT type=3Dhidden value=3D1 =
name=3Dct><INPUT=20
type=3Dhidden value=3D3 name=3Dcm><INPUT type=3Dhidden =
value=3D060b0224c1d08037c9955957=20
name=3DspBlogID><INPUT type=3Dhidden =
value=3Dhttp://hi.baidu.com/leokan/blog=20
name=3DspRefURL></FORM>
<SCRIPT language=3Djavascript>
<!--
function blogdel(str)
{
var pop=3Dnew Popup({ =
contentType:3,isReloadOnClose:false,width:340,height:80});
pop.setContent("title","=C9=BE=B3=FD=CE=C4=D5=C2");
=
pop.setContent("confirmCon","=C4=FA=C8=B7=B6=A8=D2=AA=B3=B9=B5=D7=C9=BE=B3=
=FD=D5=E2=C6=AA=CE=C4=D5=C2=BC=B0=C6=E4=CB=F9=D3=D0=C6=C0=C2=DB=C2=F0=A3=BF=
");
pop.setContent("callBack",delCallback);
pop.setContent("parameter",{fid:str,popup:pop});
pop.build();
pop.show();
return false;
}
function delCallback(para)
{
var o_pop=3Dpara["popup"];
o_pop.config.contentType=3D1;
o_pop.setContent("contentUrl","");
o_pop.reBuild();
G(para["fid"]).target=3Do_pop.iframeIdName;
eval("document."+para["fid"]).submit();
}
//-->
</SCRIPT>
| <A =
title=3D=BD=AB=B4=CB=CE=C4=D5=C2=CC=ED=BC=D3=B5=BD=B0=D9=B6=C8=CB=D1=B2=D8=
onclick=3D"return addToFavor();"=20
href=3D"http://cang.baidu.com/do/add" =
target=3D_blank>=CC=ED=BC=D3=B5=BD=CB=D1=B2=D8</A> | =E4=AF=C0=C0(<SPAN=20
id=3Dresult></SPAN>) | <A=20
href=3D"http://hi.baidu.com/leokan/blog/item/060b0224c1d08037c9955957.htm=
l#send">=C6=C0=C2=DB</A> (0)
<SCRIPT language=3Djavascript>
/*<![CDATA[*/
var pre =3D [true,'USACO 1.4.1 Packing Rectangles =CC=E2=BD=E2', 'USACO =
1.4.1 Packing =
Rectangles...','/leokan/blog/item/c5076181c65140dcbd3e1e73.html'];
var post =3D [true,'USACO 1.5.2 Prime Palindromes =CC=E2=BD=E2','USACO =
1.5.2 Prime Palindromes ...', =
'/leokan/blog/item/58852b9794fd676955fb96b4.html'];
if(pre[0] || post[0]){
document.write('<div =
style=3D"height:5px;line-height:5px;"> </div><div id=3D"in_nav">');
if(pre[0]){
document.write('=C9=CF=D2=BB=C6=AA=A3=BA<a href=3D"' + pre[3] + '" =
title=3D"' + pre[1] + '">' + pre[2] + '</a> ');
}
if(post[0]){
document.write('=CF=C2=D2=BB=C6=AA=A3=BA<a href=3D"' + post[3] + '" =
title=3D"' + post[1] + '">' + post[2] + '</a>');
}
document.write('</div>');
}
/*]]>*/
</SCRIPT>
</DIV>
<DIV class=3Dline></DIV>
<STYLE type=3Dtext/css>#in_related_doc A {
TEXT-DECORATION: none
}
</STYLE>
<DIV id=3Din_related_tmp></DIV>
<SCRIPT language=3Djavascript type=3Dtext/javascript>
/*<![CDATA[*/
function HI_MOD_IN_RELATED_DOC_CALLBACK(arg){
if(arg.length <=3D 1) return false;
var hasMore =3D arg[0];
var D=3Dfunction(A,B){A[A.length]=3DB;}
if(arg.length % 2 =3D=3D 0) D(arg, ["","","",""]);
var html =3D ['<div id=3D"in_related_doc"><div =
class=3D"tit">=CF=E0=B9=D8=CE=C4=D5=C2=A3=BA</div>'];
D(html, '<table cellpadding=3D"0" cellspacing=3D"3" border=3D"0">');
for(var i =3D 1, j =3D arg.length; i < j; i +=3D 2){
D(html, '<tr>');
D(html, '<td width=3D"15px"><a style=3D"font-size:25px" =
>•</a></td><td><a href=3D"http://hi.baidu.com/' + arg[i][3] + =
'/blog/item/' + arg[i][2] + '.html" target=3D"_blank" title=3D"' + =
arg[i][0] + '">' + arg[i][1] + '</a>');
D(html, new Array(10).join('\u3000'));
D(html, '</td>');
if(arg[i + 1][0] !=3D "")
D(html, '<td width=3D"15px"><a style=3D"font-size:25px" =
>•</a></td><td><a href=3D"http://hi.baidu.com/' + arg[i + 1][3] + =
'/blog/item/' + arg[i + 1][2] + '.html" target=3D"_blank" title=3D"' + =
arg[i + 1][0] + '">' + arg[i + 1][1] + '</a></td>');
else
D(html, '<td> </td><td> </td>');
D(html, '</tr>');
}
if(hasMore) D(html, '<tr><td colspan=3D"4"><a target=3D"_blank" =
href=3D"/sys/search?pageno=3D1&type=3D7&sort=3D1&word=3DUSACO%201%2E5%2E1=
%20Number%20Triangles%20%CC%E2%BD%E2&item=3D060b0224c1d08037c9955957">=B8=
=FC=B6=E0>></a></td></tr>');
D(html, '</table></div><div class=3D"line"> </div>');
var div =3D document.getElementById('in_related_tmp');
if(div){
div.innerHTML =3D html.join('');
while(div.firstChild){
div.parentNode.insertBefore(div.firstChild, div);
}
div.parentNode.removeChild(div);
}
}
if(RelatedDocData =3D=3D -1){ // not supported xhr
var script =3D document.createElement('script');
script.type =3D 'text/javascript';
script.src =3D =
'/sys/search?type=3D8&word=3DUSACO%201%2E5%2E1%20Number%20Triangles%20%CC=
%E2%BD%E2&item=3D060b0224c1d08037c9955957&t=3D' + new Date().getTime();
document.getElementsByTagName('HEAD')[0].appendChild(script);
}else if(RelatedDocData =3D=3D null){
GetAndEval =3D true;
}else{
eval(RelatedDocData);
}
/*]]>*/
</SCRIPT>
<DIV id=3Din_reader>
<DIV class=3Dtit>=D7=EE=BD=FC=B6=C1=D5=DF=A3=BA</DIV>
<SCRIPT>
var g_spAnnony=3Dfalse;
var g_read=3D[
{}
];
g_read.length=3Dg_read.length-1;
var _rh1=3D"";
var _rh2=3D"";
function wrreader(){
_rh1 +=3D '<table width=3D"100%" ><tr>';
_rh2+=3D'<tr>';
if(g_spAnnony){
_rh1+=3D'<td align=3D"center" width=3D"10%" ><img border=3D"0" =
width=3D"55" height=3D"55" =
src=3D"http://img.baidu.com/hi/img/portraitn.jpg"></td>';
_rh2+=3D'<td> </td>';
if(g_read.length>0){
_rh1+=3D'<td align=3D"left" width=3D"12%">';
}else{
_rh1+=3D'<td align=3D"left" width=3D"100%">';
}
_rh1+=3D"<a =
href=3D'http://passport.baidu.com/?login&tpl=3Dsp&tpl_reg=3Dsp&u=3D"+myre=
f+"' =
target=3D'_self'>=B5=C7=C2=BC</a>=BA=F3=A3=AC=C4=FA=BE=CD=B3=F6=CF=D6=D4=DA=
=D5=E2=C0=EF=A1=A3</td>";
_rh2+=3D'<td> </td>'
}
if(g_read.length=3D=3D0){
if(!g_spAnnony){
_rh1+=3D'<td align=3Dleft =
width=3D"100%">=D7=EE=BD=FC=BB=B9=C3=BB=D3=D0=B5=C7=C2=BC=D3=C3=BB=A7=BF=B4=
=B9=FD=D5=E2=C6=AA=CE=C4=D5=C2=A1=AD=A1=AD</td>';
_rh2+=3D'<td> </td>';
}
}else{
for(i=3D0,len=3Dg_read.length;i<len;i++){
_rh1+=3D'<td align=3D"center" valign=3D"bottom" width=3D"10%" =
class=3D"user"><a href=3D"/'+g_read[i][0]+'" target=3D"_blank"><img =
border=3D"0" =
src=3D"http://himg.baidu.com/sys/portraitn/item/'+g_read[i][1]+'.jpg"></a=
></td>';
_rh2+=3D'<td align=3D"center" valign=3D"top" class=3D"user"><a =
href=3D"/'+g_read[i][0]+'" target=3D"_blank">'+g_read[i][2]+'</a></td>';
}
}
_rh1+=3D'<td width=3D"100%"></td></tr>';
_rh2+=3D'<td></td></tr></table>';
document.write(_rh1+_rh2);
}
wrreader();
</SCRIPT>
</DIV>
<DIV class=3Dline></DIV>
<SCRIPT language=3DJavaScript>
allkey=3Dallkey+"142d077b0bb076f40bd18714_060b0224c1d08037c9955957_";
</SCRIPT>
<DIV id=3Din_comment><A name=3Dcomment></A>
<DIV class=3Dtit>=CD=F8=D3=D1=C6=C0=C2=DB=A3=BA</DIV>
<SCRIPT>
function writecmt(type,id,cmtname,cmturl,portraitId){
var html1=3D"";
if(type=3D=3D1){
html1=3D"<a name=3D'"+id+"' href=3D'"+cmturl+"' target=3D'_blank' =
title=3D'"+cmturl+"'><img border=3D'0' =
src=3D'http://himg.baidu.com/sys/portraitn/item/"+portraitId+".jpg'><br>"=
+cmtname+"</a>";
}else{
if(cmtname=3D=3D"" || cmtname=3D=3D"=C4=E4=C3=FB=CD=F8=D3=D1"){
if(cmturl=3D=3D""){
html1=3D"<a name=3D'"+id+"'>=C4=E4=C3=FB=CD=F8=D3=D1</a>";
}else{
html1=3D"<a name=3D'"+id+"' href=3D'"+cmturl+"' target=3D'_blank' =
title=3D'"+cmturl+"'>"+cmtname+"</a>";
}
⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -