page346.html

来自「Data Structures And Algorithms With Obje」· HTML 代码 · 共 46 行

HTML
46 行
字号 
<HTML><HEAD><TITLE>Running Time Analysis</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="tex2html5176" HREF="page347.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html5174" HREF="page344.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html5170" HREF="page345.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html5178" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H3><A NAME="SECTION0010722000000000000000">Running Time Analysis</A></H3><P>The running time of the downward pass of the insertion algorithmis identical to that of an unsuccessful search(assuming the item to be inserted is not already in the tree).That is, for a B-tree of height <I>h</I>,the worst-case running time of the downward pass is <P> <IMG WIDTH=414 HEIGHT=16 ALIGN=BOTTOM ALT="displaymath65179" SRC="img1355.gif"  ><P><P>The second pass of the insertion algorithm does the insertionand balances the tree if necessary.In the worst case,all of the nodes in the insertion path up to the root need to be balanced.Each time the <tt>insertUp</tt> method is invoked,it calls <tt>findIndex</tt> which has running time <IMG WIDTH=264 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline65187" SRC="img1356.gif"  > in the worst case.The additional time required to balance a node is <I>O</I>(<I>M</I>).Therefore, the worst-case running time of the upward pass is<P> <IMG WIDTH=401 HEIGHT=16 ALIGN=BOTTOM ALT="displaymath65180" SRC="img1357.gif"  ><P><P>Therefore, the total running time for insertion is<P> <IMG WIDTH=405 HEIGHT=16 ALIGN=BOTTOM ALT="displaymath65181" SRC="img1358.gif"  ><P>According to Theorem&nbsp;<A HREF="page340.html#theoremsrchtreeiii"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>,the height of a B-tree is  <IMG WIDTH=165 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline65191" SRC="img1359.gif"  >,where <I>n</I> is the number of keys in the B-tree.If we assume that two keys can be compared in constant time,i.e.,  <IMG WIDTH=96 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline64143" SRC="img1239.gif"  >,then the running time for insertion in a B-tree is simply  <IMG WIDTH=75 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline65197" SRC="img1360.gif"  >.<P><HR><A NAME="tex2html5176" HREF="page347.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html5174" HREF="page344.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html5170" HREF="page345.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html5178" 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>

page346.html - 源码说明

本页面展示了「Data Structures And Algorithms With Object-Oriented Design Patterns In Python (2003) source code and」中的 page346.html 源码文件，采用 HTML 编程语言编写，共 46 行代码。您可以在线阅读完整代码内容，也可以返回资源详情页下载完整源码包进行本地学习和开发。

虫虫下载站收录了大量与Object-Oriented相关的技术资源，包括源代码、技术文档、电路图等，是电子工程师和嵌入式开发者的专业学习平台。

⌨️ 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?