Package 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.<p>Hard</p> <p>A <strong>k-mirror number</strong> is a <strong>positive</strong> integer <strong>without leading zeros</strong> that reads the same both forward and backward in base-10 <strong>as well as</strong> in base-k.</p> <ul> <li>For example, <code>9</code> is a 2-mirror number. The representation of <code>9</code> in base-10 and base-2 are <code>9</code> and <code>1001</code> respectively, which read the same both forward and backward.</li> <li>On the contrary, <code>4</code> is not a 2-mirror number. The representation of <code>4</code> in base-2 is <code>100</code>, which does not read the same both forward and backward.</li> </ul> <p>Given the base <code>k</code> and the number <code>n</code>, return <em>the <strong>sum</strong> of the</em> <code>n</code> <em><strong>smallest</strong> k-mirror numbers</em>.</p> <p><strong>Example 1:</strong></p> <p><strong>Input:</strong> k = 2, n = 5</p> <p><strong>Output:</strong> 25</p> <p><strong>Explanation:</strong></p> <p>The 5 smallest 2-mirror numbers and their representations in base-2 are listed as follows:</p> <pre><code> base-10 base-2 1 1 3 11 5 101 7 111 9 1001 Their sum = 1 + 3 + 5 + 7 + 9 = 25. </code></pre> <p><strong>Example 2:</strong></p> <p><strong>Input:</strong> k = 3, n = 7</p> <p><strong>Output:</strong> 499</p> <p><strong>Explanation:</strong> The 7 smallest 3-mirror numbers are and their representations in base-3 are listed as follows:</p> <pre><code> 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. </code></pre> <p><strong>Example 3:</strong></p> <p><strong>Input:</strong> k = 7, n = 17</p> <p><strong>Output:</strong> 20379000</p> <p><strong>Explanation:</strong> The 17 smallest 7-mirror numbers are:</p> <p>1, 2, 3, 4, 5, 6, 8, 121, 171, 242, 292, 16561, 65656, 2137312, 4602064, 6597956, 6958596</p> <p><strong>Constraints:</strong></p> <ul> <li><code>2 <= k <= 9</code></li> <li><code>1 <= n <= 30</code></li> </ul>

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • kMirror

      public long kMirror(int k, int n)