Get path from every leaf node to root in a tree structure

How can I turn this tree structure

[1, [2, [3, 4]], [5, [6, [7], 8]]]

1
   2
      3
      4
   5
      6
         7
      8

.... into this "reversed tree" structure, which basically contains the paths from all the leaf nodes to 1 (the root):

[8, [5, [1]], 7, [6, [5, [1]]], 4, [2, [1]], 3, [2, [1]]]

8
   5
      1
7
   6
      5
         1
4
   2
      1
3
   2
      1

The result wouldn’t even have to be structured as a tree, four flat arrays in the correct order would also be fine.

It looks like Depth-first search might be a r开发者_运维问答elevant algorithm, but I can’t understand the pseudocode (what does incidentEdges() return?), so I’m pretty stuck.

If someone could offer a Ruby method (or really easy to understand pseudocode) to convert the original nested array into the result array, I would be infinitely grateful.

And this is not a homework assignment, rather it is the result of it being too long since I’ve studied... I need this to print a dependency tree in the proper order for a given issue in an issue tracker.

A bit more compact code:

tree = [1, [2, [3, 4]], [5, [6, [7], 8]]]

def find_reverse_leaf_paths(nodes, prefix = [], paths = []) 
  leafs = []
  nodes.each do |node|
    if node.is_a?(Numeric)
      leafs.push(node)
    else
      prefix.push(leafs.pop) unless leafs.empty?
      leafs.clear
      find_reverse_leaf_paths(node, prefix, paths)
    end 
  end 
  leafs.each do |leaf|
    paths.push(prefix + [leaf])
  end 
  prefix.pop unless leafs.empty?
  paths.map { |path| path.reverse }.reverse
end

puts find_reverse_leaf_paths(tree).inspect

You can use this code. It's not my best code, but I'm learning ruby too :D (it was a good exercise)

a = [1, [2, [3, 4]], [5, [6, [7], 8]]]

class Node
  attr_reader :value
  attr_reader :parent
  attr_reader :children

  def initialize(value, parent)
    @value = value
    @parent = parent
    @parent.add_child self unless parent == nil
    @children = []
  end

  def add_child(child)
    @children << child
  end

  def print_node(ident) 
    Range.new(0,ident).each {print ' '}
    print @value.to_s
    print "\n"
    children.each { |child| child.print_node (ident+4) }
  end

end

class Tree
  def self.from_array(array)
    process array, nil
  end


  def self.process(array, parent)
    node = nil
    array.each do |array_item| 
      if array_item.is_a? Numeric
        node = Node.new(array_item, parent) 
      else
        process(array_item, node)
      end
    end

    node
  end

  def self.print_paths_to_root node
    if node.children.empty? 
      puts print_path_to_root(node)
    else
      node.children.each do |child|
        print_paths_to_root child
      end  
    end
  end

  def self.print_path_to_root node 
    if node != nil
      node.value.to_s + '  ' + print_path_to_root(node.parent) 
    else
      ""
    end
  end
end

puts 'TREE'
root = Tree.from_array a
root.print_node 0

puts "\n\n\n"

puts 'PATH TO ROOT'
Tree.print_paths_to_root root

Just thinking off the top of my head, why not recusively traverse the tree progressively concatenating the nodes, and when you reach a leaf output the nodes in reverse order. This should give you the 4 flat arrays you wanted.

your first 2 leaf-arrays would evolve like this:

1 - node 
12 - node
123 - leaf - output 321.
12 - pop out
124 - leaf - output 421

NWS

To clarify the point I was trying to make in my previous comments to the question, I'll show some code. I use just an Array as tree, so the empty Tree must [root, []] (hence the guard for empty children).

class Array
  def paths
    root, children = self
    return [root] if children.empty? 
    children.map do |child|
      (child.is_a?(Array) ? child.paths : [[child]]).map do |tail|
        [root] + tail
      end
    end.flatten(1)
  end
end

tree = [1, [[2, [3, 4]], [5, [[6, [7]], 8]]]]
p tree.paths
# [[1, 2, 3], [1, 2, 4], [1, 5, 6, 7], [1, 5, 8]]

Granted, this is neither the input you had nor the the result you wanted ;-) but it's the same idea, isn't it? My point is that if the data structure is "logic", the code should be pretty straighforward (and functional, to walk a tree we shouldn't need an imperative algorithm!).