2081. Sum of k-Mirror Numbers
Description
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. The representation of9
in base-10 and base-2 are9
and1001
respectively, which read the same both forward and backward. - On the contrary,
4
is not a 2-mirror number. The representation of4
in base-2 is100
, which does not read the same both forward and backward.
Given the base k
and the number n
, return the sum of the n
smallest k-mirror numbers.
Example 1:
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.
Example 2:
Input: k = 3, n = 7 Output: 499 Explanation: The 7 smallest 3-mirror numbers are and their representations in base-3 are listed as follows: base-10 base-3 1 1 2 2 4 11 8 22 121 11111 151 12121 212 21212 Their sum = 1 + 2 + 4 + 8 + 121 + 151 + 212 = 499.
Example 3:
Input: k = 7, n = 17 Output: 20379000 Explanation: The 17 smallest 7-mirror numbers are: 1, 2, 3, 4, 5, 6, 8, 121, 171, 242, 292, 16561, 65656, 2137312, 4602064, 6597956, 6958596
Constraints:
2 <= k <= 9
1 <= n <= 30
Solutions
Solution 1
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