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if (n%d) cout << "n is not a multiple of d";
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The output statement will execute precisely when n%d is not zero, and that happens precisely when d does not divide n evenly, because n%d is the remainder from the integer division. The fact that boolean expressions have integer values can lead to some surprising anomalies in C++. EXAMPLE 3.11 Another Logical Error
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This program is erroneous: int main() { int n1, n2, n3; cout << "Enter three integers: "; cin >> n1 >> n2 >> n3; if (n1 >= n2 >= n3) cout << "max = x"; // LOGICAL ERROR! } Enter an integer: 0 0 1 max = 0 The source of this error is the fact that boolean expressions have numeric values. Since the expression (n1 >= n2 >= n3) is evaluated from left to right, the first part n1 >= n2 evaluates to true since 0 >= 0. But true is stored as the numeric value 1. That value is then compared to the value of n3 which is also 1, so the complete expression evaluates to true even though it is really false! (0 is not the maximum of 0, 0, and 1.) The problem here is that the erroneous line is syntactically correct, so the compiler cannot catch the error. Nor can the operating system. This is another logical error, comparable to that in the program in Example 3.4 on page 38.
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The moral from Example 3.11 is to remember that boolean expressions have numeric values, so compound conditions can be tricky. 3.9 NESTED SELECTION STATEMENTS Like compound statements, selection statements can be used wherever any other statement can be used. So a selection statement can be used within another selection statement. This is called nesting statements. EXAMPLE 3.12 Nesting Selection Statements
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This program has the same effect as the one in Example 3.10 on page 42: int main() { int n, d; cout << "Enter two positive integers: "; cin >> n >> d; if (d != 0) if (n%d == 0) cout << d << " divides " << n << endl; else cout << d << " does not divide " << n << endl; else cout << d << " does not divide " << n << endl; } The second if..else statement is nested within the if clause of the first if..else statement. So the second if..else statement will execute only when d is not zero.
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Note that the " does not divide " statement has to be used twice here. The first one, nested within the if clause of the first if..else statement, executes when d is not zero and n%d is zero. The second one executes when d is zero.
When if..else statements are nested, the compiler uses the following rule to parse the compound statement: Match each else with the last unmatched if. Using this rule, the compiler can easily decipher code as inscrutable as this:
if (a > 0) if (b > 0) ++a; else if (c > 0) if (a < 4) ++b; else if (b < 4) ++c; else --a; else if (c < 4) --b; else --c; else a = 0; // BAD CODING STYLE // BAD CODING STYLE // BAD CODING STYLE
To make this readable for humans it should be written either like this:
if (a > 0) if (b > 0) ++a; else if (c > 0) if (a < 4) ++b; else if (b < 4) ++c; else --a; else if (c < 4) --b; else --c; else a = 0;
or like this:
if (a > 0) if (b > 0) ++a; else if (c > 0) if (a < 4) ++b; else if (b < 4) ++c; else --a; else if (c < 4) --b; else --c; else a = 0; This second rendering aligns the else if pairs when they form parallel alternatives. (See
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