leetcode-problemset/leetcode-cn/originData/concatenated-divisibility.json

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        "question": {
            "questionId": "3841",
            "questionFrontendId": "3533",
            "categoryTitle": "Algorithms",
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            "title": "Concatenated Divisibility",
            "titleSlug": "concatenated-divisibility",
            "content": "<p data-end=\"378\" data-start=\"31\">You are given an array of positive integers <code data-end=\"85\" data-start=\"79\">nums</code> and a positive integer <code data-end=\"112\" data-start=\"109\">k</code>.</p>\n\n<p data-end=\"378\" data-start=\"31\">A <span data-keyword=\"permutation-array\">permutation</span> of <code data-end=\"137\" data-start=\"131\">nums</code> is said to form a <strong data-end=\"183\" data-start=\"156\">divisible concatenation</strong> if, when you <em>concatenate</em> <em>the decimal representations</em> of the numbers in the order specified by the permutation, the resulting number is <strong>divisible by</strong> <code data-end=\"359\" data-start=\"356\">k</code>.</p>\n\n<p data-end=\"561\" data-start=\"380\">Return the <strong><span data-keyword=\"lexicographically-smaller-string\">lexicographically smallest</span></strong> permutation (when considered as a list of integers) that forms a <strong>divisible concatenation</strong>. If no such permutation exists, return an empty list.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [3,12,45], k = 5</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[3,12,45]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<table data-end=\"896\" data-start=\"441\" node=\"[object Object]\" style=\"border: 1px solid black;\">\n\t<thead data-end=\"497\" data-start=\"441\">\n\t\t<tr data-end=\"497\" data-start=\"441\">\n\t\t\t<th data-end=\"458\" data-start=\"441\" style=\"border: 1px solid black;\">Permutation</th>\n\t\t\t<th data-end=\"479\" data-start=\"458\" style=\"border: 1px solid black;\">Concatenated Value</th>\n\t\t\t<th data-end=\"497\" data-start=\"479\" style=\"border: 1px solid black;\">Divisible by 5</th>\n\t\t</tr>\n\t</thead>\n\t<tbody data-end=\"896\" data-start=\"555\">\n\t\t<tr data-end=\"611\" data-start=\"555\">\n\t\t\t<td style=\"border: 1px solid black;\">[3, 12, 45]</td>\n\t\t\t<td style=\"border: 1px solid black;\">31245</td>\n\t\t\t<td style=\"border: 1px solid black;\">Yes</td>\n\t\t</tr>\n\t\t<tr data-end=\"668\" data-start=\"612\">\n\t\t\t<td style=\"border: 1px solid black;\">[3, 45, 12]</td>\n\t\t\t<td style=\"border: 1px solid black;\">34512</td>\n\t\t\t<td style=\"border: 1px solid black;\">No</td>\n\t\t</tr>\n\t\t<tr data-end=\"725\" data-start=\"669\">\n\t\t\t<td style=\"border: 1px solid black;\">[12, 3, 45]</td>\n\t\t\t<td style=\"border: 1px solid black;\">12345</td>\n\t\t\t<td style=\"border: 1px solid black;\">Yes</td>\n\t\t</tr>\n\t\t<tr data-end=\"782\" data-start=\"726\">\n\t\t\t<td style=\"border: 1px solid black;\">[12, 45, 3]</td>\n\t\t\t<td style=\"border: 1px solid black;\">12453</td>\n\t\t\t<td style=\"border: 1px solid black;\">No</td>\n\t\t</tr>\n\t\t<tr data-end=\"839\" data-start=\"783\">\n\t\t\t<td style=\"border: 1px solid black;\">[45, 3, 12]</td>\n\t\t\t<td style=\"border: 1px solid black;\">45312</td>\n\t\t\t<td style=\"border: 1px solid black;\">No</td>\n\t\t</tr>\n\t\t<tr data-end=\"896\" data-start=\"840\">\n\t\t\t<td style=\"border: 1px solid black;\">[45, 12, 3]</td>\n\t\t\t<td style=\"border: 1px solid black;\">45123</td>\n\t\t\t<td style=\"border: 1px solid black;\">No</td>\n\t\t</tr>\n\t</tbody>\n</table>\n\n<p data-end=\"1618\" data-start=\"1525\">The lexicographically smallest permutation that forms a divisible concatenation is <code>[3,12,45]</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [10,5], k = 10</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[5,10]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<table data-end=\"1421\" data-start=\"1200\" node=\"[object Object]\" style=\"border: 1px solid black;\">\n\t<thead data-end=\"1255\" data-start=\"1200\">\n\t\t<tr data-end=\"1255\" data-start=\"1200\">\n\t\t\t<th data-end=\"1216\" data-start=\"1200\" style=\"border: 1px solid black;\">Permutation</th>\n\t\t\t<th data-end=\"1237\" data-start=\"1216\" style=\"border: 1px solid black;\">Concatenated Value</th>\n\t\t\t<th data-end=\"1255\" data-start=\"1237\" style=\"border: 1px solid black;\">Divisible by 10</th>\n\t\t</tr>\n\t</thead>\n\t<tbody data-end=\"1421\" data-start=\"1312\">\n\t\t<tr data-end=\"1366\" data-start=\"1312\">\n\t\t\t<td style=\"border: 1px solid black;\">[5, 10]</td>\n\t\t\t<td style=\"border: 1px solid black;\">510</td>\n\t\t\t<td style=\"border: 1px solid black;\">Yes</td>\n\t\t</tr>\n\t\t<tr data-end=\"1421\" data-start=\"1367\">\n\t\t\t<td style=\"border: 1px solid black;\">[10, 5]</td>\n\t\t\t<td style=\"border: 1px solid black;\">105</td>\n\t\t\t<td style=\"border: 1px solid black;\">No</td>\n\t\t</tr>\n\t</tbody>\n</table>\n\n<p data-end=\"2011\" data-start=\"1921\">The lexicographically smallest permutation that forms a divisible concatenation is <code>[5,10]</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,2,3], k = 5</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>Since no permutation of <code data-end=\"177\" data-start=\"171\">nums</code> forms a valid divisible concatenation, return an empty list.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 13</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= 100</code></li>\n</ul>\n",
            "translatedTitle": "判断连接可整除性",
            "translatedContent": "<p data-end=\"378\" data-start=\"31\">给你一个正整数数组 <code data-end=\"85\" data-start=\"79\">nums</code> 和一个正整数 <code data-end=\"112\" data-start=\"109\">k</code>。</p>\n\n<p data-end=\"378\" data-start=\"31\">当&nbsp;<code data-end=\"137\" data-start=\"131\">nums</code>&nbsp;的一个 <span data-keyword=\"permutation-array\">排列</span> 中的所有数字，按照排列顺序&nbsp;<strong data-end=\"183\" data-start=\"156\">连接其十进制表示&nbsp;</strong>后形成的数可以&nbsp;<strong>被</strong> <code data-end=\"359\" data-start=\"356\">k</code>&nbsp; 整除时，我们称该排列形成了一个&nbsp;<strong>可整除连接&nbsp;</strong>。</p>\n\n<p data-end=\"561\" data-start=\"380\">返回能够形成&nbsp;<strong>可整除连接 </strong>且&nbsp;<strong><span data-keyword=\"lexicographically-smaller-string\">字典序</span> 最小 </strong>的排列（按整数列表的形式表示）。如果不存在这样的排列，返回一个空列表。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入:</strong> <span class=\"example-io\">nums = [3,12,45], k = 5</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">[3,12,45]</span></p>\n\n<p><strong>解释:</strong></p>\n\n<table data-end=\"896\" data-start=\"441\" node=\"[object Object]\" style=\"border: 1px solid black;\">\n\t<thead data-end=\"497\" data-start=\"441\">\n\t\t<tr data-end=\"497\" data-start=\"441\">\n\t\t\t<th data-end=\"458\" data-start=\"441\" style=\"border: 1px solid black;\">排列</th>\n\t\t\t<th data-end=\"479\" data-start=\"458\" style=\"border: 1px solid black;\">连接后的值</th>\n\t\t\t<th data-end=\"497\" data-start=\"479\" style=\"border: 1px solid black;\">是否能被 5 整除</th>\n\t\t</tr>\n\t</thead>\n\t<tbody data-end=\"896\" data-start=\"555\">\n\t\t<tr data-end=\"611\" data-start=\"555\">\n\t\t\t<td style=\"border: 1px solid black;\">[3, 12, 45]</td>\n\t\t\t<td style=\"border: 1px solid black;\">31245</td>\n\t\t\t<td style=\"border: 1px solid black;\">是</td>\n\t\t</tr>\n\t\t<tr data-end=\"668\" data-start=\"612\">\n\t\t\t<td style=\"border: 1px solid black;\">[3, 45, 12]</td>\n\t\t\t<td style=\"border: 1px solid black;\">34512</td>\n\t\t\t<td style=\"border: 1px solid black;\">否</td>\n\t\t</tr>\n\t\t<tr data-end=\"725\" data-start=\"669\">\n\t\t\t<td style=\"border: 1px solid black;\">[12, 3, 45]</td>\n\t\t\t<td style=\"border: 1px solid black;\">12345</td>\n\t\t\t<td style=\"border: 1px solid black;\">是</td>\n\t\t</tr>\n\t\t<tr data-end=\"782\" data-start=\"726\">\n\t\t\t<td style=\"border: 1px solid black;\">[12, 45, 3]</td>\n\t\t\t<td style=\"border: 1px solid black;\">12453</td>\n\t\t\t<td style=\"border: 1px solid black;\">否</td>\n\t\t</tr>\n\t\t<tr data-end=\"839\" data-start=\"783\">\n\t\t\t<td style=\"border: 1px solid black;\">[45, 3, 12]</td>\n\t\t\t<td style=\"border: 1px solid black;\">45312</td>\n\t\t\t<td style=\"border: 1px solid black;\">否</td>\n\t\t</tr>\n\t\t<tr data-end=\"896\" data-start=\"840\">\n\t\t\t<td style=\"border: 1px solid black;\">[45, 12, 3]</td>\n\t\t\t<td style=\"border: 1px solid black;\">45123</td>\n\t\t\t<td style=\"border: 1px solid black;\">否</td>\n\t\t</tr>\n\t</tbody>\n</table>\n\n<p data-end=\"1618\" data-start=\"1525\">可以形成可整除连接且字典序最小的排列是 <code>[3,12,45]</code>。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入:</strong> <span class=\"example-io\">nums = [10,5], k = 10</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">[5,10]</span></p>\n\n<p><strong>解释:</strong></p>\n\n<table data-end=\"1421\" data-start=\"1200\" node=\"[object Object]\" style=\"border: 1px solid black;\">\n\t<thead data-end=\"1255\" data-start=\"1200\">\n\t\t<tr data-end=\"1255\" data-start=\"1200\">\n\t\t\t<th data-end=\"1216\" data-start=\"1200\" style=\"border: 1px solid black;\">排列</th>\n\t\t\t<th data-end=\"1237\" data-start=\"1216\" style=\"border: 1px solid black;\">连接后的值</th>\n\t\t\t<th data-end=\"1255\" data-start=\"1237\" style=\"border: 1px solid black;\">是否能被 10 整除</th>\n\t\t</tr>\n\t</thead>\n\t<tbody data-end=\"1421\" data-start=\"1312\">\n\t\t<tr data-end=\"1366\" data-start=\"1312\">\n\t\t\t<td style=\"border: 1px solid black;\">[5, 10]</td>\n\t\t\t<td style=\"border: 1px solid black;\">510</td>\n\t\t\t<td style=\"border: 1px solid black;\">是</td>\n\t\t</tr>\n\t\t<tr data-end=\"1421\" data-start=\"1367\">\n\t\t\t<td style=\"border: 1px solid black;\">[10, 5]</td>\n\t\t\t<td style=\"border: 1px solid black;\">105</td>\n\t\t\t<td style=\"border: 1px solid black;\">否</td>\n\t\t</tr>\n\t</tbody>\n</table>\n\n<p data-end=\"2011\" data-start=\"1921\">可以形成可整除连接且字典序最小的排列是 <code>[5,10]</code>。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入:</strong> <span class=\"example-io\">nums = [1,2,3], k = 5</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">[]</span></p>\n\n<p><strong>解释:</strong></p>\n\n<p>由于不存在任何可以形成有效可整除连接的排列，因此返回空列表。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 13</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= 100</code></li>\n</ul>\n",
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