Introduction

In this blog post, we will explore how to solve the LeetCode problem "310" 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

A tree is an undirected graph in which any two vertices are connected by exactly one path. In other words, any connected graph without simple cycles is a tree. Given a tree of n nodes labelled from 0 to n - 1, and an array of n - 1 edges where edges[i] = [ai, bi] indicates that there is an undirected edge between the two nodes ai and bi in the tree, you can choose any node of the tree as the root. When you select a node x as the root, the result tree has height h. Among all possible rooted trees, those with minimum height (i.e. min(h)) are called minimum height trees (MHTs). Return a list of all MHTs' root labels. You can return the answer in any order. The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf. Example 1: Input: n = 4, edges = [[1,0],[1,2],[1,3]] Output: [1] Explanation: As shown, the height of the tree is 1 when the root is the node with label 1 which is the only MHT. Example 2: Input: n = 6, edges = [[3,0],[3,1],[3,2],[3,4],[5,4]] Output: [3,4] Constraints: 1 <= n <= 2 * 104 edges.length == n - 1 0 <= ai, bi < n ai != bi All the pairs (ai, bi) are distinct. The given input is guaranteed to be a tree and there will be no repeated edges.

Explanation

Here's the breakdown of the solution, followed by the Python code:

• Key Idea: The core idea is to iteratively peel off leaf nodes (nodes with degree 1) from the tree. The last one or two nodes remaining will be the roots of the minimum height trees. This approach leverages the tree's structure and works its way inwards towards the center.

• Intuition: Think of it like progressively trimming the outer layers of an onion. The center of the onion corresponds to the root(s) of the MHT(s).

• Why it works: Removing leaf nodes doesn't change the relative height differences among the remaining nodes. By repeatedly trimming leaves, we converge on the nodes that are "most central" to the original tree structure.

• Complexity:

  • Runtime Complexity: O(n), where n is the number of nodes.
  • Storage Complexity: O(n), due to the adjacency list and the leaf node queue.

Code

    from collections import defaultdict, deque

def find_min_height_trees(n: int, edges: list[list[int]]) -> list[int]:
    """
    Finds the roots of minimum height trees (MHTs) in a given tree.

    Args:
        n: The number of nodes in the tree (labeled from 0 to n-1).
        edges: A list of edges, where each edge is a list [ai, bi] indicating an undirected edge between nodes ai and bi.

    Returns:
        A list of the root labels of all MHTs.
    """

    if n <= 2:
        return [i for i in range(n)]

    adj = defaultdict(list)
    degrees = [0] * n  # Store degrees of each node

    for u, v in edges:
        adj[u].append(v)
        adj[v].append(u)
        degrees[u] += 1
        degrees[v] += 1

    leaves = deque([i for i in range(n) if degrees[i] == 1]) #initialize leaf queue

    count = n #keep track of remaining nodes

    while count > 2:
        leaf_count = len(leaves)
        count -= leaf_count #subtract leaf nodes removed during this level

        for _ in range(leaf_count):
            leaf = leaves.popleft()

            for neighbor in adj[leaf]:
                degrees[neighbor] -= 1
                if degrees[neighbor] == 1:
                    leaves.append(neighbor)

    return list(leaves)