贪婪算法.htm

数据挖掘常用的贪婪算法

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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">本章及后续章节中的许多例子都是最优化问题（ 
</SPAN><SPAN lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">optimization 
problem</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">），每个最优化问题都包含一组限制条件（ 
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o n s t r a i n t</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">）和一个优化函数（ 
</SPAN><SPAN lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">optimization 
function</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">），符合限制条件的问题求解方案称为可行解（ 
</SPAN><SPAN lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">feasible 
solution</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">），使优化函数取得最佳值的可行解称为最优解（</SPAN><SPAN 
lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">optimal 
solution</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">）。<SPAN 
lang=EN-US><o:p></o:p></SPAN></SPAN></P>
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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">渴婴问题</SPAN></B><B><SPAN 
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style="mso-spacerun: yes">&nbsp;</SPAN>有一个非常渴的、聪明的小婴儿，她可能得到的东西包括一杯水、一桶牛奶、多罐不同种类的果汁、许多不同的装在瓶子或罐子中的苏打水，即婴儿可得到</SPAN><I><SPAN 
lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">n 
</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">种不同的饮料。根据以前关于这</SPAN><I><SPAN 
lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">n 
</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">种饮料的不同体验，此婴儿知道这其中某些饮料更合自己的胃口，因此，婴儿采取如下方法为每一种饮料赋予一个满意度值：饮用</SPAN><SPAN 
lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">1</SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">盎司第</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">种饮料，对它作出相对评价，将一个数值</SPAN><I><SPAN 
lang=EN-US 
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">作为满意度赋予第</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">种饮料。<SPAN 
lang=EN-US><o:p></o:p></SPAN></SPAN></P>
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">通常，这个婴儿都会尽量饮用具有最大满意度值的饮料来最大限度地满足她解渴的需要，但是不幸的是：具有最大满意度值的饮料有时并没有足够的量来满足此婴儿解渴的需要。设</SPAN><I><SPAN 
lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">a</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">是第</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">种饮料的总量（以盎司为单位），而此婴儿需要</SPAN><I><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">t 
</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">盎司的饮料来解渴，那么，需要饮用</SPAN><I><SPAN 
lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">n</SPAN></I><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">种不同的饮料各多少量才能满足婴儿解渴的需求呢？<SPAN 
lang=EN-US><o:p></o:p></SPAN></SPAN></P>
<P class=MsoNormal 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">设各种饮料的满意度已知。令</SPAN><I><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">x</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">为婴儿将要饮用的第</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">种饮料的量，则需要解决的问题是：<SPAN 
lang=EN-US><o:p></o:p></SPAN></SPAN></P>
<P class=MsoNormal style="TEXT-ALIGN: left; mso-layout-grid-align: none" 
align=left><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">找到一组实数</SPAN><I><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">x</SPAN></I><I><SPAN 
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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">1</SPAN><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">最大，并满足：</SPAN><I><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">及</SPAN><SPAN 
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</SPAN></I><SPAN 
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style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">需要指出的是：如果</SPAN><I><SPAN 
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style="FONT-SIZE: 5pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">= 
1</SPAN><I><SPAN lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">a</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 lang=EN-US 
style="FONT-SIZE: 10pt; COLOR: black; mso-font-kerning: 0pt; mso-fareast-font-family: 仿宋_GB2312">&lt; 
<I>t</I></SPAN><SPAN 
style="FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: 仿宋_GB2312; mso-font-kerning: 0pt">，则不可能找到问题的求解方案，因为即使喝光所有的饮料也不能使婴儿解渴。<SPAN 
lang=EN-US><o:p></o:p></SPAN></SPAN></P>
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