Question

\(4.26 \quad\) forward. For example, each of the following five-digit integers is a palindrome: 12321,55555 45554 and \(11611 .\) Write a program that reads in a five-digit integer and determines whether it's a palindrome. [Hint: Use the division and modulus operators to separate the number into its individual digits.

Short answer

To determine if a five-digit number is a palindrome, extract each digit using modulus and division, then compare the first with the fifth and the second with the fourth digit to see if they match.

Step-by-step solution

Understand the Problem

A palindrome is a number that reads the same backward as forward. To determine if a five-digit number is a palindrome, we need to check if the first digit is the same as the fifth digit, and the second digit is the same as the fourth digit. The middle digit does not need to match anything since it is in the center.

Obtain Individual Digits

Use division and modulus operations to extract each digit of the five-digit number. Divide the number by 10,000 to get the first digit. Use modulus by 10,000 and then divide by 1,000 to get the second digit. Similarly, continue to isolate each digit using appropriate modulus and division.

Compare Digits

Check if the first digit is equal to the fifth digit and if the second digit is equal to the fourth digit. If both of these conditions are true, the number is a palindrome; otherwise, it is not.

Write the Program

Translate these steps into a program by reading an integer, extracting the digits, comparing them, and printing out whether the number is a palindrome.

Key concepts

C++ Programming and Palindrome Checking

C++ programming is a versatile tool for solving problems like checking if a number is a palindrome. In this context, a palindrome is a sequence that reads the same backward as forward. To determine if a five-digit integer is a palindrome in C++, you would typically get input from the user, extract each digit, compare the necessary digits, and then output the result. Using a structured approach that involves step-by-step logic, C++ allows programmers to break down the problem and solve it systematically. A good understanding of how to handle user input, process data, and output results is essential in C++ programming.

For a typical palindrome checking program, you would need to prompt the user to input a number, use mathematical operations to extract digits, and then use conditionals to compare these digits. It's important to ensure that your C++ code is clean and well-commented, which makes it easier to review and maintain. When writing a palindrome checker, organize your program into clear steps, like obtaining the number, processing it, and finally displaying the result to the user. The exercise also underscores the importance of accuracy in C++ programming: A single mistake in logic or syntax can lead to incorrect results or a non-functioning program.

Understanding the Modulus Operator

The modulus operator, represented by the symbol '%', is a powerful tool in programming languages like C++ for finding the remainder of a division of two integers. It's particularly useful in situations where you want to examine digits of a number individually, such as in palindrome checking algorithms. In the context of a five-digit number, you would use the modulus operator to isolate the last four digits by calculating the remainder of the number divided by 10,000, which effectively strips away the first digit of the number.

For example, if your number is 12345 and you apply the modulus operation \(12345 \% 10000\), you'd get 2345, as 12345 divided by 10000 leaves a remainder of 2345. It's essential to understand that the modulus operator acts on integers and returns the leftover part after division, which makes it ideal for digit extraction in programming. If the logic of using the modulus operator seems challenging, remember to conceptualize the method as 'peeling off' digits from a number, from right to left, to compare specific positions in palindrome verification.

Using the Division Operator for Digit Extraction

The division operator, denoted by a forward slash '/', is a basic yet essential part of performing arithmetic operations in C++ programming. When coupled with integer variables, division truncates the decimal part, which can be used to your advantage when working on problems like palindrome checking. To extract individual digits from a number, you'll divide the number by powers of 10. For instance, in the context of a five-digit integer, dividing the number by 10,000 obtains the first digit.

If you have 12345 and you perform the operation \(12345 / 10000\), the result is 1 because the division drops any fractional part that would have been the result of non-integer division. This division operator tactic is instrumental in palindrome checking algorithms where you need to compare specific digits. An understanding of integer division is key; it allows you to section off the number into its constituent parts. When applied correctly, it can significantly simplify complex problems and make your code more efficient and easier to read.