Package g2001_2100.s2081_sum_of_k_mirror_numbers

Class Solution

  • public class Solution
extends Object
    2081 - Sum of k-Mirror Numbers.

    Hard

    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 of 9 in base-10 and base-2 are 9 and 1001 respectively, which read the same both forward and backward.
    • On the contrary, 4 is not a 2-mirror number. The representation of 4 in base-2 is 100, 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

    • Constructor Detail

      • Solution

        public Solution()

    • Method Detail

      • kMirror

        public long kMirror​(int k,
                    int n)