Leetcode #2081: Sum of k-Mirror Numbers
In this guide, we solve Leetcode #2081 Sum of k-Mirror Numbers in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Math, Enumeration
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
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:
base-10 base-2
1 1
3 11
5 101
7 111
9 1001
Their sum = 1 + 3 + 5 + 7 + 9 = 25.
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
The time complexity is O(n) or O(1). The space complexity is , since only a constant amount of extra space is.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.