C++ Coding Test Course, Finding the Minimum Among Prime & Palindrome Numbers

Today, we will take a deep dive into one of the frequently asked algorithm problems for job seekers: ‘Finding the minimum value among prime and palindrome numbers’. Through this problem, we will review the concepts of primes and palindromes, and have a session to implement the algorithm using C++.

Problem Description

Given an integer N, the problem is to find the minimum integer that is both a prime and a palindrome within the range of N or greater.

Examples

• If N = 10, the prime and palindrome number is 11.
• If N = 30, the prime and palindrome number is 31.
• If N = 100, the prime and palindrome number is 101.

Problem Approach

A prime number is a natural number greater than 1 that has no divisors other than 1 and itself. A palindrome is a number that reads the same forwards and backwards. For example, 121, 12321, etc.

To solve the problem, we will follow these steps:

1. Start from N and examine all numbers.
2. Check if each number is prime.
3. If it’s prime, check if it’s a palindrome.
4. Find and return the minimum that satisfies all conditions.

C++ Implementation

Now, let’s write the code to solve this problem using the C++ language.

Code Explanation

#include 
#include 
#include 

using namespace std;

// Prime determination function
bool isPrime(int num) {
    if (num < 2) return false;
    for (int i = 2; i <= sqrt(num); ++i) {
        if (num % i == 0) return false;
    }
    return true;
}

// Palindrome determination function
bool isPalindrome(int num) {
    string str = to_string(num);
    int len = str.length();
    for (int i = 0; i < len / 2; ++i) {
        if (str[i] != str[len - i - 1]) return false;
    }
    return true;
}

// Function to find the minimum prime palindrome that is greater than or equal to N
int findMinPrimePalindrome(int N) {
    for (int i = N; ; ++i) {
        if (isPrime(i) && isPalindrome(i)) {
            return i;
        }
    }
}

int main() {
    int N;
    cout << "Enter an integer N: ";
    cin >> N;
    
    int result = findMinPrimePalindrome(N);
    cout << "Minimum value: " << result << endl;
    
    return 0;
}

    

Code Explanation

Through the above code, we can achieve the desired result through the following processes:

1. isPrime function: Determines whether the given integer is prime. It only checks numbers greater than or equal to 2 and checks for divisibility from 2 up to sqrt(num).
2. isPalindrome function: Determines whether the given integer is a palindrome. It converts the number to a string and compares characters from the front and back for matches.
3. findMinPrimePalindrome function: Starts from the given N and checks each number for prime and palindrome status. It returns immediately upon finding a number that is both.
4. main function: Takes an integer N from the user and finds and prints the minimum value based on that.

Example for Understanding

For example, if N=10, the function starts from 10 and checks 10, 11. Since 11 is both prime and a palindrome, it returns 11 as the minimum value.

Time Complexity

The time complexity of the algorithm we wrote varies depending on the input value N. Checking for primality takes time proportional to sqrt(N), and when considering the entire process of starting from N to find the minimum, the worst-case time complexity is O(N√N).

Points to Note While Solving

Finding prime and palindrome numbers requires an understanding of basic mathematics and string conversion. Additionally, a grasp of basic C++ syntax and data types is essential. To solve this problem, it's important to organize information well and practice a step-by-step approach.

Conclusion

Through this lecture, we had the opportunity to understand algorithms related to primes and palindromes and implement them ourselves. This problem is one of the useful algorithms that can be utilized in the field and can be beneficial while preparing for job interviews. I hope you will continue to tackle various algorithm problems as you prepare for coding tests.