[email protected] [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:

Show 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.

public class Solution {

    /** return the height of tree if let s to be the root of the tree */
    public static int bfs(ArrayList<ArrayList<Integer> > g, int s) {

        HashSet<Integer> upper = new HashSet<Integer> ();
        HashSet<Integer> lower = new HashSet<Integer> ();
        HashSet<Integer> vis = new HashSet<Integer> ();

        upper.add(s);
        vis.add(s);
        int lv = 1;

        while(!upper.isEmpty()) {

            for(int u: upper) {
                ArrayList<Integer> adj = g.get(u);
                for(int i=0; i<adj.size(); ++i) {
                    int adj_node = adj.get(i);
                    if(!vis.contains(adj_node)) {
                        lower.add(adj_node);
                    }
                }
            }

            if(!lower.isEmpty()) {
                ++lv;
            }

            upper.clear();
            for(int c: lower) {
                vis.add(c);
                upper.add(c);
            }
            lower.clear();
        }

        return lv;
    }

    public static ArrayList<Integer> topologicalSort(int n, int[][] edges, ArrayList<ArrayList<Integer> > g) {

        ArrayList<Integer> topo = new ArrayList<Integer> ();
        int[] d = new int[n];

        for(int i=0; i<edges.length; ++i) {
            int u = edges[i][0], v = edges[i][1];
            ++d[u]; ++d[v];
        }

        LinkedList<Integer> queue = new LinkedList<Integer> ();
        for(int i=0; i<n; ++i) {
            if(d[i] == 1) {
                queue.addLast(i);
            }
        }

        while(!queue.isEmpty()) {
            int top = queue.pollFirst();
            topo.add(top);

            ArrayList<Integer> adj = g.get(top);
            for(int next: adj) {
                d[next]--;
                if(d[next] == 1) {
                    queue.addLast(next);
                }
            }
        }

        return topo;
    }

    public List<Integer> findMinHeightTrees(int n, int[][] edges) {

        List<Integer> rs = new ArrayList<Integer> ();
        if(n == 1) {
            rs.add(0);
            return rs;
        }

        ArrayList<ArrayList<Integer> > g = new ArrayList<ArrayList<Integer> > ();
        for(int i=0; i<n; ++i) {
            ArrayList<Integer> row = new ArrayList<Integer> ();
            g.add(row);
        }
        for(int i=0; i<edges.length; ++i) {
            int u = edges[i][0];
            int v = edges[i][1];

            g.get(u).add(v);
            g.get(v).add(u);
        }

        HashMap<Integer, Integer> mapping = new HashMap<Integer, Integer> ();
        ArrayList<Integer> topo = topologicalSort(n, edges, g);

        int idx = topo.get(topo.size()-1);
        int min_lv = bfs(g, idx);
        rs.add(idx);

        if(topo.size() >= 2) {
            int indice = topo.get(topo.size()-2);
            if(bfs(g, indice) == min_lv) {
                rs.add(indice);
            }
        }

        return rs;

    }
}