🚀 LeetCode 3272 - Count of Good Integers

🔧 Difficulty: Hard
💡 Topic: Palindromes, Permutations, Counting, Math, Combinatorics
🎥 From: Coding Moves - YouTube Channel

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🧠 Problem Summary

You are given two positive integers n and k.

An integer x is called k-palindromic if:

• x is a palindrome.
• x is divisible by k.

An integer is called good if its digits can be rearranged to form a k-palindromic integer.

Return the count of all good integers with exactly n digits and no leading zero.

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🧪 Examples

Example 1:

Input: n = 3, k = 5

Output: 27

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🧩 Key Constraints

• 1 <= n <= 10
• 1 <= k <= 9

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🧑‍💻 Solution Strategy

1. Generate all n-digit palindromes using half-construction.
2. Filter the ones divisible by k (i.e., k-palindromes).
3. For each unique digit multiset of those palindromes:
   • Count how many permutations of those digits are valid n-digit numbers (no leading zero).
4. Use factorial math for efficient permutation counting.

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• 📦 How to Run

python solution.py

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