卖萌的弱渣

I am stupid, I am hungry.

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]]

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5

    0
    |
    1
   / \
  2   3

return [1]

Example 2:

Given n = 6, edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]

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5
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7

 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

  • 基本思路是“逐层删去叶子节点，直到剩下根节点为止”

  • Java

(Minimum-Height-Trees.java) download
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public class Solution {
    public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        if(n==1) return Collections.singletonList(0);
        List<Integer> leaves = new ArrayList<>(n);
        // <节点: 所有和节点相连的其他节点组成的set
        List<Set<Integer>> adj = new ArrayList<>();
        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]);
        }
        // leaves: 记录所有的叶子节点
        for(int i=0;i<n;i++){
            if(adj.get(i).size()==1)
                leaves.add(i);
        }

        // BFS
        while(n>2){
            n = n-leaves.size();
            List<Integer> newleaves = new ArrayList<>();
            // 找到leave并把和他相邻的点全部删除
            for(int leave: leaves){
                int j=adj.get(leave).iterator().next();
                adj.get(j).remove(leave);
                if(adj.get(j).size()==1) newleaves.add(j);
            }
            leaves = newleaves;
        }
        return leaves;

    }
}
  • Python
(Minimum-Height-Trees.py) download
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class Solution(object):
    def findMinHeightTrees(self, n, edges):
        """
        :type n: int
        :type edges: List[List[int]]
        :rtype: List[int]
        """