Question

A palindrome is a string that reads the same forward and backward. Describe an algorithm for determining whether a string of n characters is a palindrome.

Short answer

The algorithm is as follows:

$$\begin{gathered} procedurepalindrome\left(a_1,a_2,...,a_n:stringwithn\ge 1\right) \\ k:=True \\ fori=1to\frac{n}{2} \\ if{a}_i\ne a_{n-j+1}thenk=False \\ returnk \end{gathered}$$

Step-by-step solution

Describing the steps needed to write the required algorithm

We can call the algorithm as ‘palindrome’ and input is a string of symbols.

$procedurepalindrome\left(a_1,a_2,...,a_n:stringwithn\ge 1\right)$

We initially define the variable as True (we consider that the string is palindrome) and then, using definition in each step we check that the property was lost. Notice that all one symbol strings are palindromes.

k = True

For every integer between 1 and$\frac{n}{2}$ (middle of the string), if the th symbol is not the same as the$\left(n-i+1\right)$ th symbol, then we change the answer to False

$$\begin{gathered} fori=1to\frac{n}{2} \\ if{a}_i\ne a_{n-j+1}thenk=False \end{gathered}$$

Finally, we return the k which at the end of the loop contain either True or False

return k

Combining all the steps to form an algorithm

The algorithm is as follows:

$$\begin{gathered} procedurepalindrome\left(a_1,a_2,...,a_n:stringwithn\ge 1\right) \\ k:=True \\ fori=1to\frac{n}{2} \\ if{a}_i\ne a_{n-j+1}thenk=False \\ returnk \end{gathered}$$

Therefore, the required algorithm is designed for the given conditions.