no11.htm

常用经典算法及讲解

lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>第 2--N+1 行: 每行输出
3 个数据:<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>年序号<span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp; </span>( 从 1
到 N 按升序输出 );<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>是否更新<span style="mso-spacerun: yes">&nbsp;&nbsp; </span>( 当年如果更新,输出 1, 否则输出
0); <o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>当年回收额 ( N 年回收总额应等于 W ).<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>例: 设给定以下数据:<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>N=4,<span
style="mso-spacerun: yes">&nbsp; </span>k=5,<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>i:<span style="mso-spacerun: yes">&nbsp;&nbsp; </span>0<span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>1<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>2<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>3<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>4<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>5 <o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>R[i]:<span
style="mso-spacerun: yes">&nbsp;&nbsp; </span>8<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>7<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>6<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>5<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>4<span style="mso-spacerun: yes">&nbsp; </span><span
style="mso-spacerun: yes">&nbsp;&nbsp;</span>2<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>U[i]:<span
style="mso-spacerun: yes">&nbsp; </span>0.5<span style="mso-spacerun:
yes">&nbsp;&nbsp; </span>1<span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;
</span>2<span style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>3<span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>4<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>5 <o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>C[i]:<span
style="mso-spacerun: yes">&nbsp;&nbsp; </span>0<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>2<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>3<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>5<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>8<span style="mso-spacerun: yes">&nbsp;&nbsp;
</span>10<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>则正确的输出应该是<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>24.5<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>1<span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>0<span style="mso-spacerun:
yes">&nbsp;&nbsp; </span>7.5<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>2<span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>1<span style="mso-spacerun:
yes">&nbsp;&nbsp; </span>5.5<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>3<span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>1<span style="mso-spacerun:
yes">&nbsp;&nbsp; </span>5.5<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>4<span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>0<span style="mso-spacerun:
yes">&nbsp;&nbsp; </span>6.0<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>【分析】这是动态规划的一个典型的例题<span
lang=EN-US>.由题意可知,用过t年的卡车,继续使用一年的收益为d[t]=R[t]-U[t],更换新车后一年的收益为e[t]=R[0]-U[0]-C[t].
我们采用倒推分析的方法.F[j,t]表示已经使用了t年的卡车, 在第j年不论继续使用还是更新,到第N年为止,可能得到的最大收益. 规定当j&gt;N时,
F[j,t]≡0. 如果在第j年更新,则收益为p=e[t]+F[j+1,1]; 如果仍使用旧车,则收益为 q=d[t]+F[j+1,t+1]. 这里,e[t]或d[t]为第j年的收益,
F[j+1,1]或F[j+1,t+1]为从第j+1年到第N年在不同条件下的最大收益.显然,F[j,t]=Max(p,q).这就是所需要的计算公式.<o:p></o:p></span></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp; </span>在下面的程序中,数组g[j,t]用于记录使用过t年的车,在第j年的选择方案,g[j,t]=1表示更换新车,g[j,t]=0表示仍使用旧车.<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:20.0pt;mso-line-height-rule:exactly'><span
style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>【参考程序】<span lang=EN-US><o:p></o:p></span></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>program tjcoi2_3;
{ Write By Li Xuewu }<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp; </span>type arr20=array[0..20] of real;<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp; </span>var rr,uu,cc,d,e:arr20;<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>f:array
[0..22,0..21] of real;<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>g:array
[0..22,0..21] of integer;<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>i,j,k,k2,n,t:integer;<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>file1:string[20];<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>p,q:real;<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>text2,text3:text;<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>procedure init;<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp; </span>var i:integer;<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp; </span>begin<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>writeln('Input filename:');<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>readln(file1);<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>assign(text2,file1);<span
style="mso-spacerun: yes">&nbsp; </span>reset(text2);<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>readln(text2,n);<span
style="mso-spacerun: yes">&nbsp;&nbsp; </span><span style="mso-spacerun:
yes">&nbsp;</span>readln(text2,k);<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>for i:=0 to k do
read(text2,rr[i]);<span style="mso-spacerun: yes">&nbsp; </span>readln(text2);<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>for i:=0 to k do
read(text2,uu[i]);<span style="mso-spacerun: yes">&nbsp; </span>readln(text2);<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>for i:=0 to k do
read(text2,cc[i]);<span style="mso-spacerun: yes">&nbsp; </span>readln(text2);<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>close(text2);<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </span>for i:=0 to k do<o:p></o:p></span></p>

<p class=MsoPlainText style='line-height:16.0pt;mso-line-height-rule:exactly'><span
lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>begin
d[i]:=rr[i]-uu[i]; <span style="mso-spacerun:
yes">&nbsp;</span>e[i]:=d[0]-cc[i];<span style="mso-spacerun: yes">&nbsp;
</span>end;<o:p></o:p></span></p>