有效地找到二叉树中最重的路径 - python

Question

I am trying to solve the following: finding the weight of the heaviest node in the tree and also representing that node as a list. This is what I came up with, but I am pretty sure that it is a very messy solution. Any advice on doing it more efficiently within the frame of the class given?

Given the class:

    class Tree_node():
        def __init__(self,key,val):
            self.key=key
            self.val=val
            self.left=None
            self.right=None  

    def __repr__(self):
    return "[" + str(self.left) + " " + str(self.key) + " " + \
                str(self.val) + " " + str(self.right) + "]"     

I calculate the weight of the heaviest path:

def weight(node):
    if node == None:
        return 0
    if weight(node.left)>weight(node.right):
        return node.val+weight(node.left)
    else:
        return node.val+weight(node.right)

And then I try to return the heaviest path as a list:

def heavy_path(node):
    if node==None:
        return []
    elif node.val+weight(node.left)> node.val+weight(node.right):
        return [node.val] + filter_values(path_values(node.left))
    else:return [node.val] + filter_values(path_values(node.right))

def path_values(node):
    if node == None:
        return 0
    return [node.val,path_values(node.left),path_values(node.right)]

def filter_values (node):
    values = []
    sub_lists = []
    if node != 0:
        for value in node:
            if isinstance(value, list):
                sub_lists = filter_values(value)
            else:
                if value != 0:
                    values.append(value)
    return values+sub_lists

So that given a tree like [[None a 7 None] b 5 [[None c 8 None] d 3 None]]:

>>> weight(t)
16
>>> heavy_path(t)
[5, 3, 8]

What would be a better way of doing this?

Answer 1

Assuming that you are interpreting the heaviest path as being a path that always begins with the root of the tree and descends down to a single leaf. You could try merging the weight-finding and path-building operations:

def heavy_path(node):
  if not node
    return (0,[])
  [lweight,llist] = heavy_path(node.left)
  [rweight,rlist] = heavy_path(node.right)
  if lweight>rweight:
    return (node.val+lweight,[node.val]+llist)
  else:
    return (node.val+rweight,[node.val]+rlist)

Or using a time-honoured technique to speed up this kind of calculation through Memoization . Once you've used memoization once, you could just keep the pathweight values up to date as you alter your tree.

def weight(node):
  if node == None:
      return 0
  node.pathweight=node.val+max(weight(node.left),weight(node.right))
  return node.pathweight

def heavy_edge(node):
  if not node.left:
    lweight=0
  else:
    lweight=node.left.pathweight
  if not node.right:
    rweight=0
  else:
    rweight=node.right.pathweight
  if lweight>rweight:
    return [node.val,heavy_edge(node.left)]
  else:
    return [node.val,heavy_edge(node.right)]

weight(t) #Precalculate the pathweight of all the nodes in O(n) time
heavy_edge(T) #Use the precalculated pathweights to efficient find list the heaviest path in O(lg n) time