mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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185 lines
29 KiB
JSON
185 lines
29 KiB
JSON
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"questionId": "2558",
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"questionFrontendId": "2471",
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"categoryTitle": "Algorithms",
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"boundTopicId": 1962149,
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"title": "Minimum Number of Operations to Sort a Binary Tree by Level",
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"titleSlug": "minimum-number-of-operations-to-sort-a-binary-tree-by-level",
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"content": "<p>You are given the <code>root</code> of a binary tree with <strong>unique values</strong>.</p>\n\n<p>In one operation, you can choose any two nodes <strong>at the same level</strong> and swap their values.</p>\n\n<p>Return <em>the minimum number of operations needed to make the values at each level sorted in a <strong>strictly increasing order</strong></em>.</p>\n\n<p>The <strong>level</strong> of a node is the number of edges along the path between it and the root node<em>.</em></p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img src=\"https://assets.leetcode.com/uploads/2022/09/18/image-20220918174006-2.png\" style=\"width: 500px; height: 324px;\" />\n<pre>\n<strong>Input:</strong> root = [1,4,3,7,6,8,5,null,null,null,null,9,null,10]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong>\n- Swap 4 and 3. The 2<sup>nd</sup> level becomes [3,4].\n- Swap 7 and 5. The 3<sup>rd</sup> level becomes [5,6,8,7].\n- Swap 8 and 7. The 3<sup>rd</sup> level becomes [5,6,7,8].\nWe used 3 operations so return 3.\nIt can be proven that 3 is the minimum number of operations needed.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img src=\"https://assets.leetcode.com/uploads/2022/09/18/image-20220918174026-3.png\" style=\"width: 400px; height: 303px;\" />\n<pre>\n<strong>Input:</strong> root = [1,3,2,7,6,5,4]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong>\n- Swap 3 and 2. The 2<sup>nd</sup> level becomes [2,3].\n- Swap 7 and 4. The 3<sup>rd</sup> level becomes [4,6,5,7].\n- Swap 6 and 5. The 3<sup>rd</sup> level becomes [4,5,6,7].\nWe used 3 operations so return 3.\nIt can be proven that 3 is the minimum number of operations needed.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img src=\"https://assets.leetcode.com/uploads/2022/09/18/image-20220918174052-4.png\" style=\"width: 400px; height: 274px;\" />\n<pre>\n<strong>Input:</strong> root = [1,2,3,4,5,6]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> Each level is already sorted in increasing order so return 0.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li>The number of nodes in the tree is in the range <code>[1, 10<sup>5</sup>]</code>.</li>\n\t<li><code>1 <= Node.val <= 10<sup>5</sup></code></li>\n\t<li>All the values of the tree are <strong>unique</strong>.</li>\n</ul>\n",
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"translatedTitle": "逐层排序二叉树所需的最少操作数目",
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"translatedContent": "<p>给你一个 <strong>值互不相同</strong> 的二叉树的根节点 <code>root</code> 。</p>\n\n<p>在一步操作中，你可以选择 <strong>同一层</strong> 上任意两个节点，交换这两个节点的值。</p>\n\n<p>返回每一层按 <strong>严格递增顺序</strong> 排序所需的最少操作数目。</p>\n\n<p>节点的 <strong>层数</strong> 是该节点和根节点之间的路径的边数。</p>\n\n<p> </p>\n\n<p><strong>示例 1 ：</strong></p>\n<img src=\"https://assets.leetcode.com/uploads/2022/09/18/image-20220918174006-2.png\" style=\"width: 500px; height: 324px;\">\n<pre><strong>输入：</strong>root = [1,4,3,7,6,8,5,null,null,null,null,9,null,10]\n<strong>输出：</strong>3\n<strong>解释：</strong>\n- 交换 4 和 3 。第 2 层变为 [3,4] 。\n- 交换 7 和 5 。第 3 层变为 [5,6,8,7] 。\n- 交换 8 和 7 。第 3 层变为 [5,6,7,8] 。\n共计用了 3 步操作，所以返回 3 。\n可以证明 3 是需要的最少操作数目。\n</pre>\n\n<p><strong>示例 2 ：</strong></p>\n<img src=\"https://assets.leetcode.com/uploads/2022/09/18/image-20220918174026-3.png\" style=\"width: 400px; height: 303px;\">\n<pre><strong>输入：</strong>root = [1,3,2,7,6,5,4]\n<strong>输出：</strong>3\n<strong>解释：\n</strong>- 交换 3 和 2 。第 2 层变为 [2,3] 。 \n- 交换 7 和 4 。第 3 层变为 [4,6,5,7] 。 \n- 交换 6 和 5 。第 3 层变为 [4,5,6,7] 。\n共计用了 3 步操作，所以返回 3 。 \n可以证明 3 是需要的最少操作数目。\n</pre>\n\n<p><strong>示例 3 ：</strong></p>\n<img src=\"https://assets.leetcode.com/uploads/2022/09/18/image-20220918174052-4.png\" style=\"width: 400px; height: 274px;\">\n<pre><strong>输入：</strong>root = [1,2,3,4,5,6]\n<strong>输出：</strong>0\n<strong>解释：</strong>每一层已经按递增顺序排序，所以返回 0 。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li>树中节点的数目在范围 <code>[1, 10<sup>5</sup>]</code> 。</li>\n\t<li><code>1 <= Node.val <= 10<sup>5</sup></code></li>\n\t<li>树中的所有值 <strong>互不相同</strong> 。</li>\n</ul>\n",
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