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Programming and Problem Solving with C++

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  <td><font face="Times New Roman, Times, Serif" size="3">As you can see, each time the exponent increases by 1, the number of steps is multiplied by an additional order of magnitude (factor of 10). That is, if <i>N</i> is made 10 times greater, the work involved in an <i>N</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup></font><font face="Times New Roman, Times, Serif" size="3"> algorithm increases by a factor of 100, and the work involved in an <i>N</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>3</sup></font><font face="Times New Roman, Times, Serif" size="3"> algorithm increases by a factor of 1000. To put this in more concrete terms, an algorithm with a doubly nested loop, in which each loop depends on the number of data values, takes 1000 steps for 10 input values and 1 trillion steps for 10,000 values. On a computer that executes 1 million instructions per second, the latter case would take more than 11 days to run.</font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3">The table also shows that the steps outside of the innermost loop account for an insignificant portion of the total number of steps as <i>N</i> gets bigger. Because the innermost</font></td>
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