Problem Statement

Write a Recursive Approach to Check if a Given Digit String Represents a Good Number.

A digit string is good if the digits (0-indexed) at even indices are even and the digits at odd indices are prime ((2, 3, 5, or 7).

Examples:

Solution:

1. The isPrime function is used to check if a number is prime.
2. The isGoodNumber function is a recursive function that checks each digit in the string. It takes two parameters: the digit string and the current index.
3. In the isGoodNumber function, the base case is when the index reaches the end of the string, in which case it returns true.
4. Inside the recursive function, it checks if the digit at the current index satisfies the conditions: even index digits must be even and odd index digits must be prime.
5. If the conditions are not met, it returns false.
6. Otherwise, it recursively calls isGoodNumber with the next index.
7. In the main function, it tests the isGoodNumber function on the example digit strings and prints the result.

This code uses recursion to traverse each digit in the string and checks if it satisfies the conditions for a "good number". The base case ensures that the recursion stops when all digits have been checked. By checking each digit recursively, the code can determine if the digit string is "good" or not.

Code

Here is the code for this algorithm: