Solution Explanation

This problem asks us to count the number of nodes in a binary tree where the node's value is equal to the sum of its descendants' values. The solution uses a Depth-First Search (DFS) approach.

Approach:

The core idea is to perform a post-order traversal of the binary tree. For each node, we recursively calculate the sum of the values of its descendants. If this sum is equal to the node's value, we increment a counter. The recursive function returns the sum of the node's value and the sum of its descendants, allowing the parent node to easily calculate its total descendant sum.

Algorithm:

1. Base Case: If the current node is null (empty), return 0 (no descendants).

2. Recursive Step:

   • Recursively calculate the sum of the left subtree (left_sum) and the right subtree (right_sum).
   • Check if the sum of the left and right subtree sums (left_sum + right_sum) is equal to the current node's value. If they are equal, increment a global counter (ans).
   • Return the sum of the current node's value and the sums of its left and right subtrees (root.val + left_sum + right_sum). This ensures that the parent node receives the correct sum of its descendants.

3. Initialization: Initialize a global counter ans to 0.

4. Traversal: Call the recursive function starting from the root node.

5. Return Value: Return the final value of ans, which represents the count of nodes meeting the condition.

Time Complexity Analysis:

The DFS approach visits each node in the binary tree exactly once. Therefore, the time complexity is O(N), where N is the number of nodes in the tree.

Space Complexity Analysis:

The space complexity is determined by the maximum depth of the recursion stack. In the worst-case scenario (a skewed tree), the depth of the recursion stack can be equal to the height of the tree, which is O(N) in the case of a skewed tree and O(log N) in the case of a balanced tree. In average cases for reasonably balanced trees, it's O(log N).

Code Explanation (Python):

The Python code implements this algorithm effectively. The dfs function performs the post-order traversal and the recursive calculations. A nonlocal keyword is used within the nested function dfs to modify the ans variable in the outer scope.

Code Explanation (Other Languages):

The Java, C++, and Go implementations follow the same logic. The key differences are in syntax and how global variables are handled (e.g., using class members in Java and C++). The dfs function in all languages performs the post-order traversal and conditional counting.

This detailed explanation provides a comprehensive understanding of the solution's approach, algorithm, time and space complexity, and code implementation across several programming languages.