A k-mirror number is a fascinating mathematical concept - it's a positive integer that reads the same both forward and backward in both base-10 (decimal) and base-k representations.
What makes this interesting? While many numbers are palindromic in one base, finding numbers that are palindromic in multiple bases simultaneously is much rarer and more challenging.
Examples:
9is a 2-mirror number: In base-10 it's9, in base-2 it's1001- both are palindromes!4is NOT a 2-mirror number: In base-10 it's4(palindrome), but in base-2 it's100(not a palindrome)
Your Goal: Given a base k and number n, find the sum of the n smallest k-mirror numbers. This requires efficiently generating palindromes in base-10, then checking if they're also palindromes in base-k.
Input & Output
Visualization
Time & Space Complexity
Where m is the value of the nth k-mirror number. We check m numbers, and each check takes O(log m) time for palindrome verification
Space needed to store the base-k representation string for palindrome checking
Constraints
- 2 โค k โค 9
- 1 โค n โค 30
- All k-mirror numbers will fit in a 64-bit signed integer
- The answer will be the sum of exactly n k-mirror numbers