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Programming and Problem Solving with C++

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  <td><font face="Times New Roman, Times, Serif" size="3"><i>Call 2:</i> </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> is 1 and </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3"> is 4. Because </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> is less than </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3">, the value in </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">list</font><font face="Times New Roman, Times, Serif" size="3">[</font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3">] (which is 44) is printed. Execution of this call pauses while the array from </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> + 1 through </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3"> is printed.</font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3"><i>Call 3:</i> </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> is 2 and </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3"> is 4. Because </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> is less than </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3">, the value in </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">list</font><font face="Times New Roman, Times, Serif" size="3">[</font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3">] (which is 52) is printed. Execution of this call pauses while the array from </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> + 1 through </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3"> is printed.</font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3"><i>Call 4:</i> </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> is 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"> is 4. Because </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> is less than </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3">, the value in </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">list</font><font face="Times New Roman, Times, Serif" size="3">[</font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3">] (which is 61) is printed. Execution of this call pauses while the array from </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> + 1 through </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3"> is printed.</font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3"><i>Call 5:</i> </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> is 4 and </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3"> is 4. Because </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> is equal to </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3">, the value in </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">list</font><font face="Times New Roman, Times, Serif" size="3">[</font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3">] (which is 77) is printed. Execution of this call pauses while the array from </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> + 1 through </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3"> is printed.</font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3"><i>Call 6:</i> </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">first</font><font face="Times New Roman, Times, Serif" size="3"> is 5 and </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">last</font><font face="Times New Roman, Times, Serif" size="3"> is 4. Because </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">, the execution of this call is complete. Control returns to the preceding call.</font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3"><i>Call 5:</i> Execution of this call is complete. Control returns to the preceding call.</font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3"><i>Calls 4, 3, 2, and 1:</i> Each execution is completed in turn, and control returns to the preceding call.</font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3">Notice that once the deepest call (the call with the highest number) was reached, each of the calls before it returned without doing anything. When no statements are executed after the return from the recursive call to the function, the recursion is known as tail recursion. Tail recursion often indicates that the problem could be solved more easily using iteration. We used the array example because it made the recursive process easy to visualize; in practice, an array should be printed iteratively.</font></td>
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