Minimum Height Trees

mediumcodingAlgorithmsBFSGraphTrees~30 min

Asked at Google, Meta

Overview

Given a tree of n nodes labeled 0 to n-1 and n-1 undirected edges, find all root labels that minimize the tree height. These are called Minimum Height Trees (MHTs).

Constraints

1 <= n <= 20,000
The input forms a valid tree.
Return at most 2 roots (MHTs always have 1 or 2 roots).

Examples

findMinHeightTrees(4, [[1,0],[1,2],[1,3]]);
// => [1]

findMinHeightTrees(6, [[3,0],[3,1],[3,2],[3,4],[5,4]]);
// => [3, 4]

Solution

Reveal solution

function findMinHeightTrees(n, edges) {
  if (n === 1) return [0];
  const adj = Array.from({length: n}, () => new Set());
  for (const [a, b] of edges) { adj[a].add(b); adj[b].add(a); }
  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]][0];
      adj[neighbor].delete(leaf);
      if (adj[neighbor].size === 1) newLeaves.push(neighbor);
    }
    leaves = newLeaves;
  }
  return leaves;
}

Iteratively remove leaf nodes (degree 1) until 1 or 2 nodes remain.

Resources

Minimum Height Trees — LeetCode

minimum-height-trees.js

Minimum Height Trees

mediumcodingAlgorithmsBFS

Overview

Given a tree of n nodes labeled 0 to n-1 and n-1 undirected edges, find all root labels that minimize the tree height. These are called Minimum Height Trees (MHTs).

Constraints

1 <= n <= 20,000
The input forms a valid tree.
Return at most 2 roots (MHTs always have 1 or 2 roots).

Examples

findMinHeightTrees(4, [[1,0],[1,2],[1,3]]);
// => [1]

findMinHeightTrees(6, [[3,0],[3,1],[3,2],[3,4],[5,4]]);
// => [3, 4]

Solution

Reveal solution

function findMinHeightTrees(n, edges) {
  if (n === 1) return [0];
  const adj = Array.from({length: n}, () => new Set());
  for (const [a, b] of edges) { adj[a].add(b); adj[b].add(a); }
  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]][0];
      adj[neighbor].delete(leaf);
      if (adj[neighbor].size === 1) newLeaves.push(neighbor);
    }
    leaves = newLeaves;
  }
  return leaves;
}

Iteratively remove leaf nodes (degree 1) until 1 or 2 nodes remain.

Resources

Minimum Height Trees — LeetCode

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