2d barcode generator vb.net The Factorial Numbers Again in Software

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EXAMPLE 4.12 The Factorial Numbers Again
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This program has the same effect as the one in Example 4.9 on page 65: int main() { long bound; cout << "Enter a positive integer: "; cin >> bound;
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cout << "Factorial numbers that are <= " << bound << ":\n1, 1"; long f=1; for (int i=2; f <= bound; i++) { f *= i; cout << ", " << f; } } Enter a positive integer: 1000000 Factorial numbers < 1000000: 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880
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This for loop program has the same effect as the do..while loop program because it executes the same instructions. After initializing f to 1, both programs initialize i to 2 and then repeat the following five instructions: print f, multiply f by i, increment i, check the condition (f <= bound) , and terminate the loop if the condition is false.
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The for statement is quite flexible, as the following examples demonstrate. EXAMPLE 4.13 Using a Descending for Loop
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This program prints the first ten positive integers in reverse order: int main() { for (int i=10; i > 0; i--) cout << " " << i; } 10 9 8 7 6 5 4 3 2 1
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EXAMPLE 4.14 Using a for Loop with a Step Greater than One
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This program determines whether an input number is prime: int main() { long n; cout << "Enter a positive integer: "; cin >> n; if (n < 2) cout << n << " is not prime." << endl; else if (n < 4) cout << n << " is prime." << endl; else if (n%2 == 0) cout << n << " = 2*" << n/2 << endl; else { for (int d=3; d <= n/2; d += 2) if (n%d == 0) { cout << n << " = " << d << "*" << n/d << endl; exit(0); } cout << n << " is prime." << endl; }; } Enter a positive integer: 101 101 is prime. Enter a positive integer: 975313579 975313579 = 17*57371387 Note that this for loop uses an increment of 2 on its control variable i.
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EXAMPLE 4.15 Using a Sentinel to Control a for Loop
This program finds the maximum of a sequence of input numbers: int main() { int n, max; cout << "Enter positive integers (0 to quit): "; cin >> n; for (max = n; n > 0; ) { if (n > max) max = n; cin >> n; } cout << "max = " << max << endl; } Enter positive integers (0 to quit): 44 77 55 22 99 33 11 66 88 0 max = 99 This for loop is controlled by the input variable n; it continues until n 0. When an input variable controls a loop this way, it is called a sentinel. Note the control mechanism (max = n; n > 0; ) in this for loop. Its update part is missing, and its initialization max = n has no declaration. The variable max has to be declared before the for loop because it is used outside of its block, in the last output statement in the program.
EXAMPLE 4.16 Using a Loop Invariant to Prove that a for Loop is Correct
This program finds the minimum of a sequence of input numbers. It is similar to the program in Example 4.15: int main() { int n, min; cout << "Enter positive integers (0 to quit): "; cin >> n; for (min = n; n > 0; ) { if (n < min) min = n; // INVARIANT: min <= n for all n, and min equals one of the n cin >> n; } cout << "min = " << min << endl; } Enter positive integers (0 to quit): 44 77 55 22 99 33 11 66 88 0 min = 11 The full-line comment inside the block of the for loop is called a loop invariant. It states a condition that has two characteristic properties: (1) it is true at that point on every iteration of the loop; (2) the fact that it is true when the loop terminates proves that the loop performs correctly. In this case, the condition min <= n for all n is always true because the preceding if statement resets the value of min if the last input value of n was less than the previous value of min. And the condition that min equals one of the n is always true because min is initialized to the first n and the only place where min changes its value is when it is assigned to a new input value of n. Finally, the fact that the condition is true when the loop terminates means that min is the minimum of all the input numbers. And that outcome is precisely the objective of the for loop.
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