Tree: Depth-First Search - Path Sum III (Any Path)
What is the overall time complexity of the prefix sum DFS approach for counting all downward paths summing to a target in a binary tree with n nodes?
What is the overall time complexity of the prefix sum DFS approach for counting all downward paths summing to a target in a binary tree with n nodes?
medium📊 Complexity Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: DFS visits each node once
The algorithm traverses each node exactly once.Step 2: Prefix sums allow constant time checks
Using a hash map for prefix sums lets us check for valid paths in O(1) time per node.Final Answer:
Option B -> Option BQuick Check:
Linear time due to single traversal and constant-time prefix sum lookups [OK]
Quick Trick: Prefix sum DFS runs in linear time O(n) [OK]
Common Mistakes:
MISTAKES- Assuming nested loops cause O(n^2) complexity
- Confusing balanced tree height with traversal cost
- Ignoring hash map constant time lookups
Trap Explanation:
PITFALL- Mistaking nested path checks for nested loops leads to overestimating complexity.
Interviewer Note:
CONTEXT- Evaluates understanding of time complexity for prefix sum DFS solutions.
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