th

##
# MySQL 8 CTE
# tree (id int, pid int, name varchar(255))
#
WITH recursive tbl AS (
  SELECT
    t.id,
    1 AS depth,
    cast(name as CHAR(500)) AS path
  FROM tree t WHERE t.pid IS NULL
  UNION
  SELECT
    c.id,
    tbl.depth + 1,
    concat(tbl.path, ' / ', c.name)
  FROM tree c JOIN tbl ON tbl.id = c.pid
)
SELECT id, depth, path FROM tbl ORDER by path;

##
# The same with code.
# list => [id, name, pid]
#
list = [
  [15, 'category15', 0],
  [16, 'category16', 15],
  [19, 'category19', 0],
  [20, 'category20', 19],
  [21, 'category21', 20],
  [22, 'category22', 21],
  [23, 'category23', 19],
  [24, 'category24', 21],
  [25, 'category25', 22],
  [26, 'category26', 22],
  [27, 'category27', 25],
  [30, 'category30', 16],
]

def index_by_id(list)
  result = {}
  list.each do |el|
    id = el[0]
    name = el[1]
    parent_id = el[2]

    result[id] = { name: name, parent_id: parent_id }
  end

  result
end

def traverse(list)
  result = {}
  index = index_by_id(list)

  list.each do |el|
    id = el[0]
    name = el[1]
    parent_id = el[2]

    result[id] = []
    if parent_id == 0
      result[id] << name
    else
      path = []
      while parent_id != 0
        path.unshift(name)
        name = index[parent_id][:name]
        parent_id = index[parent_id][:parent_id]
      end

      path.unshift(name)
      result[id] << path.join(' / ')
    end
  end

  result
end

puts traverse(list).inspect