no11.htm

常用经典算法及讲解：贪婪

0pt'>&aring;</span><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 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;
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 lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>=<i>t</i></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'>0</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'>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'>≤</span><i><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>a</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'>）。如果</span><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 lang=EN-US
style='font-size:10.0pt;font-family:Symbol;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>&aring;</span><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
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;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>a</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 lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>&lt;<i>t</i></span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>，则输出适当的错误信息。<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'>在这个问题中，限制条件是</span><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 lang=EN-US style='font-size:10.0pt;
font-family:Symbol;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>&aring;</span><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 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;
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 lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>=<i>t </i></span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>且</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'>≤</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>x</span><span lang=EN-US style='font-size:
5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>i</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'>a</span><span lang=EN-US
style='font-size:5.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>i</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'>1</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'>i</span></i><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'>n</span></i><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>。而优化函数是</span><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 lang=EN-US style='font-size:10.0pt;
font-family:Symbol;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>&aring;</span><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 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;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>s</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><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'>。任何满足限制条件的一组实数</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'>都是可行解，而使</span><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 lang=EN-US style='font-size:10.0pt;
font-family:Symbol;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>&aring;</span><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 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;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>s</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><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'>最大的可行解是最优解。<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></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'>1-2 [</span></b><b><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>装载问题</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:仿宋_GB2312;color:black;mso-font-kerning:
0pt'><span style="mso-spacerun: yes">&nbsp;</span>有一艘大船准备用来装载货物。所有待装货物都装在货箱中且所有货箱的大小都一样，但货箱的重量都各不相同。设第</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 style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>个货箱的重量为</span><i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>w</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'>（</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><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
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'>n</span></i><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>），而货船的最大载重量为</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 style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，我们的目的是在货船上装入最多的货物。<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'>这个问题可以作为最优化问题进行描述：设存在一组变量</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'>，其可能取值为</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</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'>。如</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'>为</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'>，则货箱</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 style='font-size:10.0pt;font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>将不被装上船；如</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'>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'>，则货箱</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 style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>将被装上船。我们的目的是找到一组</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'>，使它满足限制条件</span><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 lang=EN-US style='font-size:10.0pt;
font-family:Symbol;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>&aring;</span><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 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;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>w</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><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'>≤</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'>且</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
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'>{0, 1}, 1 </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;