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)

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:

Step 1: Identify problem constraints
Path Sum III pattern applies only to trees with downward paths and no cycles.
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.
Final Answer:
Option A -> Option A
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

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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