Increasing Paths 1
Reported by candidates from Hudson River Trading's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
Hudson River Trading's August OA included a graph traversal problem asking you to count or find increasing paths through a structure. This is a classic dynamic programming plus DFS setup that looks simple until you realize you need memoization to avoid timeout. The trick is recognizing that each cell or node can be the start of multiple paths, and you can't afford to recompute them. StealthCoder will have the traversal pattern ready if you freeze mid-solution.
Pattern and pitfall
The pattern is depth-first search combined with memoization. You're asked to explore paths where each step increases in value, and you need to count valid paths or find the longest one. The naive approach is pure recursion with backtracking, which revisits the same subproblems exponentially. The win is caching results by position: memo[cell] = number of increasing paths starting from that cell. From each position, you try all valid next moves (neighbors with larger values), sum the memoized results, and store. Time complexity drops from exponential to O(nodes). The common miss is forgetting to memoize or memoizing the wrong thing. If you blank on the structure during the OA, StealthCoder fills that gap instantly.
If you see this problem in your OA tomorrow, the play is to recognize the pattern in 30 seconds. StealthCoder buys you that recognition.
You can drill Increasing Paths 1 cold, or you can hedge it. StealthCoder runs invisibly during screen share and surfaces a working solution in under 2 seconds. The proctor sees the IDE. They don't see what's behind it. Built by an Amazon engineer who passed his OA cold and still thinks the filter is broken.
Get StealthCoderRelated leaked OAs
You've seen the question.
Make sure you actually pass Hudson River Trading's OA.
Hudson River Trading reuses patterns across OAs. Built by an Amazon engineer who passed his OA cold and still thinks the filter is broken. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Increasing Paths 1 FAQ
Is this a grid problem or a general graph problem?+
The title hints at paths, so it could be either. If it's a grid, you move in 4 or 8 directions to neighbors with strictly larger values. If it's a graph, you follow edges where the destination value is greater. Either way, the algorithm is the same: DFS with memoization on the value constraint.
What's the trick Hudson River Trading is testing here?+
Recognizing when pure recursion is too slow and memoization is mandatory. They want to see you optimize a brute-force DFS. It's a real quant-shop problem: efficient graph traversal under constraints, not complex math.
How do I code this in under 15 minutes?+
Skeleton: write a recursive dfs function that returns the count of increasing paths from a node. Base case: no valid next moves means return 1 (the current path). Recursive case: try all neighbors with larger values, sum their memoized results. Wrap it in a memo dict. Call dfs from every starting position if needed.
What are the common pitfalls?+
Forgetting memoization and timing out. Off-by-one in the direction vectors if it's a grid. Not initializing the memo properly for each test case. Not handling the base case (a cell with no valid next moves still counts as one path).
Is this pattern still asked in 2024?+
Yes. Graph traversal with memoization is a perennial favorite at trading firms. It's not as trendy as sliding window or two-pointer, but it's a fundamental skill they assume senior candidates have cold.