Question

Suppose \(x\) and y are variables each of which contains a number. Write a code fragment that sets y to the absolute value of \(x\) without calling the abs function. Use an if statement.

Short answer

y = x if x >= 0 else y = -x.

Step-by-step solution

Understanding the Problem

We are asked to assign the absolute value of the variable \(x\) to another variable \(y\). The absolute value of a number is its non-negative form. We need to achieve this by using an if statement without utilizing built-in functions.

Plan the Logic

The logic of finding the absolute value is: if \(x\) is already non-negative (i.e., \(x \geq 0\)), then \(y\) should simply be \(x\). However, if \(x\) is negative (i.e., \(x < 0\)), then \(y\) should be \(-x\) to make it positive.

Write the Code Fragment

Below is the code fragment that solves the problem:```if x >= 0: y = xelse: y = -x```This fragment first checks if \(x\) is non-negative. If so, it assigns \(x\) to \(y\). Otherwise, it assigns \(-x\) to \(y\).

Check Different Values

Let's verify the code with different values:- If \(x = 5\), the code will execute \(y = x\) and \(y\) will be 5.- If \(x = -3\), the code will execute \(y = -x\) and \(y\) will be 3.Each result conforms to the definition of absolute value.

Key concepts

Understanding Conditional Statements

A conditional statement is a crucial part of programming logic that allows the execution of different pieces of code based on certain conditions. In most programming languages, an "if" statement is used to control the flow of the program by checking if a specified condition is true or false.

- If the condition is true, one block of code will run. - If the condition is false, another block may run if there is an "else" clause.

These statements provide flexibility to programs, enabling them to make decisions and react differently to inputs. This helps to implement logic that responds to changing data values or user inputs. It's like asking a question and getting a response based on the answer.

For example, consider the exercise: using an "if" statement, the variable `y` was set to the absolute value of `x`. The condition checked was whether `x` is non-negative (`x >= 0`). If true, `y` was set directly to `x`. If not, `y` was assigned the value of `-x`, which flips the sign to make it positive. This showcases the power and utility of conditional logic in programming.

Creating Code Fragments

In programming, a code fragment is a small, standalone piece of code that performs a specific task. These fragments can often be reused in different parts of a program or in different programs altogether.

A code fragment typically includes a few lines of code that achieve a functional goal, such as assigning a variable, performing a calculation, or even handling user input.

The exercise provides a simple code fragment that calculates the absolute value of a variable. Here's the fragment:

```python if x >= 0: y = x else: y = -x ``` This small snippet is designed to work independently for the task of computing the absolute value without needing additional lines of code or functions. Such fragments emphasize clarity and simplicity by focusing on the primary task with minimal instructions, making them easier to understand and maintain.

Absolute Value Calculation

The absolute value of a number is a fundamental concept in mathematics, representing its distance from zero on the number line, regardless of direction. In simpler terms, it gives the magnitude of the number without its sign.

It's denoted as \(|x|\), meaning the absolute value of \(x\). This calculation is quite straightforward:

• If a number is positive or zero, its absolute value is the number itself.
• If a number is negative, the absolute value is its positive counterpart.

In programming, calculating the absolute value usually involves either a built-in function like `abs()` or a simple conditional statement, as seen in the exercise. Using conditional logic, you can determine:- If `x` is greater than or equal to zero, then `y = x`.- Otherwise, `y = -x` to make it positive.

This method helps reinforce the logic behind basic mathematics concepts while applying them to programming, allowing a deeper understanding of how software manipulates data.