Tree Node Depth Sum
You are tasked with calculating the sum of the depths of all nodes in a binary tree. The depth of a node is defined as the number of edges from the root to that node. This is a fundamental operation in tree traversal and analysis, useful for understanding the structure and balance of a tree.
Problem Description
Given the root of a binary tree, calculate the sum of the depths of all its nodes. The root node has a depth of 0.
Requirements
- You need to traverse the entire binary tree.
- For each node, you need to determine its depth.
- The sum of all these depths should be returned.
Expected Behavior
The function should accurately calculate the total depth sum for any valid binary tree.
Edge Cases
- An empty tree (root is null).
- A tree with only a root node.
- A skewed tree (all nodes on one side).
Examples
Example 1:
Input:
1
/ \
2 3
/ \
4 5
Output: 7
Explanation:
- Node 1 (root): depth 0
- Node 2: depth 1
- Node 3: depth 1
- Node 4: depth 2
- Node 5: depth 2
Total depth sum = 0 + 1 + 1 + 2 + 2 = 6.
Correction: The explanation for Example 1 should be 0 + 1 + 1 + 2 + 2 = 6. The provided output of 7 is incorrect.
Example 2:
Input:
1
Output: 0
Explanation:
- Node 1 (root): depth 0
Total depth sum = 0.
Example 3:
Input:
1
\
2
\
3
Output: 3
Explanation:
- Node 1 (root): depth 0
- Node 2: depth 1
- Node 3: depth 2
Total depth sum = 0 + 1 + 2 = 3.
Constraints
- The number of nodes in the tree will be between 0 and 1000.
- Node values are integers and do not affect the calculation.
- The tree is a binary tree, meaning each node has at most two children (left and right).
Notes
- You'll need a way to represent the tree nodes. A common approach is to use a structure or class with fields for the node's value, a pointer/reference to its left child, and a pointer/reference to its right child.
- Consider using recursion or an iterative approach with a stack or queue for traversal.
- Pay close attention to how you track the depth as you move through the tree.