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📄 usaco 3_1_2 score inflation 题解_leokan的blog.mht

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size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      size=3D1>http://hi.baidu.com/leokan/</FONT></A></STRONG></P>
      <P><STRONG>=C4=A3=D0=CD=B5=C4=C7=F3=BD=E2:<FONT color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>=B7=BD=B7=A8=D2=BB:=D6=
=B1=BD=D3=BD=A8=C1=A2=C4=A3=D0=CD<FONT=20
      color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>score:array[1..n]=A1=FB=
S<FONT=20
      color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>timearray[1..n]=A1=FBT=
<FONT=20
      color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>f:array[1..m]=A1=FB0=20
      {f[x]=3Df(x)}<FONT color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>for i=A1=FB1 to =
m do<FONT=20
      color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>for j=A1=FB1 to =
n do=20
      {f(x)=3Dmax{f(x-Ti)+Si} <FONT color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>&nbsp;&nbsp;&nbsp; if =

      f[i-time[j]]+score[j]&gt;f[i] and i-time[j]&gt;0<FONT =
color=3D#ffffff=20
      =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A =
href=3D"http://hi.baidu.com/leokan/"><FONT=20
      color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;=20
      then f[i]=A1=FBf[i-time[j]]+score[j]<FONT color=3D#ffffff=20
      =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A =
href=3D"http://hi.baidu.com/leokan/"><FONT=20
      color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>=D5=E2=D6=D6=B7=BD=B7=A8=
=CA=C7=BF=C9=D0=D0=B5=C4=B7=BD=B7=A8=D6=AE=D2=BB,=B5=AB=CA=C7=D0=A7=C2=CA=
=B2=BB=B8=DF,=BB=B9=D3=D0=D2=BB=D6=D6=B7=BD=B7=A8<FONT=20
      color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>=B7=BD=B7=A8=B6=FE:=B3=
=E4=B7=D6=C0=FB=D3=C3=D2=D1=BE=AD=B5=C3=B5=BD=B5=C4=D7=B4=CC=AC<FONT=20
      color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>f:array[1..m]=A1=FB(f[=
i]=3DSi)<FONT=20
      color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>for i=A1=FB1 to =
m do<FONT=20
      color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>for j=A1=FB1 to =
i div 2=20
      do<FONT color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>&nbsp;&nbsp;&nbsp; if =

      f[i-j]+f[j]&gt;f[i] then f[i]:=3Df[i-j]+f[j];<FONT color=3D#ffffff =

      =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A =
href=3D"http://hi.baidu.com/leokan/"><FONT=20
      color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A><BR>=D5=E2=D6=D6=B7=BD=B7=A8=
=D6=B1=BD=D3=C0=FB=D3=C3=D2=D4=C7=B0=B5=C3=B5=BD=B5=C4=C3=BF=D2=BB=D6=D6=D7=
=B4=CC=AC=A1=C6Si,=A1=C6Ti=C7=F3=BD=E2,=BD=AB=D7=B4=CC=AC=CF=E0=BC=D3,=B6=
=F8=B2=BB=CA=C7=BD=ABSi,Ti=CF=E0=BC=D3,=BF=C9=D2=D4=CB=B5=D0=A7=C2=CA=BB=E1=
=B8=FC=B8=DF.<FONT=20
      color=3D#ffffff =
size=3D1>=B1=BE=CC=FB=D4=AD=B4=B4,=C7=EB=CE=F0=D7=AA=D4=D8</FONT><A=20
      href=3D"http://hi.baidu.com/leokan/"><FONT color=3D#ffffff=20
      =
size=3D1>http://hi.baidu.com/leokan/</FONT></A></STRONG></P><STRONG>
      <HR>
      </STRONG>
      =
<P><STRONG>=CE=D2=B5=C4=B1=C8USACO=B5=C4=CF=EA=CF=B8=B6=E0=C1=CB</STRONG>=
</P>
      <P><STRONG>We use dynamic programming to calculate the best way to =
use t=20
      minutes for all t from 0 to tmax. </STRONG></P>
      <P><STRONG>When we find out about a new category of problem with =
points p=20
      and length t, we update the best for j minutes by taking the =
better of=20
      what was there already and what we can do by using a p point =
problem with=20
      the best for time j - t. </STRONG></P><PRE><STRONG>#include =
&lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;string.h&gt;
#include &lt;assert.h&gt;

#define MAXCAT 10000
#define MAXTIME 10000

int best[MAXTIME+1];

void
main(void)
{
    FILE *fin, *fout;
    int tmax, ncat;
    int i, j, m, p, t;

    fin =3D fopen("inflate.in", "r");
    fout =3D fopen("inflate.out", "w");
    assert(fin !=3D NULL &amp;&amp; fout !=3D NULL);

    fscanf(fin, "%d %d", &amp;tmax, &amp;ncat);

    for(i=3D0; i&lt;ncat; i++) {
 fscanf(fin, "%d %d", &amp;p, &amp;t);
 for(j=3D0; j+t &lt;=3D tmax; j++)
     if(best[j]+p &gt; best[j+t])
      best[j+t] =3D best[j]+p;
    }

 m =3D 0;
    for(i=3D0; i&lt;=3Dtmax; i++)
 if(m &lt; best[i])
     m =3D best[i];

    fprintf(fout, "%d\n", m);
    exit(0);
}
</STRONG></PRE>
      <P><STRONG>Greg Price writes: After the main `for' loop that does =
the=20
      actual DP work, we don't need to look at the entire array of best =
point=20
      totals to find the highest one. The array is always nondecreasing, =
so we=20
      simply output the last element of the array. =
</STRONG></P><PRE><STRONG>#include &lt;fstream.h&gt;

ifstream fin("inflate.in");
ofstream fout("inflate.out");

const short maxm =3D 10010;
long best[maxm], m, n;

void
main()
{
    short i, j, len, pts;

    fin &gt;&gt; m &gt;&gt; n;

    for (j =3D 0; j &lt;=3D m; j++)
        best[j] =3D 0;

    for (i =3D 0; i &lt; n; i++) {
        fin &gt;&gt; pts &gt;&gt; len;
        for (j =3D len; j &lt;=3D m; j++)
            if (best[j-len] + pts &gt; best[j])
                best[j] =3D best[j-len] + pts;
    }
    fout &lt;&lt; best[m] &lt;&lt; endl; // This is always the highest =
total.
}</STRONG></PRE></DIV></TD></TR></TBODY></TABLE><BR>
<DIV class=3Dopt><A =
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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/ec65ea1188a010c2a6ef3f6f">=
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<A onclick=3D"return blogdel('blogdelform')"=20
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12345

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