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EXAMPLE 4.17 More than One Control Variable in a for Loop
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The for loop in this program uses two control variables: int main() { for (int m=95, n=11; m%n > 0; m -= 3, n++) cout << m << "%" << n << " = " << m%n << endl; } 95%11 = 7 92%12 = 8 89%13 = 11 86%14 = 2 83%15 = 8 The two control variables m and n are declared and initialized in the control mechanism of this for loop. Then m is decremented by 3 and n is incremented on each iteration of the loop, generating the sequence of (m,n) pairs (95,11), (92,12), (89,13), (86,14), (83,15), (80,16). The loop terminates with the pair (80,16) because 16 divides 80.
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This program prints a multiplication table: #include <iomanip> // defines setw() #include <iostream> // defines cout using namespace std; int main() { for (int x=1; x <= 12; x++) { for (int y=1; y <= 12; y++) cout << setw(4) << x*y; cout << endl; } } 1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 8 10 12 14 16 18 20 22 24 3 6 9 12 15 18 21 24 27 30 33 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72 7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 80 88 96 9 18 27 36 45 54 63 72 81 90 99 108 10 20 30 40 50 60 70 80 90 100 110 120 11 22 33 44 55 66 77 88 99 110 121 132 12 24 36 48 60 72 84 96 108 120 132 144 Each iteration of the outer x loop prints one row of the multiplication table. For example, on the first iteration when x = 1, the inner y loop iterates 12 times, printing 1*y for each value of y from 1 to 12. And then on the second iteration of the outer x loop when x = 2, the inner y loop iterates 12 times again, this time printing 2*y for each value of y from 1 to 12. Note that the separate cout << endl statement must be inside the outer loop and outside the inner loop in order to produce exactly one line for each iteration of the outer loop. This program uses the stream manipulator setw to set the width of the output field for each integer printed. The expression setw(4) means to set the output field width to 4 columns for the next output.
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This aligns the outputs into a readable table of 12 columns of right-justified integers. Stream manipulators are defined in the <iomanip> header, so this program had to include the directive #include <iomanip> in addition to including the <iostream> header.
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EXAMPLE 4.19 Testing a Loop Invariant
This program computes and prints the discrete binary logarithm of an input number (the greatest integer the base 2 logarithm of the number). It tests its loop invariant by printing the relevant values on each iteration: #include <cmath> // defines pow() and log() #include <iostream> // defines cin and cout #include <iomanip> // defines setw() using namespace std;
int main() { long n; cout << "Enter a positive integer: "; cin >> n; int d=0; // the discrete binary logarithm of n double p2d=1; // = 2^d for (int i=n; i > 1; i /= 2, d++) { // INVARIANT: 2^d <= n/i < 2*2^d p2d=pow(2,d); // = 2^d cout << setw(2) << p2d << " <= " << setw(2) << << " < " << setw(2) << 2*p2d << endl; } p2d=pow(2,d); // = 2^d cout << setw(2) << p2d << " <= " << setw(2) << n << " < " << setw(2) << 2*p2d << endl; cout << " The discrete binary logarithm of " << << " is " << d << endl; double lgn = log(n)/log(2); // base 2 logarithm cout << "The continuous binary logarithm of " << << " is " << lgn << endl; } Enter a positive integer: 63 1 <= 1 < 2 2 <= 2 < 4 4 <= 4 < 8 8 <= 9 < 16 16 <= 21 < 32 32 <= 63 < 64 The discrete binary logarithm of 63 is 5 The continuous binary logarithm of 63 is 5.97728
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