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EXAMPLE 4.2 Using a while Loop to Compute a Sum of Reciprocals
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This program computes the sum of reciprocals s = 1 + 1/2 + 1/3 + + 1/n, where n is integer for which n s: int main() { int bound; cout << "Enter a positive integer: "; cin >> bound; i double sum=0.0; 0 int i=0; 1 while (sum < bound) 2 3 sum += 1.0/++i; 4 cout << "The sum of the first " << i 5 << " reciprocals is " << sum << endl; 6 } 7 With input 3 for n, this run computes 1 + 1/2 + 1/3 + + 1/11 = 3.01988: 8 Enter a positive integer: 3 9 The sum of the first 11 reciprocals is 3.01988 10 11 The trace of this run is shown at right. The sum does not exceed 3 until the 11th iteration. the smallest
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sum 0.00000 1.00000 1.50000 1.83333 2.08333 2.28333 2.45000 2.59286 2.71786 2.82897 2.92897 3.01988
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EXAMPLE 4.3 Using a while Loop to Repeat a Computation
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This program prints the square root of each number input by the user. It uses a while loop to allow any number of computations in a single run of the program: int main() { double x; cout << "Enter a positive number: "; cin >> x; while (x > 0) { cout << "sqrt(" << x << ") = " << sqrt(x) << endl; cout << "Enter another positive number (or 0 to quit): "; cin >> x; } } Enter a positive number: 49 sqrt(49) = 7 Enter another positive number (or 0 to quit): 3.14159 sqrt(3.14159) = 1.77245 Enter another positive number (or 0 to quit): 100000 sqrt(100000) = 316.228 Enter another positive number (or 0 to quit): 0
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The condition (x > 0) in Example 4.3 uses the variable x to control the loop. Its value is changed inside the loop by means of an input statement. A variable that is used this way is called a loop control variable.
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4.2 TERMINATING A LOOP We have already seen how the break statement is used to control the switch statement. (See Example 3.17 on page 47.) The break statement is also used to control loops. EXAMPLE 4.4 Using a break Statement to Terminate a Loop
This program has the same effect as the one in Example 4.1 on page 60: int main() { int n, i=1; cout << "Enter a positive integer: "; cin >> n; long sum=0; while (true) { if (i > n) break; // terminates the loop immediately sum += i++; } cout << "The sum of the first " << n << " integers is " << sum; } Enter a positive integer: 100 The sum of the first 100 integers is 5050 This runs the same as in Example 4.1: as soon as the value of i reaches n, the loop terminates and the output statement at the end of the program executes. Note that the control condition on the while loop itself is true, which means continue forever. This is the standard way to code a while loop when it is being controlled from within.
One advantage of using a break statement inside a loop is that it causes the loop to terminate immediately, without having to finish executing the remaining statements in the loop block. EXAMPLE 4.5 The Fibonacci Numbers
The Fibonacci numbers F0 , F1 , F2 , F3 , ... are defined recursively by the equations F0 = 0 F1 = 1 F n = Fn 1 + Fn 2 For example, letting n = 2 in the third equation yields F2 = F2 1 + F2 2 = F1 + F0 = 0 + 1 = 1 Similarly, with n = 3, F3 = F3 1 + F3 2 = F2 + F1 = 1 + 1 = 2 and with n = 4, F4 = F4 1 + F4 2 = F3 + F2 = 2 + 1 = 3 The first ten Fibonacci numbers are shown in the table at right. This program prints all the Fibonacci numbers up to an input limit: int main() { long bound; cout << "Enter a positive integer: "; cin >> bound; cout << "Fibonacci numbers < " << bound << ":\n0, 1"; long f0=0, f1=1;
0 1 2 3 4 5 6 7 8 9
0 1 1 2 3 5 8 13 21 35