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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_1132</title> <link rel="stylesheet" href="reset.css" type="text/css" media="all"> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> </head> <body> <table summary="top nav" border="0" width="100%"> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_1131.html">< previous page</a></td> <td align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_1132</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_1133.html">next page ></a></td> </tr> <tr> <td align="left" colspan="3" style="background: #ffffff; padding: 20px;"> <table border="0" width="100%" cellpadding="0"><tr><td align="center"> <table border="0" cellpadding="2" cellspacing="0" width="100%"><tr><td align="left"></td> <td align="right"></td> </tr></table></td></tr><tr><td align="left"><p></p><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="right"><font face="Times New Roman, Times, Serif" size="2" color="#FF0000">Page 1132</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Courier New, Courier, Mono New, Courier, Mono" size="2">聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽Move聽circle聽3聽from聽1聽to聽3<br />From聽second:聽聽聽聽聽2聽聽聽聽聽聽2聽聽聽聽聽1聽聽聽聽聽3<br />From聽聽first:聽聽聽聽聽1聽聽聽聽聽聽2聽聽聽聽聽3聽聽聽聽聽1<br />From聽聽first:聽聽聽聽聽0聽聽聽聽聽聽2聽聽聽聽聽1聽聽聽聽聽3<br />聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽Move聽circle聽1聽from聽2聽to聽1<br />From聽second:聽聽聽聽聽0聽聽聽聽聽聽3聽聽聽聽聽2聽聽聽聽聽1<br />聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽Move聽circle聽2聽from聽2聽to聽3<br />From聽second:聽聽聽聽聽1聽聽聽聽聽聽1聽聽聽聽聽2聽聽聽聽聽3<br />From聽聽first:聽聽聽聽聽0聽聽聽聽聽聽1聽聽聽聽聽3聽聽聽聽聽2<br />聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽Move聽circle聽1聽from聽1聽to聽3<br />From聽second:聽聽聽聽聽0聽聽聽聽聽聽2聽聽聽聽聽1聽聽聽聽聽3</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="17"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Recursive Algorithms with Structured Variables</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">In our definition of a recursive algorithm, we said there were two cases: the recursive or general case, and the base case for which an answer can be expressed nonrecursively. In the general case for all our algorithms so far, a parameter was expressed in terms of a smaller value each time. When structured variables are used, the recursive case is often in terms of a smaller structure rather than a smaller value; the base case occurs when there are no values left to process in the structure.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">We examine a recursive algorithm for printing the contents of a onedimensional array of <i>n</i> elements to show what we mean.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Print聽Array</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table cellspacing="0" border="0" width="336" cellpadding="4"><tr><td valign="top"><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Courier New, Courier, Mono New, Courier, Mono" size="2">IF聽more聽elements<br />聽聽聽Print聽the聽value聽of聽the聽first聽element<br />聽聽聽Print聽Array聽of聽n聽-聽1聽elements</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td></tr></table><br /><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">The recursive case is to print the values in an array that is one element smaller; that is, the length of the array decreases by 1 with each recursive call. The base case is when the length of the array becomes 0that is, when there are no more elements to print.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Our parameters must include the index of the first element (the one to be printed). How do we know when there are no more elements to print (that is, when the length of the array to be printed is 0)? We know we have printed the last element in the array when the index of the next element to be printed is beyond the index of the last element in the array. Therefore, the index of the last array element must be passed as a parameter. We call the indices </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> and </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3">. When </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> is greater than </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3">, we are finished. The name of the array is </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">list</font><font face="Times New Roman, Times, Serif" size="3">.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td></tr></table><p><font size="0"></font></p>聽 </td> </tr> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_1131.html">< previous page</a></td> <td align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_1132</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_1133.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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