Binary Tree Traversal Sum Of Each Depth

问题

I am looking for an algorithm or modification of an efficient way to get the sum of run through of a tree depth, for example:

                Z
               / \
              /   \
             /     \
            /       \
           X         Y
          / \      /  \
         /   \    /    \
        A     B  C      D

The number of final leaves is four so us have four final sums and they would be this respectively.

[Z+X+A] [Z+X+B] [Z+Y+C] [Z+Y+D]

If someone could guide me in the right direction into getting the sums of all possible depths, that would be great.

This will be done in python with fairly large trees.

回答1:

You can recurse over the nodes of the tree keeping the sum from the root down to this point. When you reach a leaf node, you return the current sum in a list of one element. In the internal nodes, you concatenate the lists returned from children.

Sample Code:

class Node:
    def __init__(self, value, children):
        self.value = value
        self.children = children

def tree_sums(root, current_sum):
    current_sum += root.value
    if len(root.children) == 0:
        return [current_sum]
    subtree_sums = []
    for child in root.children:
        subtree_sums += tree_sums(child, current_sum)
    return subtree_sums

tree = Node(1, [Node(2, []), Node(3, [])])
assert tree_sums(tree, 0) == [3, 4]

回答2:

Here is what you are looking for. In this example, trees are stored as dicts with a "value" and a "children" keys, and "children" maps to a list.

def triesum(t):
    if not t['children']:
        return [t['value']]
    return [t['value'] + n for c in t['children'] for n in triesum(c)]

Example

trie = {'value': 5, 'children': [
    {'value': 7, 'children': [
        {'value': 8, 'children': []},
        {'value': 2, 'children': []}
    ]},
    {'value': 4, 'children': [
        {'value': 3, 'children': []},
        {'value': 6, 'children': []}
    ]}
]}

print sorted(triesum(trie)) == sorted([5 + 7 + 8, 5 + 7 + 2, 5 + 4 + 3, 5 + 4 + 6])
    # prints True

来源：https://stackoverflow.com/questions/27595162/binary-tree-traversal-sum-of-each-depth

标签

python

algorithm

recursion

binary-tree