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# 310 Minimum Height Trees

### Problem:

For a 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:

Given n = 4, edges = \[\[1, 0], \[1, 2], \[1, 3]]

```
    0
    |
    1
   / \
  2   3
```

return \[1]

Example 2:

Given n = 6, edges = \[\[0, 3], \[1, 3], \[2, 3], \[4, 3], \[5, 4]]

```
 0  1  2
  \ | /
    3
    |
    4
    |
    5
```

return \[3, 4]

Hint:

How many MHTs can a graph have at most? Note:

(1) According to the definition of tree on Wikipedia: “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.”

(2) The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.

### Solutions:

```java
public class Solution {
    public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        HashMap<Integer, LinkedList<Integer>> adj = new HashMap<Integer, LinkedList<Integer>>();
        init(adj, n, edges);
        List<Integer> leaves = new LinkedList<Integer>();
        for (Integer i:adj.keySet()) {
            if (adj.get(i).size() == 1) {
                leaves.add(i);
            }
        }
        if (leaves.size() == 0) {
            leaves.add(0);
            return leaves;
        }
        while (n > 2) {
            n = n - leaves.size();
            List<Integer> newLeaves = new LinkedList<Integer>();
            for (Integer i:leaves) {
                int nb = adj.get(i).get(0);
                adj.get(nb).remove(i);
                if (adj.get(nb).size() == 1) {
                    newLeaves.add(nb);
                }
            }
            leaves = newLeaves;
        }
        return leaves;
    }
    private void init(HashMap<Integer, LinkedList<Integer>> adj, int n, int[][] edges) {
        for (int i = 0; i < n; i ++) {
            adj.put(i, new LinkedList<Integer>());
        }
        for (int i = 0; i < edges.length; i ++) {
            adj.get(edges[i][0]).add(edges[i][1]);
            adj.get(edges[i][1]).add(edges[i][0]);
        }
    }
}
```