g2001_2100.s2081_sum_of_k_mirror_numbers

Class Solution

java.lang.Object

g2001_2100.s2081_sum_of_k_mirror_numbers.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 Summary

Constructors

Constructor and Description
Solution()

Method Summary

Modifier and Type	Method and Description
long	kMirror(int k, int n)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Solution

public Solution()

Method Detail

kMirror

public long kMirror(int k,
                    int n)