Chapter 3: Problem 4
Does the following sequence produce division by zero? $$\begin{array}{l} j=-1 ; \\ \text { if }((j>0) \& \&(1 /(j+1)>10)) \\ \quad \text { cout }<<\quad i<<\text { end } 1 ; \end{array}$$
Short Answer
Expert verified
Answer: No, the given sequence does not produce a division by zero.
Step by step solution
01
Analyze the initial conditions
The sequence starts with an initial value of j = -1. There is no division operation in this part of the sequence.
02
Examine the conditional statement
The conditional statement checks if j > 0 and if 1 / (j + 1) > 10. If both these conditions are true, it indicates that division is being performed by the term (j + 1).
03
Check for division by zero
Division by zero occurs if the divisor is zero. In this case, it means (j + 1) = 0. Solving this equation, we have j = -1.
04
Verify the condition with j = -1
When j = -1, the conditional statement becomes: ((-1 > 0) && (1 / (−1 + 1) > 10)). The first part of the condition (-1 > 0) is false, thus making the entire conditional statement false.
05
Conclusion
Since the conditional statement is false when j = -1, the division operation does not happen, and there is no division by zero in this sequence.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Problem-Solving in C++
When confronted with a potential division by zero in a C++ program, like the one presented in the exercise, the problem-solving process is crucial to validate code integrity and prevent runtime errors. Problem-solving in C++ often involves a step-by-step analysis to dissect the code logically.
Step 1 entails a review of initial conditions. Here, the variable 'j' is initialized with a value of -1. This step is foundational; understanding variable states is key for what follows.
In Step 2, we scrutinize the conditional statement—a core construct in C++ for controlling program flow. The evaluation determines whether subsequent operations, including potential divisions, are executed. The programmer must read and understand these conditions to anticipate the program's behavior.
Step 3 involves checking for situations that could cause errors, like division by zero. In C++, due diligence in checking divisor values before division is a good practice to avoid crashes.
Finally, Step 4 and 5 consolidate the analysis—the given conditions are applied to 'j', leading to the conclusion that no division by zero occurs. This process exemplifies problem-solving in C++: starting from initial conditions, analyzing control structures, and testing edge cases to ensure the program's reliability.
Step 1 entails a review of initial conditions. Here, the variable 'j' is initialized with a value of -1. This step is foundational; understanding variable states is key for what follows.
In Step 2, we scrutinize the conditional statement—a core construct in C++ for controlling program flow. The evaluation determines whether subsequent operations, including potential divisions, are executed. The programmer must read and understand these conditions to anticipate the program's behavior.
Step 3 involves checking for situations that could cause errors, like division by zero. In C++, due diligence in checking divisor values before division is a good practice to avoid crashes.
Finally, Step 4 and 5 consolidate the analysis—the given conditions are applied to 'j', leading to the conclusion that no division by zero occurs. This process exemplifies problem-solving in C++: starting from initial conditions, analyzing control structures, and testing edge cases to ensure the program's reliability.
Conditional Statements
Conditional statements are the decision-making heart of a C++ program. They enable the execution of code blocks based on a condition's truth value. In our example, the conditional 'if' statement evaluates two conditions that must both be true because of the logical AND operator '&&'.
A well-constructed conditional statement considers all possible outcomes and behaves appropriately for each. In the given exercise, the conditional statement checks if ‘j’ is greater than zero and if the result of ‘1/(j+1)’ is greater than ten.
The syntax of an 'if' statement in C++ can be understood as follows:
A well-constructed conditional statement considers all possible outcomes and behaves appropriately for each. In the given exercise, the conditional statement checks if ‘j’ is greater than zero and if the result of ‘1/(j+1)’ is greater than ten.
The syntax of an 'if' statement in C++ can be understood as follows:
- The 'if' keyword initiates the statement.
- A condition or a series of conditions are provided in parentheses.
- If the condition is true, the code block enclosed in curly braces { ... } is executed.
Logical Operators
Logical operators in C++—such as && (logical AND), || (logical OR), and ! (logical NOT)—are fundamental in combining multiple conditions within a conditional statement. The provided exercise showcases the use of '&&', which requires both conditions to be true for the entire expression to evaluate as true.
These operators follow boolean algebra principles, where 'true' and 'false' are primary values. When constructing complex conditions:
These operators follow boolean algebra principles, where 'true' and 'false' are primary values. When constructing complex conditions:
- The '&&' operator acts as a gatekeeper, allowing a series of conditions to pass only if all are true.
- The '||' operator is more permissive, needing at least one true condition to pass the expression as true.
- The '!' operator inverses the truth value of a single condition.