310. Minimum Height Trees

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.

Given a tree of n nodes labelled from 0 to n - 1, and an array of n - 1 edges where edges[i] = [ai, bi] indicates that there is an undirected edge between the two nodes ai and bi in the tree, you can choose any node of the tree as the root. When you select a node x as the root, the result tree has height h. Among all possible rooted trees, those with minimum height (i.e. min(h)) are called minimum height trees (MHTs).

Return a list of all MHTs ' root labels. You can return the answer in any order.

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

Example 1:

Input: n = 4, edges = [[1,0],[1,2],[1,3]]
Output: [1]
Explanation: As shown, the height of the tree is 1 when the root is the node with label 1 which is the only MHT.

Example 2:

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

Example 3:

Input: n = 1, edges = []
Output: [0]

Example 4:

Input: n = 2, edges = [[0,1]]
Output: [0,1]

Constraints:

• 1 <= n <= 2 * 104
• edges.length == n - 1
• 0 <= ai, bi < n
• ai != bi
• All the pairs (ai, bi) are distinct.
• The given input is guaranteed to be a tree and there will be no repeated edges.

# @lc code=start
using LeetCode

function find_min_height_trees(n::Int, edges::Vector{Vector{Int}})
    (n == 1) && return [1]
    neighbor = [Set{Int}() for i in 1:n]
    for (u, v) in edges
        push!(neighbor[u], v)
        push!(neighbor[v], u)
    end
    q = [i for i in 1:n if length(neighbor[i]) == 1]
    dep_q = ones(Int, size(q))
    m_dep = 1
    visited = fill(false, n)
    visited[q] .= true
    res = q[:]
    while !isempty(q)
        u, dep = popfirst!(q), popfirst!(dep_q)
        for nei in neighbor[u]
            visited[nei] && continue
            visited[nei] = true
            push!(q, nei)
            push!(dep_q, dep + 1)
        end
        if dep > m_dep
            m_dep = dep
            res = [u; q]
        end
    end
    return res
end
# @lc code=end

find_min_height_trees (generic function with 1 method)

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