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Chapter 7: Problem 32

(Palindromes) A palindrome is a string that is spelled the same way forward and backward. Examples of palindromes include "radar" and "able was i ere i saw elba." Write a recursive function testPalindrome that returns true if a string is a palindrome, and false otherwise. Note that like an array, the square brackets ( [] ) operator can be used to iterate through the characters in a string.

Short Answer

Expert verified
The function testPalindrome recursively checks if the first and last characters are the same and then calls itself on the substring excluding those characters until the base case of length 0 or 1 is reached.

Step by step solution

01

Understanding the Problem

The goal is to write a recursive function that takes a string as input and returns true if the string is a palindrome (reads the same backward as forward), and false otherwise. Palindromes should be checked character by character from the ends towards the center.
02

Defining the Base Case

The base case for our recursion happens when the string has a length of 0 or 1. In either case, we can return true because a single character or an empty string is trivially a palindrome.
03

Defining the Recursive Case

For the recursive case, first compare the first and last characters of the string. If they are not equal, return false. If they are equal, invoke the recursive function on the substring excluding the first and last characters.
04

Coding the Function

Write a function testPalindrome that accepts a string parameter. Inside the function, implement the base and recursive cases as defined in the previous steps.
05

Returning the Result

The function should return the result of the base case or the recursive call, which will eventually evaluate to true or false indicating whether the string is a palindrome or not.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Palindrome Detection
When we talk about palindromes in the context of strings, we're referring to words or phrases that retain their meaning when their letters are reversed. The magic of a palindrome lies in its symmetry, which is why 'radar' is a classic example, reading the same forwards and backwards.

Detecting a palindrome programmatically relies on this property of symmetry. Understanding palindrome detection is not just a fun linguistic exercise but also a common problem in computer science and programming interviews. The core principle is to compare characters from both ends of the string, moving towards the center, confirming that each corresponding pair is identical.
Recursive Functions
Recursion is a coding technique where a function calls itself to solve a problem. Recursive functions consist of two essential parts: the base case and the recursive case. The base case stops the recursion by returning a value without making any further recursive calls. On the other hand, the recursive case continues to call itself with modified arguments that push towards the base case.

In the context of palindrome detection, a recursive function can simplify the problem by reducing the string size with each call, inching ever closer to a simple, easily solvable condition.
String Manipulation
Strings are a sequence of characters that can be manipulated in various ways for different purposes. In C++, strings can be accessed and altered using different functions and operators. For palindrome detection, key string operations include accessing elements with the square brackets operator ( [] ) and creating substrings.

Substrings play a crucial role as they enable the recursive function to progressively reduce the problem size by focusing on a smaller section of the string, excluding the characters that have already been compared.
Base Case in Recursion
The base case in recursion is the 'anchor' that prevents the function from calling itself indefinitely. It represents the simplest instance of the problem, which can be answered directly.

For palindrome detection, the base case occurs when the length of the string is down to 0 or 1, inherently satisfying the palindrome condition. The design of an effective base case is critical because it ensures that the recursion will lead to a definitive answer rather than creating an endless loop.
Character Comparison
Character comparison is the act of checking if two characters in a string are equal, a fundamental operation in many string manipulation tasks, including palindrome detection.

In C++, characters are compared using the equality operator ( == ). When implementing a recursive palindrome function, the comparison is done between the first and the last character of the current string or substring being considered. If at any point the characters do not match, the recursion is halted, and the function returns false, signaling that the string is not a palindrome.

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Most popular questions from this chapter

(Fill in the Blanks) Fill in the blanks in each of the following: a) The names of the four elements of array p (int p[4];) are ___, ___ , ___ and ___. b) Naming an array, stating its type and specifying the number of elements in the array is called __ the array. c) By convention, the first subscript in a two-dimensional array identifies an element's ___ and the second subscript identifies an element's ___. d) An m-by-n array contains __ rows, __ columns and ___ elements. c) The name of the element in row 3 and column 5 of array \(d\) is __.

(Bucket Sort) A bucket sort begins with a one-dimensional array of positive integers to be sorted and a two-dimensional array of integers with rows subscripted from 0 to 9 and columns subscripted from 0 to \(n-1\), where \(n\) is the number of values in the array to be sorted. Each row of the two- dimensional array is referred to as a bucket. Write a function bucketsort that takes an integer array and the array size as arguments and performs as follows: a) Place each value of the one-dimensional array into a row of the bucket array based on the value's ones digit. For example, 97 is placed in row 7,3 is placed in row 3 and 100 is placed in row \(0 .\) This is called a "distribution pass." b) Loop through the bucket array row by row, and copy the values back to the original array. This is called a "gathering pass." The new order of the preceding values in the onedimensional array is 100,3 and 97 c) Repeat this process for cach subsequent digit position (tens, hundreds, thousands, etc.). On the second pass, 100 is placed in row 0,3 is placed in row 0 (because 3 has no tens digit) and 97 is placed in row \(9 .\) After the gathering pass, the order of the values in the one-dimensional array is 100,3 and \(97 .\) On the third pass, 100 is placed in row 1,3 is placed in row zero and 97 is placed in row zero (after the 3). After the last gathering pass, the original array is now in sorted order. Note that the two-dimensional array of buckets is 10 times the size of the integer array being sorted. This sorting technique provides better performance than an insertion sort, but requires much more memory. The insertion sort requires space for only one additional element of data. This is an example of the space-time trade-off: The bucket sort uses more memory than the insertion sort, but performs better. This version of the bucket sort requires copying all the data back to the original array on each pass. Another possibility is to create a second two-dimensional bucket array and repeatedly swap the data between the two bucket arrays.

(Write \(C++\) Statements) Write one or more statements that perform the following tasks for an array called fractions: a) Define a constant integer variable arraySize initialized to 10 b) Declare an array with arraySize elements of type double, and initialize the elements to 0 . c) Name the fourth element of the array. d) Refer to array element 4. c) Assign the value 1.667 to array element 9 f) Assign the value 3.333 to the seventh element of the array. g) Print array elements 6 and 9 with two digits of precision to the right of the decimal point, and show the output that is actually displayed on the screen. h) Print all the array elements using a for statement. Define the integer variable i as a control variable for the loop. Show the output.

(Single Array Questions) Write single statements that perform the following one-dimensional array operations: a) Initialize the 10 elements of integer array counts to zero. b) Add 1 to each of the 15 elements of integer array bonus. c) Read 12 values for double array month 7 yTemperatures from the keyboard. d) Print the 5 values of integer array bestscores in column format.

(Polling) The Internet and the web are enabling more people to network, join a cause, voice opinions, and so on. The presidential candidates in 2008 used the Internet intensively to get out their messages and raise money for their campaigns. In this exercise, you'll write a simple polling program that allows users to rate five social-consciousness issues from 1 (least important) to 10 (most important). Pick five causes that are important to you (e.g., political issues, global environmental issues). Use a one-dimensional array topics (of type string) to store the five causes. To summarize the survey responses, use a 5 -row, 10 -column two-dimensional array responses (of type int), each row corresponding to an element in the topics array. When the program runs, it should ask the user to rate each issue. Have your friends and family respond to the survey. Then have the program display a summary of the results, including: a) \(A\) tabular report with the five topics down the left side and the 10 ratings across the top, listing in each column the number of ratings received for each topic. b) To the right of each row, show the average of the ratings for that issue. c) Which issue received the highest point total? Display both the issue and the point total. d) Which issue received the lowest point total? Display both the issue and the point total.
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