贪婪算法.htm

数据挖掘常用的贪婪算法

[</SPAN></B><B><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">最小代价通讯网络</SPAN></B><B><SPAN 
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</SPAN></B><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">城市及城市之间所有可能的通信连接可被视作一个无向图，图的每条边都被赋予一个权值，权值表示建成由这条边所表示的通信连接所要付出的代价。包含图中所有顶点（城市）的连通子图都是一个可行解。设所有的权值都非负，则所有可能的可行解都可表示成无向图的一组生成树，而最优解是其中具有最小代价的生成树。<SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">在这个问题中，需要选择一个无向图中的边集合的子集，这个子集必须满足如下限制条件：所有的边构成一个生成树。而优化函数是子集中所有边的权值之和。<SPAN 
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</SPAN><SPAN 
style="FONT-SIZE: 12pt; COLOR: blue; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">算法思想<SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">在贪婪算法（</SPAN><SPAN 
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method</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">）中采用逐步构造最优解的方法。在每个阶段，都作出一个看上去最优的决策（在一定的标准下）。决策一旦作出，就不可再更改。作出贪婪决策的依据称为贪婪准则（</SPAN><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">greedy 
criterion</SPAN><SPAN 
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align=left><B><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">例</SPAN></B><B><SPAN 
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[</SPAN></B><B><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">找零钱</SPAN></B><B><SPAN 
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</SPAN></B><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">一个小孩买了价值少于</SPAN><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美元的糖，并将</SPAN><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美元的钱交给售货员。售货员希望用数目最少的硬币找给小孩。假设提供了数目不限的面值为</SPAN><SPAN 
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5</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美分、</SPAN><SPAN 
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0</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美分、</SPAN><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美分、及</SPAN><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美分的硬币。售货员分步骤组成要找的零钱数，每次加入一个硬币。选择硬币时所采用的贪婪准则如下：每一次选择应使零钱数尽量增大。为保证解法的可行性（即：所给的零钱等于要找的零钱数），所选择的硬币不应使零钱总数超过最终所需的数目。<SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">假设需要找给小孩</SPAN><SPAN 
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7</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美分，首先入选的是两枚</SPAN><SPAN 
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5</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美分的硬币，第三枚入选的不能是</SPAN><SPAN 
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5</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美分的硬币，否则硬币的选择将不可行（零钱总数超过</SPAN><SPAN 
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7</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美分），第三枚应选择</SPAN><SPAN 
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0</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美分的硬币，然后是</SPAN><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美分的，最后加入两个</SPAN><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">美分的硬币。<SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">贪婪算法有种直觉的倾向，在找零钱时，直觉告诉我们应使找出的硬币数目最少（至少是接近最少的数目）。可以证明采用上述贪婪算法找零钱时所用的硬币数目的确最少（见练习</SPAN><SPAN 
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align=left><B><SPAN 
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[</SPAN></B><B><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">机器调度</SPAN></B><B><SPAN 
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</SPAN></B><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">现有</SPAN><I><SPAN 
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</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">件任务和无限多台的机器，任务可以在机器上得到处理。每件任务的开始时间为</SPAN><I><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">s</SPAN></I><I><SPAN 
lang=EN-US 
style="FONT-SIZE: 5pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">i</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">，完成时间为</SPAN><I><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">f</SPAN></I><I><SPAN 
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</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">，</SPAN><I><SPAN 
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lang=EN-US 
style="FONT-SIZE: 5pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">i 
</SPAN></I><SPAN lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">&lt; 
<I>f</I></SPAN><I><SPAN lang=EN-US 
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</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">。</SPAN><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">[<I>s</I></SPAN><I><SPAN 
lang=EN-US 
style="FONT-SIZE: 5pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">i 
</SPAN></I><SPAN lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">, 
<I>f</I></SPAN><I><SPAN lang=EN-US 
style="FONT-SIZE: 5pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">i 
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</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">为处理任务</SPAN><I><SPAN 
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</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">的时间范围。两个任务</SPAN><I><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">i</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">，</SPAN><I><SPAN 
lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">j 
</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">重指两个任务的时间范围区间有重叠，而并非是指</SPAN><I><SPAN 
lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">i</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">，</SPAN><I><SPAN 
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</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">的起点或终点重合。例如：区间</SPAN><SPAN 
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1</SPAN><SPAN 
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]</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">与区间</SPAN><SPAN 
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2</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">，</SPAN><SPAN 
lang=EN-US 
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