MinimumHeightTrees.java

package com.fishercoder.solutions;

import java.util.*;

/**
 * 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.
 */
public class MinimumHeightTrees {

    public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        if (n == 1)
            return Collections.singletonList(0);

        List<Set<Integer>> adj = new ArrayList<>(n);
        for (int i = 0; i < n; ++i)
            adj.add(new HashSet<>());
        for (int[] edge : edges) {
            adj.get(edge[0]).add(edge[1]);
            adj.get(edge[1]).add(edge[0]);
        }

        List<Integer> leaves = new ArrayList<>();
        for (int i = 0; i < n; ++i)
            if (adj.get(i).size() == 1)
                leaves.add(i);

        while (n > 2) {
            n -= leaves.size();
            List<Integer> newLeaves = new ArrayList<>();
            for (int i : leaves) {
                int j = adj.get(i).iterator().next();
                adj.get(j).remove(i);
                if (adj.get(j).size() == 1)
                    newLeaves.add(j);
            }
            leaves = newLeaves;
        }
        return leaves;
    }

}