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In the following DFS code snippet for counting paths summing to targetSum using prefix sums, which line is most likely to cause incorrect results due to improper handling of the prefix_counts map?

medium🐛 Buggy Code Q7 of Q15
Tree: Depth-First Search - Path Sum III (Any Path)
In the following DFS code snippet for counting paths summing to targetSum using prefix sums, which line is most likely to cause incorrect results due to improper handling of the prefix_counts map? ```python def dfs(node, current_sum): if not node: return current_sum += node.val 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] = prefix_counts.get(current_sum, 0) - 1 ```
ALine updating prefix_counts before recursive calls
BLine adding to result using prefix_counts
CLine decrementing prefix_counts after recursive calls
DLine checking for null node
Step-by-Step Solution
Solution:
  1. Step 1: Understand prefix_counts usage

    prefix_counts tracks how many times a prefix sum has occurred on the current path.
  2. Step 2: Decrement after recursion

    After visiting children, prefix_counts[current_sum] must be decremented to backtrack correctly.
  3. Step 3: Bug in decrement line

    If decrement line uses get() without ensuring the key exists or decrements incorrectly, it causes wrong counts.
  4. Final Answer:

    Option C -> Option C
  5. Quick Check:

    Incorrect decrement leads to overcounting or undercounting paths [OK]
Quick Trick: Backtrack prefix_counts correctly after recursion [OK]
Common Mistakes:
MISTAKES
  • Not decrementing prefix_counts causing stale counts
  • Decrementing before recursion instead of after
  • Ignoring null node checks
Trap Explanation:
PITFALL
  • Decrementing prefix_counts incorrectly looks like proper backtracking but breaks path count accuracy.
Interviewer Note:
CONTEXT
  • Tests ability to identify subtle bugs in prefix sum DFS implementations.
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