2081. Sum of k-Mirror Numbers

About this solution

Sum of k-Mirror Numbers is a unknown-difficulty LeetCode problem covering the Math pattern. The Java solution below uses an idiomatic approach that is clean, readable, and directly submittable on LeetCode. Study the logic carefully — recognising the underlying pattern is the key skill that transfers to similar problems in interviews.

Key Techniques

Math

Math problems test number theory, combinatorics, and modular arithmetic. Common tools: GCD/LCM (Euclidean algorithm), prime sieve, modular inverse (Fermat's little theorem), digit manipulation, and bit tricks. Overflow is a key concern in C# — use long when products may exceed 2³¹.

2081.java

Java

class Solution {

    // This method returns the sum of the first n k-mirror numbers.
    public long kMirror(int base, int count) {
        long sum = 0; // Initialize sum of k-mirror numbers

        // Loops indefinitely until 'count' number of k-mirror numbers are found
        for (int length = 1;; ++length) {
            // Find the start and end range based on the half-length to construct palindrome
            // prefixes
            int start = (int) Math.pow(10, (length - 1) / 2);
            int end = (int) Math.pow(10, (length + 1) / 2);

            // Loop to generate all palindrome numbers of the current length
            for (int i = start; i < end; i++) {
                long palindrome = i;

                // Construct the second half of the palindrome number based on the length's
                // parity
                for (int j = length % 2 == 0 ? i : i / 10; j > 0; j /= 10)
                    palindrome = palindrome * 10 + j % 10; // Append digits in reverse order to form the palindrome

                // Convert palindrome to its representation in the given base
                String baseRepresentation = Long.toString(palindrome, base);

                // Check if the base representation is a palindrome
                if (isPalindrome(baseRepresentation.toCharArray())) {
                    sum += palindrome; // Add current palindrome to sum
                    if (--count == 0) // Decrement count and check if 'n' k-mirror numbers are found
                        return sum; // Return the sum if 'n' k-mirror numbers are found
                }
            }
        }
    }

    // This method checks if the character array forms a palindrome
    private boolean isPalindrome(char[] charArray) {
        // Compare characters from opposite ends moving towards the center
        for (int i = 0, j = charArray.length - 1; i < j; i++, j--) {
            if (charArray[i] != charArray[j])
                return false; // Return false if mismatch is found
        }
        return true; // Return true if the entire array is a palindrome
    }
}

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