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            "questionId": "3847",
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            "categoryTitle": "Algorithms",
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            "title": "Minimum Swaps to Sort by Digit Sum",
            "titleSlug": "minimum-swaps-to-sort-by-digit-sum",
            "content": "<p>You are given an array <code>nums</code> of <strong>distinct</strong> positive integers. You need to sort the array in <strong>increasing</strong> order based on the sum of the digits of each number. If two numbers have the same digit sum, the <strong>smaller</strong> number appears first in the sorted order.</p>\n\n<p>Return the <strong>minimum</strong> number of swaps required to rearrange <code>nums</code> into this sorted order.</p>\n\n<p>A <strong>swap</strong> is defined as exchanging the values at two distinct positions in the array.</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 = [37,100]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">1</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<ul>\n\t<li>Compute the digit sum for each integer: <code>[3 + 7 = 10, 1 + 0 + 0 = 1] &rarr; [10, 1]</code></li>\n\t<li>Sort the integers based on digit sum: <code>[100, 37]</code>. Swap <code>37</code> with <code>100</code> to obtain the sorted order.</li>\n\t<li>Thus, the minimum number of swaps required to rearrange <code>nums</code> is 1.</li>\n</ul>\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 = [22,14,33,7]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">0</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<ul>\n\t<li>Compute the digit sum for each integer: <code>[2 + 2 = 4, 1 + 4 = 5, 3 + 3 = 6, 7 = 7] &rarr; [4, 5, 6, 7]</code></li>\n\t<li>Sort the integers based on digit sum: <code>[22, 14, 33, 7]</code>. The array is already sorted.</li>\n\t<li>Thus, the minimum number of swaps required to rearrange <code>nums</code> is 0.</li>\n</ul>\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 = [18,43,34,16]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<ul>\n\t<li>Compute the digit sum for each integer: <code>[1 + 8 = 9, 4 + 3 = 7, 3 + 4 = 7, 1 + 6 = 7] &rarr; [9, 7, 7, 7]</code></li>\n\t<li>Sort the integers based on digit sum: <code>[16, 34, 43, 18]</code>. Swap <code>18</code> with <code>16</code>, and swap <code>43</code> with <code>34</code> to obtain the sorted order.</li>\n\t<li>Thus, the minimum number of swaps required to rearrange <code>nums</code> is 2.</li>\n</ul>\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;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>nums</code> consists of <strong>distinct</strong> positive integers.</li>\n</ul>\n",
            "translatedTitle": "数位和排序需要的最小交换次数",
            "translatedContent": "<p>给你一个由 <strong>互不相同</strong>&nbsp;的正整数组成的数组 <code>nums</code>，需要根据每个数字的数位和（即每一位数字相加求和）按&nbsp;<strong>升序&nbsp;</strong>对数组进行排序。如果两个数字的数位和相等，则较小的数字排在前面。</p>\n\n<p>返回将 <code>nums</code> 排列为上述排序顺序所需的&nbsp;<strong>最小&nbsp;</strong>交换次数。</p>\n\n<p>一次&nbsp;<strong>交换&nbsp;</strong>定义为交换数组中两个不同位置的值。</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 = [37,100]</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">1</span></p>\n\n<p><strong>解释:</strong></p>\n\n<ul>\n\t<li>计算每个整数的数位和：<code>[3 + 7 = 10, 1 + 0 + 0 = 1] → [10, 1]</code></li>\n\t<li>根据数位和排序：<code>[100, 37]</code>。将 <code>37</code> 与 <code>100</code> 交换，得到排序后的数组。</li>\n\t<li>因此，将 <code>nums</code> 排列为排序顺序所需的最小交换次数为 1。</li>\n</ul>\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 = [22,14,33,7]</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">0</span></p>\n\n<p><strong>解释:</strong></p>\n\n<ul>\n\t<li>计算每个整数的数位和：<code>[2 + 2 = 4, 1 + 4 = 5, 3 + 3 = 6, 7 = 7] → [4, 5, 6, 7]</code></li>\n\t<li>根据数位和排序：<code>[22, 14, 33, 7]</code>。数组已经是排序好的。</li>\n\t<li>因此，将 <code>nums</code> 排列为排序顺序所需的最小交换次数为 0。</li>\n</ul>\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 = [18,43,34,16]</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>解释:</strong></p>\n\n<ul>\n\t<li>计算每个整数的数位和：<code>[1 + 8 = 9, 4 + 3 = 7, 3 + 4 = 7, 1 + 6 = 7] → [9, 7, 7, 7]</code></li>\n\t<li>根据数位和排序：<code>[16, 34, 43, 18]</code>。将 <code>18</code> 与 <code>16</code> 交换，再将 <code>43</code> 与 <code>34</code> 交换，得到排序后的数组。</li>\n\t<li>因此，将 <code>nums</code> 排列为排序顺序所需的最小交换次数为 2。</li>\n</ul>\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;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>nums</code> 由 <strong>互不相同</strong> 的正整数组成。</li>\n</ul>\n",
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                "First, sort the array based on digit sum (and value as a tiebreaker). Then, map each original value to its index in the sorted array.",
                "Now, the problem reduces to finding the minimum number of swaps to sort this mapped array. The answer is <code>n - number_of_cycles</code> in the permutation."
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