node-depths

Node Depths

Difficulty: easy
Category: Binary Trees

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The distance between a node in a Binary Tree and the tree's root is called the node's depth.

Write a function that takes in a Binary Tree and returns the sum of its nodes' depths.

Each BinaryTree node has an integer value, a left child node, and a right child node. Children nodes can either be BinaryTree nodes themselves or None / null.

Sample Input

tree =     1
        /     \
      2       3
    /   \    /   \
  4     5  6     7
/   \  /
8    9 10

Sample Output

16
// The depth of the node with value 2 is 1.
// The depth of the node with value 3 is 1.
// The depth of the node with value 4 is 2.
// The depth of the node with value 5 is 2.
// Etc..
// Summing all of these depths yields 16.