Minimum Height Trees

Source

• leetcode: 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:

How many MHTs can a graph have at most?

题解

Java

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;
}