> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/graphs-bfs-and-dfs/minimum-height-trees.md).

# Minimum Height Trees

For an undirected graph with tree characteristics, we can choose any node as the root. The result graph is then a rooted tree. Among all possible rooted trees, those with minimum height are called minimum height trees (MHTs). Given such a graph, write a function to find all the MHTs and return a list of their root labels.

**Format**\
The graph contains `n` nodes which are labeled from `0` to `n - 1`. You will be given the number `n` and a list of undirected `edges` (each edge is a pair of labels).

You can assume that no duplicate edges will appear in `edges`. Since all edges are undirected, `[0, 1]` is the same as `[1, 0]` and thus will not appear together in `edges`.

**Example 1 :**

```
Input: n = 4, edges = [[1, 0], [1, 2], [1, 3]]

        0
        |
        1
       / \
      2   3 

Output: [1]
```

**Example 2 :**

```
Input: n = 6, edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]

     0  1  2
      \ | /
        3
        |
        4
        |
        5 

Output: [3, 4]
```

**Note**:

* According to the [definition of tree on Wikipedia](https://en.wikipedia.org/wiki/Tree_\(graph_theory\)): “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.”
* The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.

```java
class Solution {
    // Basically, the idea is to eat up all the leaves at the same time,
    // until one/two leaves are left.
    public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        if (n == 1)
            return Collections.singletonList(0);
        // Adjacency List GRAPH
        List<Set<Integer>> graph = new ArrayList<>(n);
        for (int i = 0; i < n; ++i)
            graph.add(new HashSet<>());
        for (int[] edge : edges) {
            graph.get(edge[0]).add(edge[1]);
            graph.get(edge[1]).add(edge[0]);
        }
        // Creating a set of leaves(nodes with one 1 connection)
        List<Integer> leaves = new ArrayList<>();
        for (int i = 0; i < n; ++i)
            if (graph.get(i).size() == 1)
                leaves.add(i);
        // While Number of remaining nodes > 2
        while (n > 2) {
            n -= leaves.size();
            // Creating list for new leaves that will be created
            // when we remove the old lists
            List<Integer> newLeaves = new ArrayList<>();
            for (int i : leaves) {
                // Getting the only connection present in the set
                int j = graph.get(i).iterator().next();
                // Removing this connection from the inner node
                graph.get(j).remove(i);
                // Now if the inner node becomes a leaf
                // then we will add it to the new leaves list
                if (graph.get(j).size() == 1)
                    newLeaves.add(j);
            }
            leaves = newLeaves;
        }
        return leaves;
    }
}
```