no33.htm

常用经典算法及讲解

lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>3</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>和</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>5</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>的路径也不会是最短的。例如，若选择的子路径（非最短路径）是</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>3</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>2</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>5 (</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>耗费为</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>9 )</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，则</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>1</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>到</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>5</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>的路径为</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>1</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>3</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>2</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>5 (</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>耗费为</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>11 )</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，这比选择最短子路径</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>3</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>4</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>5</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>而得到的</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>1</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>到</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>5</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>的路径</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>1</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>3</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>4</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>5 (</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>耗费为</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>9) </span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>耗费更大。<span lang=EN-US><o:p></o:p></span></span></p>

<p class=MsoNormal align=left style='text-align:left;text-indent:20.0pt;
mso-char-indent-count:2.0;mso-char-indent-size:10.0pt;mso-layout-grid-align:
none;text-autospace:none'><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>所以在最短路径问题中，假如在的第一次决策时到达了某个节点</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>v</span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，那么不管</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>v </span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>是怎样确定的，此后选择从</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>v </span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>到</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>d </span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>的路径时，都必须采用最优策略。<span
lang=EN-US><o:p></o:p></span></span></p>

<p class=MsoNormal align=left style='text-align:left;text-indent:20.1pt;
mso-char-indent-count:2.0;mso-char-indent-size:10.05pt;mso-layout-grid-align:
none;text-autospace:none'><b><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>例<span lang=EN-US>3</span></span></b><b><span
lang=EN-US style='font-size:10.0pt;font-family:Arial;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>-2 [0/1</span></b><b><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>背包问题</span></b><b><span lang=EN-US style='font-size:10.0pt;font-family:
Arial;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>]</span></b><span
lang=EN-US style='font-size:10.0pt;font-family:Arial;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'> </span><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>考察</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>1 3 . 4</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>节的</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>0 / 1</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>背包问题。如前所述，在该问题中需要决定</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>x</span></i><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>1 </span></i><span lang=EN-US style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>.. </span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>x</span></i><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>n</span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>的值。假设按</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>= 1</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>，</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>2</span><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，<span
lang=EN-US>.，</span></span><i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>n </span></i><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>的次序来确定</span><i><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>x</span></i><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i </span></i><span style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>的值。如果置</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>x</span></i><span lang=EN-US style='font-size:5.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>1 </span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>= 0</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，则问题转变为相对于其余物品（即物品</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>2</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>3</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，<span lang=EN-US>.，</span></span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>n</span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>），背包容量仍为</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>c </span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>的背包问题。若置</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>x</span></i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>1 </span><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>= 1</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>，问题就变为关于最大背包容量为</span><i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>c</span></i><span
lang=EN-US style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>-</span><i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>w</span></i><span
lang=EN-US style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>1 </span><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>的问题。现设</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>r</span></i><span lang=EN-US style='font-size:10.0pt;
font-family:Symbol;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>&Icirc;</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>{<i>c</i></span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>，</span><i><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>c</span></i><span lang=EN-US
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>-</span><i><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>w</span></i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>1 </span><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>} </span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>为剩余的背包容量。<span lang=EN-US><o:p></o:p></span></span></p>

<p class=MsoNormal align=left style='text-align:left;text-indent:20.0pt;
mso-char-indent-count:2.0;mso-char-indent-size:10.0pt;mso-layout-grid-align:
none;text-autospace:none'><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>在第一次决策之后，剩下的问题便是考虑背包容量为</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>r </span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>时的决策。不管</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>x</span></i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>1 </span><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>是</span><span lang=EN-US style='font-size:
10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>0</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>或是</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>1</span><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>[<i>x</i></span><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>2 </span><span style='font-size:10.0pt;font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>，<span lang=EN-US>.，</span></span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>x</span></i><i><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;