page463.html
来自「wqeqwvrw rkjqhwrjwq jkhrjqwhrwq jkhrwq」· HTML 代码 · 共 54 行
HTML
54 行
<HTML>
<HEAD>
<TITLE>Summary</TITLE>
</HEAD>
<BODY bgcolor="#FFFFFF">
<img src="cover75.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cover75.gif" alt="Logo" align=right>
<b>Data Structures and Algorithms
with Object-Oriented Design Patterns in C++</b><br>
<A NAME="tex2html7642" HREF="page464.html" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page464.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="next_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/next_motif.gif"></A> <A NAME="tex2html7640" HREF="page459.html" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page459.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="up_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/up_motif.gif"></A> <A NAME="tex2html7636" HREF="page462.html" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page462.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="previous_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/previous_motif.gif"></A> <A NAME="tex2html7644" HREF="page9.html" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page9.html"><IMG WIDTH=65 HEIGHT=24 ALIGN=BOTTOM ALT="contents" SRC="contents_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/contents_motif.gif"></A> <A NAME="tex2html7645" HREF="page620.html" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page620.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="index_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/index_motif.gif"></A> <BR><HR>
<H4><A NAME="SECTION0015340400000000000000">Summary</A></H4>
<P>
For many divide-and-conquer algorithms
the running time is given by the general recurrence
shown in Equation <A HREF="page459.html#eqnalgsdandq" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page459.html#eqnalgsdandq"><IMG ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A>.
Solutions to the recurrence depend on the relative
values of the constants <I>a</I>, <I>b</I> and <I>k</I>.
Specifically, the solutions satisfy the following bounds:
<P><A NAME="eqnalgsdandqsoln"> </A> <IMG WIDTH=500 HEIGHT=66 ALIGN=BOTTOM ALT="equation33113" SRC="img1914.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1914.gif" ><P>
<P>
Table <A HREF="page463.html#tblalgstimes2" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page463.html#tblalgstimes2"><IMG ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A> how to apply Equation <A HREF="page463.html#eqnalgsdandqsoln" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page463.html#eqnalgsdandqsoln"><IMG ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A>
to find the running times of the divide-and-conquer algorithms
described in the preceding sections.
Comparing the solutions in Table <A HREF="page463.html#tblalgstimes2" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page463.html#tblalgstimes2"><IMG ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A> with those
given in Table <A HREF="page459.html#tblalgstimes" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page459.html#tblalgstimes"><IMG ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A> shows the results obtained using
the general formula agree with the analyses done in the preceding sections.
<P>
<P><A NAME="33645"> </A>
<P>
<A NAME="tblalgstimes2"> </A>
<DIV ALIGN=CENTER><P ALIGN=CENTER><TABLE COLS=7 BORDER FRAME=HSIDES RULES=GROUPS>
<COL ALIGN=LEFT><COL ALIGN=LEFT><COL ALIGN=CENTER><COL ALIGN=CENTER><COL ALIGN=CENTER><COL ALIGN=CENTER><COL ALIGN=LEFT>
<TBODY>
<TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>
program </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> recurrence
</TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>a</I> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>b</I> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>k</I> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> case </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> solution </TD></TR>
</TBODY><TBODY>
<TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Program <A HREF="page456.html#progalgs1c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page456.html#progalgs1c"><IMG ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <I>T</I>(<I>n</I>)=<I>T</I>(<I>n</I>/2)+<I>O</I>(1)
</TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 1 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 2 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 0 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <IMG WIDTH=42 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap_inline68839" SRC="img1908.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1908.gif" > </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <IMG WIDTH=83 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline68869" SRC="img1915.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1915.gif" > </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>
Program <A HREF="page457.html#progalgs2c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page457.html#progalgs2c"><IMG ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <I>T</I>(<I>n</I>)=2<I>T</I>(<I>n</I>/2)+<I>O</I>(1)
</TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 2 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 2 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 0 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <IMG WIDTH=42 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline68825" SRC="img1902.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1902.gif" > </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <IMG WIDTH=64 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline68875" SRC="img1916.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1916.gif" > </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>
Program <A HREF="page458.html#progalgs3c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page458.html#progalgs3c"><IMG ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <I>T</I>(<I>n</I>)=2<I>T</I>(<I>n</I>/2)+<I>O</I>(<I>n</I>)
</TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 2 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 2 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 1 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <IMG WIDTH=42 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap_inline68839" SRC="img1908.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1908.gif" > </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <IMG WIDTH=83 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline68881" SRC="img1917.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1917.gif" > </TD></TR>
</TBODY>
<CAPTION ALIGN=BOTTOM><STRONG>Table:</STRONG> Computing Running Times using Equation <A HREF="page463.html#eqnalgsdandqsoln" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page463.html#eqnalgsdandqsoln"><IMG ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A></CAPTION></TABLE>
</P></DIV><P><HR><A NAME="tex2html7642" HREF="page464.html" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page464.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="next_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/next_motif.gif"></A> <A NAME="tex2html7640" HREF="page459.html" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page459.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="up_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/up_motif.gif"></A> <A NAME="tex2html7636" HREF="page462.html" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page462.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="previous_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/previous_motif.gif"></A> <A NAME="tex2html7644" HREF="page9.html" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page9.html"><IMG WIDTH=65 HEIGHT=24 ALIGN=BOTTOM ALT="contents" SRC="contents_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/contents_motif.gif"></A> <A NAME="tex2html7645" HREF="page620.html" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page620.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="index_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/index_motif.gif"></A> <P><ADDRESS>
<img src="bruno.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/bruno.gif" alt="Bruno" align=right>
<a href="javascript:if(confirm('http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/copyright.html \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/copyright.html'" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/copyright.html">Copyright © 1997</a> by <a href="javascript:if(confirm('http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/signature.html \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/signature.html'" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/signature.html">Bruno R. Preiss, P.Eng.</a> All rights reserved.
</ADDRESS>
</BODY>
</HTML>
⌨️ 快捷键说明
复制代码Ctrl + C
搜索代码Ctrl + F
全屏模式F11
增大字号Ctrl + =
减小字号Ctrl + -
显示快捷键?