no44.htm

常用经典算法及讲解

color:black;mso-font-kerning:0pt'>K</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'>K</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>节点死亡，回溯到</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>E</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，而</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>E</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>也不能进一步扩充，它也死亡了。接着，回溯到</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>B</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>，它也死亡了，</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 style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>再次变为</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>E</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
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>节点。它可被进一步扩充，到达节点</span><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>C</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>。此时</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;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>= 3 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'>c p</span></i><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'>。从</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>C</span><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>点能够移动到</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>F</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'>G</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>。假定移动到</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>F</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'>F</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>变为新的</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>E</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
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>节点并且活节点为</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>A, C,F</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>。在</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>F</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'>r</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 5</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 p</span></i><span lang=EN-US style='font-size:10.0pt;
mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>= 2 5</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>。从</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>F</span><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>点，能移动到</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>L</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'>M</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>。假定移动到</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>L</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>。此时</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;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'>c p</span></i><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>= 5 0</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>。既然</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>L</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>是一个叶节点，它表示了一个比目前找到的最优解（即节点</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>K</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>）更好的可行解，我们把这个解作为最优解。节点</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>L</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>死亡，回溯到节点</span><span
lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;
color:black;mso-font-kerning:0pt'>F</span><span style='font-size:10.0pt;
font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>。继续下去，搜索整棵树。在搜索期间发现的最优解即为最后的解。<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 lang=EN-US>4</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'>-3 [</span></b><b><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>旅行商问题</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
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>在这个问题中，给出一个</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'>顶点网络（有向或无向），要求找出一个包含所有</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'>个顶点的具有最小耗费的环路。任何一个包含网络中所有</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'>个顶点的环路被称作一个旅行（</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>t o u r</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>）。在旅行商问题中，要设法找到一条最小耗费的旅行。<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'>图</span><span lang=EN-US style='font-size:
10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>1 6
- 4</span><span style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>给出了一个四顶点网络。在这个网络中，一些旅行如下： </span><span lang=EN-US
style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;
mso-font-kerning:0pt'>1 , 2 , 4 , 3 , 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'>1 , 3 , 2 , 4 , 1</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'>1 , 4 , 3 , 2 , 1</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>。旅行</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>2 , 4 , 3 , 1 , 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'>4 , 3 , 1 , 2 , 4</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'>3 , 1 , 2 , 4 , 3</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>和旅行</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>1 , 2 , 4 , 3 , 1</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>一样。而旅行</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 , 2 , 1</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>是旅行</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>1 , 2 , 4 , 3 , 1</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>的“逆”。旅行</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>1 , 2 , 4 , 3 , 1</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>的耗费为</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>6 6</span><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>；而</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 , 2 , 4 , 1</span><span
style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:
0pt'>的耗费为</span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:
仿宋_GB2312;color:black;mso-font-kerning:0pt'>2 5</span><span style='font-size:
10.0pt;font-family:仿宋_GB2312;color:black;mso-font-ker