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"title": "Smallest Missing Genetic Value in Each Subtree",
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"content": "<p>There is a <strong>family tree</strong> rooted at <code>0</code> consisting of <code>n</code> nodes numbered <code>0</code> to <code>n - 1</code>. You are given a <strong>0-indexed</strong> integer array <code>parents</code>, where <code>parents[i]</code> is the parent for node <code>i</code>. Since node <code>0</code> is the <strong>root</strong>, <code>parents[0] == -1</code>.</p>\n\n<p>There are <code>10<sup>5</sup></code> genetic values, each represented by an integer in the <strong>inclusive</strong> range <code>[1, 10<sup>5</sup>]</code>. You are given a <strong>0-indexed</strong> integer array <code>nums</code>, where <code>nums[i]</code> is a <strong>distinct </strong>genetic value for node <code>i</code>.</p>\n\n<p>Return <em>an array </em><code>ans</code><em> of length </em><code>n</code><em> where </em><code>ans[i]</code><em> is</em> <em>the <strong>smallest</strong> genetic value that is <strong>missing</strong> from the subtree rooted at node</em> <code>i</code>.</p>\n\n<p>The <strong>subtree</strong> rooted at a node <code>x</code> contains node <code>x</code> and all of its <strong>descendant</strong> nodes.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/08/23/case-1.png\" style=\"width: 204px; height: 167px;\" />\n<pre>\n<strong>Input:</strong> parents = [-1,0,0,2], nums = [1,2,3,4]\n<strong>Output:</strong> [5,1,1,1]\n<strong>Explanation:</strong> The answer for each subtree is calculated as follows:\n- 0: The subtree contains nodes [0,1,2,3] with values [1,2,3,4]. 5 is the smallest missing value.\n- 1: The subtree contains only node 1 with value 2. 1 is the smallest missing value.\n- 2: The subtree contains nodes [2,3] with values [3,4]. 1 is the smallest missing value.\n- 3: The subtree contains only node 3 with value 4. 1 is the smallest missing value.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/08/23/case-2.png\" style=\"width: 247px; height: 168px;\" />\n<pre>\n<strong>Input:</strong> parents = [-1,0,1,0,3,3], nums = [5,4,6,2,1,3]\n<strong>Output:</strong> [7,1,1,4,2,1]\n<strong>Explanation:</strong> The answer for each subtree is calculated as follows:\n- 0: The subtree contains nodes [0,1,2,3,4,5] with values [5,4,6,2,1,3]. 7 is the smallest missing value.\n- 1: The subtree contains nodes [1,2] with values [4,6]. 1 is the smallest missing value.\n- 2: The subtree contains only node 2 with value 6. 1 is the smallest missing value.\n- 3: The subtree contains nodes [3,4,5] with values [2,1,3]. 4 is the smallest missing value.\n- 4: The subtree contains only node 4 with value 1. 2 is the smallest missing value.\n- 5: The subtree contains only node 5 with value 3. 1 is the smallest missing value.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> parents = [-1,2,3,0,2,4,1], nums = [2,3,4,5,6,7,8]\n<strong>Output:</strong> [1,1,1,1,1,1,1]\n<strong>Explanation:</strong> The value 1 is missing from all the subtrees.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == parents.length == nums.length</code></li>\n\t<li><code>2 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>0 <= parents[i] <= n - 1</code> for <code>i != 0</code></li>\n\t<li><code>parents[0] == -1</code></li>\n\t<li><code>parents</code> represents a valid tree.</li>\n\t<li><code>1 <= nums[i] <= 10<sup>5</sup></code></li>\n\t<li>Each <code>nums[i]</code> is distinct.</li>\n</ul>\n",
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"If the subtree doesn't contain 1, then the missing value will always be 1.",
"What data structure allows us to dynamically update the values that are currently not present?"
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