310. Minimum Height Trees LeetCode Solution

Last updated: February 17, 2025

In this guide, you will get 310. Minimum Height Trees LeetCode Solution with the best time and space complexity. The solution to Minimum Height Trees problem is provided in various programming languages like C++, Java, and Python. This will be helpful for you if you are preparing for placements, hackathons, interviews, or practice purposes. The solutions provided here are very easy to follow and include detailed explanations.

Problem Statement
Complexity Analysis
Minimum Height Trees solution in C++
Minimum Height Trees solution in Java
Minimum Height Trees solution in Python
Additional Resources

310. Minimum Height Trees LeetCode Solution image

Problem Statement of Minimum Height Trees

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.

Complexity Analysis

Time Complexity: O(n)
Space Complexity: O(n)

310. Minimum Height Trees LeetCode Solution in C++

class Solution {
 public:
  vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {
    if (n == 1 || edges.empty())
      return {0};

    vector<int> ans;
    unordered_map<int, unordered_set<int>> graph;

    for (const vector<int>& edge : edges) {
      const int u = edge[0];
      const int v = edge[1];
      graph[u].insert(v);
      graph[v].insert(u);
    }

    for (const auto& [label, children] : graph)
      if (children.size() == 1)
        ans.push_back(label);

    while (n > 2) {
      n -= ans.size();
      vector<int> nextLeaves;
      for (const int leaf : ans) {
        const int u = *graph[leaf].begin();
        graph[u].erase(leaf);
        if (graph[u].size() == 1)
          nextLeaves.push_back(u);
      }
      ans = nextLeaves;
    }

    return ans;
  }
};
/* code provided by PROGIEZ */

310. Minimum Height Trees LeetCode Solution in Java

class Solution {
  public List<Integer> findMinHeightTrees(int n, int[][] edges) {
    if (n == 0 || edges.length == 0)
      return List.of(0);

    List<Integer> ans = new ArrayList<>();
    Map<Integer, Set<Integer>> graph = new HashMap<>();

    for (int i = 0; i < n; ++i)
      graph.put(i, new HashSet<>());

    for (int[] edge : edges) {
      final int u = edge[0];
      final int v = edge[1];
      graph.get(u).add(v);
      graph.get(v).add(u);
    }

    for (Map.Entry<Integer, Set<Integer>> entry : graph.entrySet()) {
      final int label = entry.getKey();
      Set<Integer> children = entry.getValue();
      if (children.size() == 1)
        ans.add(label);
    }

    while (n > 2) {
      n -= ans.size();
      List<Integer> nextLeaves = new ArrayList<>();
      for (final int leaf : ans) {
        final int u = (int) graph.get(leaf).iterator().next();
        graph.get(u).remove(leaf);
        if (graph.get(u).size() == 1)
          nextLeaves.add(u);
      }
      ans = nextLeaves;
    }

    return ans;
  }
}
// code provided by PROGIEZ

310. Minimum Height Trees LeetCode Solution in Python

class Solution:
  def findMinHeightTrees(self, n: int, edges: list[list[int]]) -> list[int]:
    if n == 1 or not edges:
      return [0]

    ans = []
    graph = collections.defaultdict(set)

    for u, v in edges:
      graph[u].add(v)
      graph[v].add(u)

    for label, children in graph.items():
      if len(children) == 1:
        ans.append(label)

    while n > 2:
      n -= len(ans)
      nextLeaves = []
      for leaf in ans:
        u = next(iter(graph[leaf]))
        graph[u].remove(leaf)
        if len(graph[u]) == 1:
          nextLeaves.append(u)
      ans = nextLeaves

    return ans
 # code by PROGIEZ

Additional Resources

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