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34 lines
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<TITLE>CLHS: Section 4.3.5.1</TITLE>
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<H1><A REV=MADE HREF="http://www.lispworks.com/"><IMG WIDTH=80 HEIGHT=65 ALT="[LISPWORKS]" SRC="../Graphics/LWSmall.gif" ALIGN=Bottom></A><A REL=TOP HREF="../Front/index.htm"><IMG WIDTH=237 HEIGHT=65 ALT="[Common Lisp HyperSpec (TM)]" SRC="../Graphics/CLHS_Sm.gif" ALIGN=Bottom></A> <A REL=PREV HREF="04_ce.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Previous]" SRC="../Graphics/Prev.gif" ALIGN=Bottom></A><A REL=UP HREF="04_ce.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Up]" SRC="../Graphics/Up.gif" ALIGN=Bottom></A><A REL=NEXT HREF="04_ceb.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Next]" SRC="../Graphics/Next.gif" ALIGN=Bottom></A></H1>
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<H2>
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4.3.5.1 Topological Sorting</H2> <P>
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Topological sorting proceeds by finding a class C in SC such that no other <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>class</I></A> precedes that element according to the elements in R. The class C is placed first in the result. Remove C from SC, and remove all pairs of the form (C,D), D<ELEMENT-OF>SC, from R. Repeat the process, adding <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>classes</I></A> with no predecessors to the end of the result. Stop when no element can be found that has no predecessor. <P>
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If SC is not empty and the process has stopped, the set R is inconsistent. If every <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>class</I></A> in the finite set of <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>classes</I></A> is preceded by another, then R contains a loop. That is, there is a chain of classes C1,...,Cn such that Ci precedes Ci+1, 1<=i<n, and Cn precedes C1. <P>
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Sometimes there are several <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>classes</I></A> from SC with no predecessors. In this case select the one that has a direct <A REL=DEFINITION HREF="26_glo_s.htm#subclass"><I>subclass</I></A> rightmost in the <A REL=DEFINITION HREF="26_glo_c.htm#class_precedence_list"><I>class precedence list</I></A> computed so far. (If there is no such candidate <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>class</I></A>, R does not generate a partial ordering---the Rc, c<ELEMENT-OF>SC, are inconsistent.) <P>
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In more precise terms, let {N1,...,Nm}, m>=2, be the <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>classes</I></A> from SC with no predecessors. Let (C1...Cn), n>=1, be the <A REL=DEFINITION HREF="26_glo_c.htm#class_precedence_list"><I>class precedence list</I></A> constructed so far. C1 is the most specific <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>class</I></A>, and Cn is the least specific. Let 1<=j<=n be the largest number such that there exists an i where 1<=i<=m and Ni is a direct <A REL=DEFINITION HREF="26_glo_s.htm#superclass"><I>superclass</I></A> of Cj; Ni is placed next. <P>
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The effect of this rule for selecting from a set of <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>classes</I></A> with no predecessors is that the <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>classes</I></A> in a simple <A REL=DEFINITION HREF="26_glo_s.htm#superclass"><I>superclass</I></A> chain are adjacent in the <A REL=DEFINITION HREF="26_glo_c.htm#class_precedence_list"><I>class precedence list</I></A> and that <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>classes</I></A> in each relatively separated subgraph are adjacent in the <A REL=DEFINITION HREF="26_glo_c.htm#class_precedence_list"><I>class precedence list</I></A>. For example, let T1 and T2 be subgraphs whose only element in common is the class J. Suppose that no superclass of J appears in either T1 or T2, and that J is in the superclass chain of every class in both T1 and T2. Let C1 be the bottom of T1; and let C2 be the bottom of T2. Suppose C is a <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>class</I></A> whose direct <A REL=DEFINITION HREF="26_glo_s.htm#superclass"><I>superclasses</I></A> are C1 and C2 in that order, then the <A REL=DEFINITION HREF="26_glo_c.htm#class_precedence_list"><I>class precedence list</I></A> for C starts with C and is followed by all <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>classes</I></A> in T1 except J. All the <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>classes</I></A> of T2 are next. The <A REL=DEFINITION HREF="26_glo_c.htm#class"><I>class</I></A> J and its <A REL=DEFINITION HREF="26_glo_s.htm#superclass"><I>superclasses</I></A> appear last. <P>
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<A REL=COPYRIGHT HREF="../Front/Help.htm#Legal"><I>Copyright 1996-2005, LispWorks Ltd. All rights reserved.</I></A><P>
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