[LeetCode 310] Minimum Height Trees
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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.
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; }
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