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  <b>|</b><font face="宋体" size="2">第一章</font><b>|</b><font face="宋体" size="2"><a href="text2-0.htm">第二章</a></font><b>|</b><font face="宋体" size="2"><a href="text3-0.htm">第三章</a></font><b>|</b><font face="宋体" size="2"><a href="text4-0.htm">第四章</a></font><b>|</b><font face="宋体" size="2"><a href="text5-0.htm">第五章</a></font><b>|</b><font face="宋体" size="2"><a href="text6-0.htm">第六章</a></font><b>|</b><font face="宋体" size="2"><a href="text7-0.htm">第七章</a></font><b>|</b><font face="宋体" size="2"><a href="text8-0.htm">第八章</a></font><b>|</b><font face="宋体" size="2"><a href="text9-0.htm">第九章</a></font><b>|</b><font face="宋体" size="2"><a href="text10-0.htm">第十章</a></font><b>|</b><font size="2" face="宋体"><a href="textA-0.htm">算法分析</a><b><font color="#000000">|</font></b> 
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  <b>|</b><font face="宋体" size="2">第一章</font><b>|</b><font face="宋体" size="2"><a href="../text2/text2-0.htm">第二章</a></font><b>|</b><font face="宋体" size="2"><a href="../text3/text3-0.htm">第三章</a></font><b>|</b><font face="宋体" size="2"><a href="../text4/text4-0.htm">第四章</a></font><b>|</b><font face="宋体" size="2"><a href="../text5/text5-0.htm">第五章</a></font><b>|</b><font face="宋体" size="2"><a href="../text6/text6-0.htm">第六章</a></font><b>|</b><font face="宋体" size="2"><a href="../text7/text7-0.htm">第七章</a></font><b>|</b><font face="宋体" size="2"><a href="../text8/text8-0.htm">第八章</a></font><b>|</b><font face="宋体" size="2"><a href="../text9/text9-0.htm">第九章</a></font><b>|</b><font face="宋体" size="2"><a href="../text10/text10-0.htm">第十章</a></font><b>|</b><font size="2" face="宋体"><a href="../textA/textA-0.htm">算法分析</a><b><font color="#000000">|</font></b> 
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<pre><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b>
(3) <font color="#ff0033" size="5">Asymptotic Notation ( O、<img src="image/wR.gif" width="23" height="25">、<img src="image/oR.gif" width="24" height="23"> )</font>

     Program1 with a complexity of c1<img src="image/Image6.gif" width="26" height="20">  + c2n
     Program2 with a complexity of  c3n

    <font color="#FF0033"><i> Program2 is faster than program1 ?</i></font>
       
 <font color="#ff0033">&#149;</font>c1 =1, c2 =1, c3 = 100
    c1<img src="image/Image6.gif" width="26" height="21">  + c2n  <=  c3n        ( n <= 98 )
    c1<img src="image/Image6.gif" width="26" height="21">  + c2n   >   c3n        ( n > 98  )             </b><font color="#FF0033"><i><font size="5">Break even point</font></i></font><b>
                                                                         
 <font color="#ff0033">&#149;</font> c1 =1, c2 =1, c3 = 1000
    c1 <img src="image/Image6.gif" width="26" height="21"> + c2n  <=  c3n        ( n <= 998 )
   <font color="#FF0033">
<font color="#000000">《1》</font><font size="5">O</font></font>
【<font color="#0000FF">definition</font>】f(n) = O(g(n)) iff there exist positive constants c 
 and  n0 such that f(n) <= cg(n) for all n, n>=n0

<font size="3"> 3n + 2 = O(n)                  3n  + 2 <= 4n             <i>                for n >=2  c = 4 , n0=2</i>
10 </font><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image6.gif" width="26" height="21"></font></b></font></b></font></b></font><font size="3"> +4n + 2=O(</font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image6.gif" width="26" height="21"></font></b></font></b></font></b></font></b></font><font size="3"> )     10 </font><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image6.gif" width="26" height="21"></font></b></font></b></font></b></font><font size="3"> +4n + 2 <=11</font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image6.gif" width="26" height="21"></font></b></font></b></font></b></font></b></font></b></font><font size="3">    <i> for n >=5  c =11, n0=5 </i>
6*</font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image8.gif" width="20" height="26"></font></b></font><font size="3">+</font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image6.gif" width="26" height="21"></font></b></font></b></font></b></font></b></font><font size="3"> =O(</font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image8.gif" width="20" height="26"></font></b></font></b></font><font size="3"> )              6 *</font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image8.gif" width="20" height="26"></font></b></font><font size="3">+ <=7*</font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image8.gif" width="20" height="26"></font></b></font><font size="3">                     <i> for n >=4  c =7  , n0=4  </i>
3n + 3=O(</font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image6.gif" width="26" height="21"></font></b></font></b></font></b></font></b></font><font size="3"> )                 3n+3 <=3*</font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image6.gif" width="26" height="21"></font></b></font></b></font></b></font></b></font><font size="3">                          <i> for n >=2  c =3  , n0=2</i>
3n+2 <img src="image/Image10.gif" width="10" height="11"> O(1)                                                                          <i>c, n0   not exist  </i>
10</font><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" size="4"><b><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image6.gif" width="26" height="21"></font></b></font></b></font></b></font><font size="3">+4n +2 </font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image10.gif" width="10" height="11"></font></b></font><font size="3">O(n)                                                            <i>c, n0  not exist </i>
</font>
</b></font><font face="Arial, Helvetica, sans-serif" size="4"><b><font color="#FF0033">O(1)   O(logn)    O(n)    O(nlogn)   O(</font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b><font size="3"><img src="image/Image6.gif" width="26" height="21"></font></b></font><font color="#FF0033"> )    O( </font><font face="Arial, Helvetica, sans-serif" size="4"><b><img src="image/Image11.gif" width="18" height="22"></b></font><font color="#FF0033">)    O( <img src="image/Image12.gif" width="30" height="21">)  </font></b></font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b>

【<font color="#0000FF">Theorem1.2</font>】  If  f(n) = am </b></font><font face="Arial, Helvetica, sans-serif" size="4"><b><font color="#FF0033"><img src="image/Image12.gif" width="30" height="20"></font></b></font><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b>+ ……+a1n +a0   then f(n)=O( </b></font><font face="Arial, Helvetica, sans-serif" size="4"><b><font color="#FF0033"><img src="image/Image12.gif" width="30" height="21"></font></b></font><b><font face="宋体">)</font></b><font face="Arial, Helvetica, sans-serif" color="#000000" size="4"><b>
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