feat: add solution 2003. Smallest Missing Genetic Value in Each Subtree

Author: tzuyi0817

solutions/2003. Smallest Missing Genetic Value in Each Subtree/README.md

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+# [2003. Smallest Missing Genetic Value in Each Subtree](https://leetcode.com/problems/smallest-missing-genetic-value-in-each-subtree)
+
+## Description
+
+<div class="elfjS" data-track-load="description_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>
+
+<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>
+
+<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>
+
+<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>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2021/08/23/case-1.png" style="width: 204px; height: 167px;">
+<pre><strong>Input:</strong> parents = [-1,0,0,2], nums = [1,2,3,4]
+<strong>Output:</strong> [5,1,1,1]
+<strong>Explanation:</strong> The answer for each subtree is calculated as follows:
+- 0: The subtree contains nodes [0,1,2,3] with values [1,2,3,4]. 5 is the smallest missing value.
+- 1: The subtree contains only node 1 with value 2. 1 is the smallest missing value.
+- 2: The subtree contains nodes [2,3] with values [3,4]. 1 is the smallest missing value.
+- 3: The subtree contains only node 3 with value 4. 1 is the smallest missing value.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2021/08/23/case-2.png" style="width: 247px; height: 168px;">
+<pre><strong>Input:</strong> parents = [-1,0,1,0,3,3], nums = [5,4,6,2,1,3]
+<strong>Output:</strong> [7,1,1,4,2,1]
+<strong>Explanation:</strong> The answer for each subtree is calculated as follows:
+- 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.
+- 1: The subtree contains nodes [1,2] with values [4,6]. 1 is the smallest missing value.
+- 2: The subtree contains only node 2 with value 6. 1 is the smallest missing value.
+- 3: The subtree contains nodes [3,4,5] with values [2,1,3]. 4 is the smallest missing value.
+- 4: The subtree contains only node 4 with value 1. 2 is the smallest missing value.
+- 5: The subtree contains only node 5 with value 3. 1 is the smallest missing value.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<pre><strong>Input:</strong> parents = [-1,2,3,0,2,4,1], nums = [2,3,4,5,6,7,8]
+<strong>Output:</strong> [1,1,1,1,1,1,1]
+<strong>Explanation:</strong> The value 1 is missing from all the subtrees.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>n == parents.length == nums.length</code></li>
+	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
+	<li><code>0 &lt;= parents[i] &lt;= n - 1</code> for <code>i != 0</code></li>
+	<li><code>parents[0] == -1</code></li>
+	<li><code>parents</code> represents a valid tree.</li>
+	<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
+	<li>Each <code>nums[i]</code> is distinct.</li>
+</ul>
+</div>
+
+<p>&nbsp;</p>
+
+## Solutions
+
+**Solution: `Depth-First Search`**
+
+- Time complexity: <em>O(n)</em>
+- Space complexity: <em>O(n)</em>
+
+<p>&nbsp;</p>
+
+### **JavaScript**
+
+```js
+/**
+ * @param {number[]} parents
+ * @param {number[]} nums
+ * @return {number[]}
+ */
+const smallestMissingValueSubtree = function (parents, nums) {
+  const n = parents.length;
+  const result = Array.from({ length: n }, () => 1);
+  const oneNode = nums.indexOf(1);
+
+  if (oneNode === -1) return result;
+
+  const tree = Array.from({ length: n }, () => []);
+  const visited = new Set();
+  let currentNode = oneNode;
+  let minMiss = 1;
+  let prevNode = -1;
+
+  for (let node = 1; node < n; node++) {
+    const parent = parents[node];
+
+    tree[parent].push(node);
+  }
+
+  const visitNode = node => {
+    visited.add(nums[node]);
+
+    for (const neighbor of tree[node]) {
+      visitNode(neighbor);
+    }
+  };
+
+  while (currentNode !== -1) {
+    visited.add(nums[currentNode]);
+
+    for (const node of tree[currentNode]) {
+      if (node === prevNode) continue;
+
+      visitNode(node);
+    }
+
+    while (visited.has(minMiss)) {
+      minMiss += 1;
+    }
+
+    result[currentNode] = minMiss;
+    prevNode = currentNode;
+    currentNode = parents[currentNode];
+  }
+
+  return result;
+};
+```

solutions/2003. Smallest Missing Genetic Value in Each Subtree/solution.js

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+/**
+ * @param {number[]} parents
+ * @param {number[]} nums
+ * @return {number[]}
+ */
+const smallestMissingValueSubtree = function (parents, nums) {
+  const n = parents.length;
+  const result = Array.from({ length: n }, () => 1);
+  const oneNode = nums.indexOf(1);
+
+  if (oneNode === -1) return result;
+
+  const tree = Array.from({ length: n }, () => []);
+  const visited = new Set();
+  let currentNode = oneNode;
+  let minMiss = 1;
+  let prevNode = -1;
+
+  for (let node = 1; node < n; node++) {
+    const parent = parents[node];
+
+    tree[parent].push(node);
+  }
+
+  const visitNode = node => {
+    visited.add(nums[node]);
+
+    for (const neighbor of tree[node]) {
+      visitNode(neighbor);
+    }
+  };
+
+  while (currentNode !== -1) {
+    visited.add(nums[currentNode]);
+
+    for (const node of tree[currentNode]) {
+      if (node === prevNode) continue;
+
+      visitNode(node);
+    }
+
+    while (visited.has(minMiss)) {
+      minMiss += 1;
+    }
+
+    result[currentNode] = minMiss;
+    prevNode = currentNode;
+    currentNode = parents[currentNode];
+  }
+
+  return result;
+};