Maximum Path Quality of a Graph
A hard-tier problem at 60% community acceptance, tagged with Array, Backtracking, Graph. Reported in interviews at SAP and 2 others.
Maximum Path Quality of a Graph is a hard backtracking problem that shows up in assessments at SAP, DoorDash, and Atlassian. You're traversing a graph to find the path with the maximum quality, not the shortest path or most frequent node. That twist catches people off guard. The acceptance rate sits around 59%, which means plenty of candidates solve it, but the backtracking logic trips up those who default to greedy or dynamic programming patterns that don't apply here. If this problem hits your live OA and you blank on how to set up the recursion correctly, StealthCoder surfaces a working solution in seconds, invisible to the proctor.
Companies that ask "Maximum Path Quality of a Graph"
Maximum Path Quality of a Graph is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Built by an engineer at a top-10 tech company who can solve these problems cold but didn't want to trust himself in a 90-minute screen share.
Get StealthCoderThe trick is recognizing that you need to explore all possible paths from a source node using backtracking, not optimizing at each step. You'll track visited nodes to avoid cycles, calculate path quality along the way, and backtrack to explore alternate routes. The naive approach fails because the maximum quality path isn't always the 'locally best' choice. Many candidates try BFS or Dijkstra and waste time. The graph structure, array-based node representation, and quality accumulation all point to depth-first exploration with state restoration. Since you're checking every viable path, time complexity can be exponential in the worst case, but constraints are usually small enough that backtracking works. When you hit this live, the hardest part is trusting that you need to try all paths. StealthCoder is the hedge when that instinct doesn't click under pressure.
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Maximum Path Quality of a Graph recycles across companies for a reason. It's hard-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Built by an engineer at a top-10 tech company who can solve these problems cold but didn't want to trust himself in a 90-minute screen share. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Maximum Path Quality of a Graph interview FAQ
Is this really a hard problem or does it feel harder than it is?+
It's genuinely hard because the pattern isn't Dijkstra or BFS. You need backtracking with careful state management. The 59% acceptance rate reflects that. The difficulty comes from unlearning shortest-path intuition and committing to exhaustive search instead.
Do I need to use a visited set?+
Yes. You track visited nodes during each path to avoid cycles, then unmark them when you backtrack. This is core to the backtracking pattern. Without proper visited management, you'll either infinite loop or miss valid paths.
How does this differ from other graph backtracking problems?+
Most graph backtracking focuses on finding if a path exists or counting paths. This one maximizes a quality metric while respecting node-visit constraints. You're accumulating state and comparing final values across all explored paths.
Do SAP, DoorDash, and Atlassian ask this the same way?+
The core problem is consistent across those companies, but constraints, graph size, or quality definitions might vary slightly per company. The backtracking approach holds regardless. Expect it as a late-round or final-round problem.
What's the most common mistake on this one?+
Trying to optimize greedily instead of exploring all paths. Or forgetting to restore visited state during backtrack, which corrupts later path explorations. Both are fixable once you see the solution, but they're silent bugs under time pressure.
Want the actual problem statement? View "Maximum Path Quality of a Graph" on LeetCode →