# 310. Minimum Height Trees

```
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]



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.
```

Credits:Special thanks to @dietpepsi for adding this problem and creating all test cases.

## Solution <a href="#solution" id="solution"></a>

```java
public class Solution {
 private Map<Integer, Node> map;

    public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        List<Integer> result = new ArrayList<>();
        if (n <= 0 || edges == null) return result;
   map = new HashMap<>();
        for(int i = 0; i < n;i ++) {
            map.put(i, new Node(new ArrayList<Edge>(), i));
        }

        for (int i = 0; i < edges.length; i++) {
            int start = edges[i][0];
            int end = edges[i][1];

            if (!map.containsKey(start)) {
                map.put(start, new Node(new ArrayList<Edge>(), start));
            }

            if (!map.containsKey(end)) {
                map.put(end, new Node(new ArrayList<Edge>(), end));
            }

            Node startNode = map.get(start);
            Node endNode = map.get(end);
            Edge edge = new Edge(startNode, endNode);
            startNode.edges.add(edge);
            endNode.edges.add(edge);
        }

        // remove leaves until 2 nodes
        List<Node> leaves = new ArrayList<>();
        for (Node node : map.values()) {
            if (node.edges.size() == 1) {
                leaves.add(node);
            }
        }

        while (map.size() > 2) {
            for (Node leave : leaves) {
                map.remove(leave.val);

                List<Edge> edges1 = leave.edges;
                for (Edge edge : edges1) {
                    if (edge.n1 != leave) {
                        edge.n1.removeEdge(edge);
                    }

                    if (edge.n2 != leave) {
                        edge.n2.removeEdge(edge);
                    }
                }
            }

            leaves = new ArrayList<>();
            for (Node node : map.values()) {
                if (node.edges.size() == 1) {
                    leaves.add(node);
                }
            }
        }

        for (Node node : map.values()) {
            result.add(node.val);
        }

        return result;
    }

    private class Node {
        int val;
        List<Edge> edges;

        public Node(List<Edge> edges, int val) {
            this.edges = edges;
            this.val = val;
        }

        public void removeEdge(Edge edge) {
            edges.remove(edge);
        }
    }

    private class Edge {
        Node n1;
        Node n2;

        public Edge(Node n2, Node n1) {
            this.n2 = n2;
            this.n1 = n1;
        }
    }
}
```


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