Sum of k-Mirror Numbers — LeetCode 2081 Python Solution

The problem

A k-mirror number is a positive integer without leading zeros that reads the same both forward and backward in base-10 as well as in base-k. For example, 9 is a 2-mirror number.

Example

Input

k = 2, n = 5

Output

25

Explanation

The 5 smallest 2-mirror numbers and their representations in base-2 are listed as follows:

Python solution

class Solution:
    def kMirror(self, k: int, n: int) -> int:
        def check(x: int, k: int) -> bool:
            s = []
            while x:
                s.append(x % k)
                x //= k
            return s == s[::-1]

        ans = 0
        for l in count(1):
            x = 10 ** ((l - 1) // 2)
            y = 10 ** ((l + 1) // 2)
            for i in range(x, y):
                v = i
                j = i if l % 2 == 0 else i // 10
                while j > 0:
                    v = v * 10 + j % 10
                    j //= 10
                if check(v, k):
                    ans += v
                    n -= 1
                    if n == 0:
                        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 2081. Sum of k-Mirror Numbers is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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