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📁 Programming and Problem Solving with C++
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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_1109</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_1108.html">&lt;&nbsp;previous page</a></td>				<td align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_1109</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_1110.html">next page&nbsp;&gt;</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 1109</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="Times New Roman, Times, Serif" size="3">Testing: To exhaustively test this program, all possible configurations of a deck of 52 cards have to be generated. Although this is theoretically possible, it is not realistic. There are 52! [52 factorial] possible arrangements of a deck of cards, and 52! equals</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">52 * 51 * 50 *  2 * 1</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">This is a large number. Try multiplying it out.</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">Therefore, another method of testing is required. At a minimum, the questions to be examined are:</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">1. Does the program recognize a winning hand?</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">2. Does the program recognize a losing hand?</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">To answer these questions, we must examine at least one hand declared to be a winner and several hands declared to be losers. Specifying 20 as the number of games to play, we ran the program to see if there were any winning hands. There were none.</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">From past experience, we know this solitaire game is difficult. We let the simulation run, specifying 100 games and an initial seed of 3. There were two winning hands. Intermediate output statements were put in to examine the winning hands. They were correct. Several losing hands were also printed; they were indeed losing hands. Satisfied that the program was working correctly, we set up runs that varied in length, number of shuffles, and seed for the random number generator. The results are listed below. There is no strategy behind the particular choices of parameters; they are random.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table cellpadding="0" cellspacing="0" border="0" width="100%"><tr><td height="12"></td></tr><tr><td><table cellspacing="0" width="461" cellpadding="7"><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>Number of Games</i></font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>Number of Shuffles</i></font></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2"><i>Seed</i></font></td></tr></table></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>Games Won</i></font></td></tr><tr><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2"> 100</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">1</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">3</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">2</font></td></tr></table></td></tr><tr><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">100</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">2</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">4</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">0</font></td></tr></table></td></tr><tr><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">500</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">3</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">4</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">3</font></td></tr></table></td></tr><tr><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">1,000</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">6</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">3</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">6</font></td></tr></table></td></tr><tr><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">5,000</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">10</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">327</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">11</font></td></tr></table></td></tr><tr><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">10,000</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">4</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">4</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">40</font></td></tr></table></td></tr><tr><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">10,000</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">4</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">3</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">45</font></td></tr></table></td></tr><tr><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">10,000</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">4</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">120</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">44</font></td></tr></table></td></tr></table></td></tr></table><br /><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">Testing and Debugging</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 this chapter, all the functions that deleted a value from a data structure assumed that an item was there to be deleted (</font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">DeleteTop</font><font face="Times New Roman, Times, Serif" size="3"> and </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">RemoveTop</font><font face="Times New Roman, Times, Serif" size="3">) or that the specific item to be deleted was in the list (</font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">Delete</font><font face="Times New Roman, Times, Serif" size="3">). The calling code was responsible for guaranteeing this precondition.</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>  </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_1108.html">&lt;&nbsp;previous page</a></td>				<td align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_1109</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_1110.html">next page&nbsp;&gt;</a></td>			</tr>		</table>		</body>	</html>

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