Which of the following changes to the algorithm is necessary to correctly count all such paths?
hard🎤 Interviewer Follow-up Q15 of Q15
Tree: Depth-First Search - Path Sum III (Any Path)
Suppose the problem is modified so that paths can move both downwards and upwards (i.e., any connected path in the tree, not necessarily parent-to-child). Which of the following changes to the algorithm is necessary to correctly count all such paths?
AConvert the tree to an undirected graph and use DFS from every node with prefix sums, resetting counts after each start.
BUse the brute force approach checking all paths from every node without prefix sums.
CUse the same prefix sum DFS approach but run it twice: once from root down and once from leaves up.
DModify the prefix sum map to store sums for paths in both directions simultaneously during one DFS.
Step-by-Step Solution
Solution:
Step 1: Understand path direction relaxation
Allowing upward and downward moves means paths are any connected sequences, not just parent-to-child.
Step 2: Model tree as undirected graph and run DFS from every node
To count all paths, treat tree as undirected graph and run DFS from each node, using prefix sums and resetting counts to avoid cross-branch contamination.
Final Answer:
Option A -> Option A
Quick Check:
Undirected DFS from every node with prefix sums counts all connected paths [OK]
Quick Trick:Undirected graph DFS needed for arbitrary path directions [OK]
Common Mistakes:
MISTAKES
Trying to reuse one-directional prefix sum DFS without modification
Assuming running DFS twice covers all paths
Trying to store both directions in one prefix sum map
Trap Explanation:
PITFALL
One-directional prefix sums fail for upward paths; naive brute force is too slow; combined prefix sums in one DFS is complex and error-prone.
Interviewer Note:
CONTEXT
Tests candidate's ability to adapt algorithm to relaxed constraints and understand graph vs tree traversal.
Master "Path Sum III (Any Path)" in Tree: Depth-First Search
3 interactive learning modes - each teaches the same concept differently
