【Leetcode】Minimum Height Trees
2016-05-22 20:57
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题目链接:https://leetcode.com/problems/minimum-height-trees/
题目:
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]]
/ \
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]
思路:
多画几个图,直觉最多2种MHT,即最长路径的中心点最多两个。
类似于拓扑排序,从度为1的结点开始一层层剥离,直到最中心两个或一个点。
算法:
题目:
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]
思路:
多画几个图,直觉最多2种MHT,即最长路径的中心点最多两个。
类似于拓扑排序,从度为1的结点开始一层层剥离,直到最中心两个或一个点。
算法:
public List<Integer> findMinHeightTrees(int n, int[][] edges) { HashMap<Integer, List<Integer>> maps = new HashMap<Integer, List<Integer>>(); int[] digree = new int ;// 出入度 // 记录图的拓扑 for (int i = 0; i < edges.length; i++) { digree[edges[i][0]]++; digree[edges[i][1]]++; List<Integer> list; if (!maps.containsKey(edges[i][0])) { list = new ArrayList<Integer>(); } else { list = maps.get(edges[i][0]); } list.add(edges[i][1]); maps.put(edges[i][0], list); if (!maps.containsKey(edges[i][1])) { list = new ArrayList<Integer>(); } else { list = maps.get(edges[i][1]); } list.add(edges[i][0]); maps.put(edges[i][1], list); } //获取度为1的点 即叶子节点 List<Integer> leaves = new ArrayList<Integer>(); for (int i = 0; i < n; i++) { if (digree[i] == 1) leaves.add(i); } int num = n;//图中剩余结点 List<Integer> tmp;//记录遍历过程中新产生的叶结点 //沿着叶结点一圈圈剥开图 while (num > 2) { tmp = new ArrayList<Integer>(); for (int leave : leaves) { num--; digree[leave] = 0; List<Integer> connectedLeave = maps.get(leave); for (int c : connectedLeave) { digree[c]--;//删除跟叶结点相邻的边 并将邻结点度数减一 if (digree[c] == 1) tmp.add(c); } } leaves = tmp; } return leaves; }
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