leetcode-problemset/leetcode-cn/originData/sum-of-k-mirror-numbers.json

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        "question": {
            "questionId": "2202",
            "questionFrontendId": "2081",
            "categoryTitle": "Algorithms",
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            "title": "Sum of k-Mirror Numbers",
            "titleSlug": "sum-of-k-mirror-numbers",
            "content": "<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>\n\n<ul>\n\t<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>\n\t<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>\n</ul>\n\n<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>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> k = 2, n = 5\n<strong>Output:</strong> 25\n<strong>Explanation:\n</strong>The 5 smallest 2-mirror numbers and their representations in base-2 are listed as follows:\n  base-10    base-2\n    1          1\n    3          11\n    5          101\n    7          111\n    9          1001\nTheir sum = 1 + 3 + 5 + 7 + 9 = 25. \n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> k = 3, n = 7\n<strong>Output:</strong> 499\n<strong>Explanation:\n</strong>The 7 smallest 3-mirror numbers are and their representations in base-3 are listed as follows:\n  base-10    base-3\n    1          1\n    2          2\n    4          11\n    8          22\n    121        11111\n    151        12121\n    212        21212\nTheir sum = 1 + 2 + 4 + 8 + 121 + 151 + 212 = 499.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> k = 7, n = 17\n<strong>Output:</strong> 20379000\n<strong>Explanation:</strong> The 17 smallest 7-mirror numbers are:\n1, 2, 3, 4, 5, 6, 8, 121, 171, 242, 292, 16561, 65656, 2137312, 4602064, 6597956, 6958596\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= k &lt;= 9</code></li>\n\t<li><code>1 &lt;= n &lt;= 30</code></li>\n</ul>\n",
            "translatedTitle": "k 镜像数字的和",
            "translatedContent": "<p>一个 <strong>k 镜像数字</strong>&nbsp;指的是一个在十进制和 k 进制下从前往后读和从后往前读都一样的&nbsp;<strong>没有前导 0</strong>&nbsp;的&nbsp;<strong>正</strong>&nbsp;整数。</p>\n\n<ul>\n\t<li>比方说，<code>9</code>&nbsp;是一个 2 镜像数字。<code>9</code>&nbsp;在十进制下为&nbsp;<code>9</code>&nbsp;，二进制下为&nbsp;<code>1001</code>&nbsp;，两者从前往后读和从后往前读都一样。</li>\n\t<li>相反地，<code>4</code>&nbsp;不是一个 2 镜像数字。<code>4</code>&nbsp;在二进制下为&nbsp;<code>100</code>&nbsp;，从前往后和从后往前读不相同。</li>\n</ul>\n\n<p>给你进制&nbsp;<code>k</code>&nbsp;和一个数字&nbsp;<code>n</code>&nbsp;，请你返回 k 镜像数字中 <strong>最小</strong> 的 <code>n</code>&nbsp;个数 <strong>之和</strong>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><b>示例 1：</b></p>\n\n<pre><b>输入：</b>k = 2, n = 5\n<b>输出：</b>25\n<strong>解释：\n</strong>最小的 5 个 2 镜像数字和它们的二进制表示如下：\n  十进制       二进制\n    1          1\n    3          11\n    5          101\n    7          111\n    9          1001\n它们的和为 1 + 3 + 5 + 7 + 9 = 25 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>k = 3, n = 7\n<b>输出：</b>499\n<strong>解释：\n</strong>7 个最小的 3 镜像数字和它们的三进制表示如下：\n  十进制       三进制\n    1          1\n    2          2\n    4          11\n    8          22\n    121        11111\n    151        12121\n    212        21212\n它们的和为 1 + 2 + 4 + 8 + 121 + 151 + 212 = 499 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><b>输入：</b>k = 7, n = 17\n<b>输出：</b>20379000\n<b>解释：</b>17 个最小的 7 镜像数字分别为：\n1, 2, 3, 4, 5, 6, 8, 121, 171, 242, 292, 16561, 65656, 2137312, 4602064, 6597956, 6958596\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= k &lt;= 9</code></li>\n\t<li><code>1 &lt;= n &lt;= 30</code></li>\n</ul>\n",
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                    "lang": "C++",
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                    "code": "class Solution {\npublic:\n    long long kMirror(int k, int n) {\n        \n    }\n};",
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                    "code": "class Solution {\n    public long kMirror(int k, int n) {\n\n    }\n}",
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                    "code": "class Solution(object):\n    def kMirror(self, k, n):\n        \"\"\"\n        :type k: int\n        :type n: int\n        :rtype: int\n        \"\"\"",
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                    "code": "class Solution:\n    def kMirror(self, k: int, n: int) -> int:",
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                    "code": "public class Solution {\n    public long KMirror(int k, int n) {\n\n    }\n}",
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                    "code": "/**\n * @param {number} k\n * @param {number} n\n * @return {number}\n */\nvar kMirror = function(k, n) {\n\n};",
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                    "code": "# @param {Integer} k\n# @param {Integer} n\n# @return {Integer}\ndef k_mirror(k, n)\n\nend",
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                    "lang": "Swift",
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                    "code": "class Solution {\n    func kMirror(_ k: Int, _ n: Int) -> Int {\n\n    }\n}",
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                    "lang": "Go",
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                    "code": "func kMirror(k int, n int) int64 {\n\n}",
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                    "code": "object Solution {\n    def kMirror(k: Int, n: Int): Long = {\n\n    }\n}",
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                    "code": "class Solution {\n    fun kMirror(k: Int, n: Int): Long {\n\n    }\n}",
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                    "lang": "Rust",
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                    "code": "impl Solution {\n    pub fn k_mirror(k: i32, n: i32) -> i64 {\n\n    }\n}",
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                    "code": "class Solution {\n\n    /**\n     * @param Integer $k\n     * @param Integer $n\n     * @return Integer\n     */\n    function kMirror($k, $n) {\n\n    }\n}",
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                    "code": "(define/contract (k-mirror k n)\n  (-> exact-integer? exact-integer? exact-integer?)\n\n  )",
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                    "code": "defmodule Solution do\n  @spec k_mirror(k :: integer, n :: integer) :: integer\n  def k_mirror(k, n) do\n\n  end\nend",
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            "hints": [
                "Since we need to reduce search space, instead of checking if every number is a palindrome in base-10, can we try to \"generate\" the palindromic numbers?",
                "If you are provided with a d digit number, how can you generate a palindrome with 2*d or 2*d - 1 digit?",
                "Try brute-forcing and checking if the palindrome you generated is a \"k-Mirror\" number."
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