[LeetCode 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]

Hint:

1. 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.

Solution:

build graph first, then find leaf and remove them among their neighbors, level by level. Until left less 2 nodes

public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        List<Integer> leaf = new ArrayList<>();
        if(n<=1) {
            leaf.add(0);
            return leaf;
        }
        Map<Integer, List<Integer>> graph = new HashMap<>();
        for(int i=0;i<n;i++) graph.put(i, new ArrayList<>());
        int[] neighbors = new int[n];
        for(int[] edge : edges) {
            neighbors[edge[0]]++;
            neighbors[edge[1]]++;
            graph.get(edge[0]).add(edge[1]);
            graph.get(edge[1]).add(edge[0]);
        }
        
        for(int i=0;i<n;i++) {
            if(graph.get(i).size() ==1 ) leaf.add(i);
        }
        while(n>2) {
            List<Integer> newLeaf = new ArrayList<>();
            for(int l : leaf) {
                n--;
                for(int nb : graph.get(l)) {
                    if(--neighbors[nb] == 1) newLeaf.add(nb);
                }
            }
            leaf = newLeaf;
        }
        return leaf;
    }