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 undirectededges (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 inedges.

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 byexactly 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.

Solution:

public class Solution {
    public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        List<Integer> leaves = new ArrayList<Integer>();
        if (edges==null || edges.length==0) {
            leaves.add(n-1);
            return leaves;
        }
        HashMap<Integer, ArrayList<Integer>> graph = new HashMap<Integer, ArrayList<Integer>>();
        int[] indegree = new int[n];
       
        for (int i=0; i<n; i++) {
            graph.put(i, new ArrayList<Integer>());
        }
       
        //build the graph
        for (int[] edge : edges) {
            graph.get(edge[0]).add(edge[1]);
            graph.get(edge[1]).add(edge[0]);
            indegree[edge[0]]++;
            indegree[edge[1]]++;
        }
       
        //find the leaves
        for (int i=0; i<n; i++) {
            if (indegree[i] == 1) {
                leaves.add(i);
            }
        }
       
        //topological sort until n<=2
        while (n > 2) {
            List<Integer> newLeaf = new ArrayList<Integer>();
            for (Integer leaf : leaves) {
                List<Integer> neighbors = graph.get(leaf);
                for (Integer neighbor : neighbors) {
                    indegree[neighbor]--;
                    graph.get(neighbor).remove(leaf);
                    if (indegree[neighbor] == 1)
                        newLeaf.add(neighbor);
                }
                //delete leaf from graph
                n--;
            }
            leaves = newLeaf;
        }
       
        return leaves;
    }
}