Minimum Height Trees

Similar Problems:

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]

Note:

- 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.”
- The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

// https://code.dennyzhang.com/minimum-height-trees // Basic Ideas: // There are at most 2 MHTs // We keep removing leaf nodes. The remaining one or two nodes are targets // Complexity: Time O(n), Space O(n) func findMinHeightTrees(n int, edges [][]int) []int { if n == 1 { return []int{0} } relations := make([]map[int]bool, n) for i:= 0; i<n; i++ { relations[i] = map[int]bool{}} for _, edge := range edges { p, q := edge[0], edge[1] relations[p][q], relations[q][p] = true, true } queue := []int{} // start with leaf nodes for i:=0; i<n; i++ { if len(relations[i]) == 1 { queue = append(queue, i) } } for n>2 { // explore current level n -= len(queue) items := []int{} for _, node := range queue { for node2 := range relations[node] { delete (relations[node2], node) // inner layer if len(relations[node2]) == 1 { items = append(items, node2) } } } queue = items } return queue }