Minimum Height Trees

Desicription

For an 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 :

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Input: n = 4, edges = [[1, 0], [1, 2], [1, 3]]

0
|
1
/ \
2 3

Output: [1]

Example 2 :

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

0 1 2
\ | /
3
|
4
|
5

Output: [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.

Solution

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class Solution {
public:
std::vector<int> findMinHeightTrees(int n, std::vector<std::vector<int>>& edges) {
auto graph = std::unordered_map<int, std::unordered_set<int>>();
for(const auto& edge : edges) {
graph[edge[0]].insert(edge[1]);
graph[edge[1]].insert(edge[0]);
}

auto leaf = std::queue<int>();
for(const auto& point : graph) {
if(point.second.size() == 1) {
leaf.push(point.first);
}
}
while(graph.size() > 2) {

auto leafCount = leaf.size();
while(leafCount--) {
const auto point = leaf.front();
leaf.pop();

graph[*graph[point].begin()].erase(point);
if(graph[*graph[point].begin()].size() == 1) {
leaf.push(*graph[point].begin());
}
graph.erase(point);
}
}

auto res = std::vector<int>();
for(const auto& point : graph) {
res.push_back(point.first);
}

return res.empty() ? std::vector<int>{0} : res;
}
};