Tree: Depth-First Search - Path Sum III (Any Path)
Given the following code snippet implementing the prefix sum DFS approach for Path Sum III, what is the output for the tree [10,5,-3,3,2,null,11,3,-2,null,1] and targetSum = 8?
```python
class TreeNode:
def __init__(self, val=0, left=None, right=None):
self.val = val
self.left = left
self.right = right
class Solution:
def pathSum(self, root, targetSum):
prefix_counts = {0: 1}
self.result = 0
def dfs(node, current_sum):
if not node:
return
current_sum += node.val
self.result += prefix_counts.get(current_sum - targetSum, 0)
prefix_counts[current_sum] = prefix_counts.get(current_sum, 0) + 1
dfs(node.left, current_sum)
dfs(node.right, current_sum)
prefix_counts[current_sum] -= 1
dfs(root, 0)
return self.result
```