Introduction

In this blog post, we will explore how to solve the LeetCode problem "2003" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

There is a family tree rooted at 0 consisting of n nodes numbered 0 to n - 1. You are given a 0-indexed integer array parents, where parents[i] is the parent for node i. Since node 0 is the root, parents[0] == -1. There are 105 genetic values, each represented by an integer in the inclusive range [1, 105]. You are given a 0-indexed integer array nums, where nums[i] is a distinct genetic value for node i. Return an array ans of length n where ans[i] is the smallest genetic value that is missing from the subtree rooted at node i. The subtree rooted at a node x contains node x and all of its descendant nodes. Example 1: Input: parents = [-1,0,0,2], nums = [1,2,3,4] Output: [5,1,1,1] Explanation: 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. Example 2: Input: parents = [-1,0,1,0,3,3], nums = [5,4,6,2,1,3] Output: [7,1,1,4,2,1] Explanation: 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. Example 3: Input: parents = [-1,2,3,0,2,4,1], nums = [2,3,4,5,6,7,8] Output: [1,1,1,1,1,1,1] Explanation: The value 1 is missing from all the subtrees. Constraints: n == parents.length == nums.length 2 <= n <= 105 0 <= parents[i] <= n - 1 for i != 0 parents[0] == -1 parents represents a valid tree. 1 <= nums[i] <= 105 Each nums[i] is distinct.

Explanation

Here's a breakdown of the solution:

• Build the Tree: Represent the tree using an adjacency list where each node stores its children. This allows for efficient traversal of the subtree.
• Depth-First Search (DFS): Traverse the tree in a post-order manner (process children before the parent). This enables calculating the missing value for each subtree bottom-up. During DFS, maintain a set to keep track of the values present in the current subtree.

• Calculate Missing Value: After visiting all children of a node, iterate from 1 to n+1 to find the smallest missing value within the set of genetic values of that subtree.

• Time Complexity: O(N (degree + logN)) where N is the number of nodes and degree is the max degree of any node, or O(N sqrt(N)), whichever is smaller; Space Complexity: O(N)

Code

    def smallestMissingValueSubtree(parents, nums):
    n = len(parents)
    children = [[] for _ in range(n)]
    for i in range(1, n):
        children[parents[i]].append(i)

    ans = [1] * n
    subtree_values = [set() for _ in range(n)]

    def dfs(node):
        subtree_values[node].add(nums[node])
        for child in children[node]:
            dfs(child)
            if len(subtree_values[child]) > len(subtree_values[node]):
                subtree_values[node], subtree_values[child] = subtree_values[child], subtree_values[node]
            subtree_values[node].update(subtree_values[child])

        missing = 1
        while missing in subtree_values[node]:
            missing += 1
        ans[node] = missing

    dfs(0)
    return ans