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📁 Data Structures And Algorithms With Object-Oriented Design Patterns In Python (2003) source code and
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<HTML><HEAD><TITLE>Spreading Keys Evenly</TITLE></HEAD><BODY bgcolor="#FFFFFF"> <a href="../index.html" target="_top"><img src="../icons/usins.gif" alt="Logo" align=right></a><b>Data Structures and Algorithms with Object-Oriented Design Patterns in Python</b><br><A NAME="tex2html3623" HREF="page211.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html3621" HREF="page208.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html3615" HREF="page209.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html3625" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H3><A NAME="SECTION008112000000000000000">Spreading Keys Evenly</A></H3><P>Let  <IMG WIDTH=14 HEIGHT=14 ALIGN=MIDDLE ALT="tex2html_wrap_inline57875" SRC="img85.gif"  > be the probability that the hash function  <IMG WIDTH=51 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline61583" SRC="img832.gif"  >.A hash function which spreads keys evenly has the property thatfor  <IMG WIDTH=73 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline61585" SRC="img833.gif"  >,  <IMG WIDTH=68 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline61587" SRC="img834.gif"  >In other words,the hash values computed by the function  <IMG WIDTH=24 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline58645" SRC="img261.gif"  >are <em>uniformly distributed</em><A NAME=10605>&#160;</A>.Unfortunately,in order to say something about the distribution of the hash values,we need to know something about the distribution of the keys.<P>In the absence of any information to the contrary,we assume that the keys are equiprobable.Let  <IMG WIDTH=18 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline61591" SRC="img835.gif"  > be the set of keys that map to the value <I>i</I>.That is,  <IMG WIDTH=168 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline61595" SRC="img836.gif"  >.If this is the case,the requirement to spread the keys uniformly implies that   <IMG WIDTH=96 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline61597" SRC="img837.gif"  >.An equal number of keys should map into each array position.<P><HR><A NAME="tex2html3623" HREF="page211.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html3621" HREF="page208.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html3615" HREF="page209.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html3625" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <P><ADDRESS><img src="../icons/bruno.gif" alt="Bruno" align=right><a href="../copyright.html">Copyright &#169; 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a>  All rights reserved.</ADDRESS></BODY></HTML>
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