Binary Tree Path Sum

Question

The question asks the candidate to find all root-to-leaf paths in a binary tree where the sum of the node values in each path equals a given target sum.

Codemia · Accepted Answer

To solve the Binary Tree Path Sum problem, we will use a depth-first search (DFS) approach. The idea is to traverse the tree from the root to each leaf node, keeping track of the current path and the sum of the values along that path. When we reach a leaf node, we will check if the sum of the values in the current path equals the target sum.

We will implement a recursive function that takes the current node, the current path, and the current sum as parameters. If the current node is null, we return. If we reach a leaf node, we check if the current sum equals the target sum and, if so, add the current path to our list of valid paths. We will also backtrack by removing the current node from the path after exploring its children.

The time complexity of this approach is O(N), where N is the number of nodes in the binary tree, since we may visit each node once. The space complexity is O(H), where H is the height of the tree, due to the recursion stack. In the worst case, for a skewed tree, H can be equal to N.

Here is a Python implementation of the solution:

```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: TreeNode, targetSum: int):
        def dfs(node, current_path, current_sum):
            if not node:
                return
            current_path.append(node.val)
            current_sum += node.val
            if not node.left and not node.right and current_sum == targetSum:
                result.append(list(current_path))
            dfs(node.left, current_path, current_sum)
            dfs(node.right, current_path, current_sum)
            current_path.pop()

result = []
        dfs(root, [], 0)
        return result
```
This code defines a TreeNode class and a Solution class with a method to find all paths that sum to the target value.

Interviewers are looking for clarity in your explanation of the approach, the ability to write clean and efficient code, and your understanding of the underlying data structures. They also assess how well you can handle edge cases and your ability to analyze the complexity of your solution.

Binary Tree Path Sum

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