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Which of the following problems CANNOT be solved efficiently using the Path Sum III (Any Path) pattern (downward paths with prefix sums)?

easy🔍 Pattern Recognition Q2 of Q15
Tree: Depth-First Search - Path Sum III (Any Path)
Which of the following problems CANNOT be solved efficiently using the Path Sum III (Any Path) pattern (downward paths with prefix sums)?
ACount paths in a graph with cycles where paths can move in any direction and sum to target.
BCount number of downward paths in a binary tree with sum equal to target using prefix sums.
CCount paths in a binary tree where the sum of node values equals target, paths go downward only.
DFind number of paths in a tree where paths can start and end anywhere but must be downward.
Step-by-Step Solution
Solution:

  1. Step 1: Identify problem constraints

    Path Sum III pattern applies only to trees with downward paths and no cycles.

  2. Step 2: Analyze each option

    Counting paths in a graph with cycles where paths can move in any direction and sum to target involves graphs with cycles and arbitrary path directions, which breaks prefix sum assumptions.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Only tree downward path sums fit prefix sum pattern; graphs with cycles do not [OK]
Quick Trick: Graphs with cycles break prefix sum assumptions [OK]
Common Mistakes:
MISTAKES
  • Assuming prefix sums work on graphs with cycles
  • Confusing downward path restriction
Trap Explanation:
PITFALL
  • Candidates often think prefix sums apply to any path sum problem, ignoring graph cycles and path direction constraints.
Interviewer Note:
CONTEXT
  • Tests anti-pattern recognition and understanding of prefix sum applicability limits.
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