310. Minimum Height Trees

At a Glance

• Topic: Depth-First Search
• Pattern: Analyze Pattern
• Difficulty: Medium
• LeetCode: 310

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 = [...

Approach & Solution Steps

Topological Sort / Leaves Trimming. Continuously remove leaves (nodes with degree 1) until 1 or 2 nodes remain. Those are the roots for MHTs.

Optimal JS Solution

function findMinHeightTrees(n, edges) {
  if (n === 1) return [0];
  const adj = Array.from({length: n}, () => new Set());
  for (const [u, v] of edges) {
    adj[u].add(v);
    adj[v].add(u);
  }
  let leaves = [];
  for (let i = 0; i < n; i++) {
    if (adj[i].size === 1) leaves.push(i);
  }
  let remaining = n;
  while (remaining > 2) {
    remaining -= leaves.length;
    const newLeaves = [];
    for (const leaf of leaves) {
      const neighbor = adj[leaf].values().next().value;
      adj[neighbor].delete(leaf);
      if (adj[neighbor].size === 1) newLeaves.push(neighbor);
    }
    leaves = newLeaves;
  }
  return leaves;
}

Edge Cases & Pitfalls

• Always consider empty or null inputs.
• Watch out for off-by-one index errors.