Question

Suppose x, y, z, and w are int variables. What value is assigned to each of these variables after the last statement executes? x = 5; z = 3; y = x - z; z = 2 * y + 3; w = x - 2 * y + z; z = w - x; w++;

Short answer

After executing all statements, x = 5, y = 2, z = 3, w = 9.

Step-by-step solution

Initial Assignments

Start by assigning the initial values. We have:- \(x = 5\)- \(z = 3\)

Calculate y

Use the equation for \(y\):\[ y = x - z = 5 - 3 = 2 \]Assign this value to \(y\).

Update z

Update \(z\) using the new value of \(y\):\[ z = 2 \cdot y + 3 = 2 \cdot 2 + 3 = 4 + 3 = 7 \]

Calculate w

Calculate \(w\) using the updated values:\[ w = x - 2 \cdot y + z = 5 - 2 \cdot 2 + 7 = 5 - 4 + 7 = 8 \]

Final Update of z

Update \(z\) using the current value of \(w\):\[ z = w - x = 8 - 5 = 3 \]

Increment w

Finally, increment \(w\) by 1:\[ w = 8 + 1 = 9 \]

Key concepts

Step-by-Step Calculation

Breaking down a problem into smaller, manageable steps is critical in programming and mathematics. This is known as a step-by-step calculation. Let's apply this to our exercise where multiple integer variables receive assignments and new values.

Initially, we have the assignments for the variables: \(x = 5\) and \(z = 3\). Each step follows logically from the previous one, ensuring clarity.

• First, calculating \(y = x - z\), we find \(y = 5 - 3 = 2\).
• Next, updating \(z\) with its new formula: \(z = 2 \cdot y + 3\), we calculate \(z = 2 \cdot 2 + 3 = 7\).
• Then, using these updated values to compute \(w = x - 2 \cdot y + z\), results in \(w = 5 - 4 + 7 = 8\).
• Again, the variable \(z\) changes as \(z = w - x\), giving \(z = 8 - 5 = 3\).
• Lastly, incrementing \(w\) simply means adding one: \(w = w + 1 = 9\).

These calculations demonstrate how breaking down tasks into smaller steps ensures accurate results.

Arithmetic Operations

Arithmetic operations form a fundamental part of solving equations in programming. They include operations like addition, subtraction, multiplication, and division. In our exercise, these basic operations are applied repeatedly to compute the values of multiple integer variables.

Consider the following operations:

• Subtraction is used to calculate \(y\) where \(y = x - z\), simplifying to \(5 - 3 = 2\).
• Multiplication and addition are employed to update \(z\) with the formula \(z = 2 \cdot y + 3\), leading to \(7\).
• Combining subtraction, multiplication, and addition again for \(w\) where \(w = x - 2 \cdot y + z\) results in \(8\).
• Utilizing subtraction once more, we adjust \(z\) as \(z = w - x\), equating to \(3\).
• Incrementing \(w\) means adding one, achieving \(w = 9\).

Understanding these operations helps in tracing and predicting the outcomes of similar computational problems.

Algorithm Tracing

Algorithm tracing involves following an algorithm step by step to determine the output or intermediate values. This strategy is hands-on for verifying that each calculation is executed correctly, as seen in our exercise example.

This method requires:

• Setting initial conditions based on variable assignments.
• Calculating and updating each variable systemically.
• Checking and re-checking each step to confirm the expected result.

For instance, by initially assigning \(x = 5\) and \(z = 3\), each subsequent computation was straightforward. Tracing through each assignment and calculation confirmed the accuracy of our final results: \(y = 2\), \(z = 3\), and \(w = 9\).

Algorithm tracing is a qualifying technique to recognize potential errors early in complex calculations.

Integer Variables

Understanding integer variables is crucial, especially when dealing with arithmetic and programming. An integer variable holds whole numbers, both positive and negative, including zero.

In our task:

• Each variable (\(x\), \(y\), \(z\), and \(w\)) stores integers, simplifying the arithmetic processes.
• Integer operations avoid the complexity of floating-point arithmetic, easing calculations.
• Tracking every integer through operations like addition or multiplication demonstrates how they maintain their integrity.

Recognizing when to use integer variables can significantly impact program efficiency, preventing errors related to data typing and calculation precision.