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Which of the following algorithmic changes is necessary to solve this new problem?

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Tree: Depth-First Search - Path Sum
The classic Path Sum problem asks if there exists a root-to-leaf path with a sum equal to targetSum. Suppose the problem is modified to find if any path (not necessarily root-to-leaf or downward) in the binary tree sums to targetSum. Which of the following algorithmic changes is necessary to solve this new problem?
AUse BFS traversal instead of DFS to find the path sum more efficiently.
BModify the DFS to only consider root-to-leaf paths but allow negative node values.
CUse a prefix sum hashmap to track cumulative sums and detect any path sum in O(n) time.
DApply a greedy approach to select nodes with values closest to <code>targetSum</code>.
Step-by-Step Solution
Solution:

  1. Step 1: Understand the problem change

    Now, any path (not necessarily root-to-leaf or downward) can be considered, including paths that start and end anywhere in the tree.

  2. Step 2: Recognize the limitation of classic DFS

    The classic DFS approach only works for root-to-leaf paths and cannot detect arbitrary paths.

  3. Step 3: Use prefix sums with hashmap

    By tracking prefix sums of the path from the root to the current node and storing them in a hashmap, we can detect if any subpath sums to targetSum in O(n) time.

  4. Step 4: Evaluate options

    Use a prefix sum hashmap to track cumulative sums and detect any path sum in O(n) time. correctly describes this approach. Modify the DFS to only consider root-to-leaf paths but allow negative node values. is insufficient because it still restricts to root-to-leaf. Use BFS traversal instead of DFS to find the path sum more efficiently. (BFS) does not help with arbitrary path sums. Apply a greedy approach to select nodes with values closest to targetSum. (greedy) is not applicable.

  5. Final Answer:

    Option C -> Option C

  6. Quick Check:

    Prefix sums + hashmap detect any path sum [OK]
Quick Trick: Use prefix sums and hashmap for any path sum [OK]
Common Mistakes:
MISTAKES
  • Assuming root-to-leaf DFS works for any path
  • Trying BFS without prefix sums
  • Ignoring paths that go upward or sideways
Trap Explanation:
PITFALL
  • Option B looks plausible but still restricts to root-to-leaf paths only.
Interviewer Note:
CONTEXT
  • Tests knowledge of advanced path sum variants and prefix sum technique.
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