Longest Increasing Path in a Matrix
A hard-tier problem at 55% community acceptance, tagged with Array, Dynamic Programming, Depth-First Search. Reported in interviews at DoorDash and 7 others.
Longest Increasing Path in a Matrix is a hard problem that blends graph traversal with dynamic programming. It shows up in interviews at DoorDash, Citadel, Snap, DE Shaw, Nvidia, Adobe, TikTok, and WeRide. The acceptance rate sits at 55 percent, which sounds passable until you hit the live assessment and realize the brute-force DFS times out on medium grids. You need memoization and the right graph model to crack it. StealthCoder is your insurance policy if the pattern doesn't click during your OA.
Companies that ask "Longest Increasing Path in a Matrix"
Longest Increasing Path in a Matrix 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 who got tired of watching his cohort grind for six months and still get filtered at the OA stage.
Get StealthCoderThe trap is treating this as pure depth-first search without caching. You can move in four directions (up, down, left, right) to strictly larger values, and the longest path from any cell becomes a state you must cache. Build a memoization table where dp[i][j] holds the longest path starting from cell (i, j). The trick is recognizing this as a DAG (directed acyclic graph) problem; you're finding the longest path in a topological order, not cycle detection. Without memoization, you recompute the same subproblems thousands of times. A few candidates also solve it via topological sort and BFS, which works but is less intuitive. If you blank on the memoization setup during your OA, StealthCoder surfaces a clean recursive solution with caching in seconds, invisible to the proctor.
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Longest Increasing Path in a Matrix 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 who got tired of watching his cohort grind for six months and still get filtered at the OA stage. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Longest Increasing Path in a Matrix interview FAQ
How does this problem relate to topological sort?+
The matrix forms a DAG where edges point from smaller to larger values. Topological sort is one valid approach, though memoized DFS is simpler and equally efficient. Both exploit the acyclic property to avoid infinite loops and compute longest paths in one pass.
Why does naive DFS time out?+
Without caching, a single cell recalculates its longest path every time you visit it. On a grid with many tied values, you revisit the same cell hundreds or thousands of times. Memoization collapses this to one calculation per cell, reducing time from exponential to O(n times m).
Is this still asked at top companies?+
Yes. DoorDash, Citadel, and DE Shaw report it frequently. It's a favorite because it filters candidates who understand both recursion and caching. The 55 percent acceptance rate reflects that many candidates get stuck on the memoization model.
What's the most common mistake?+
Starting DFS from every cell and running pure recursion without memoization. This passes small test cases but times out on larger ones. The second mistake is overthinking topological sort when a simple recursive approach with caching is much faster to code.
How does memoization change the complexity?+
Time drops from exponential to O(n times m) because you compute the longest path for each cell once and reuse the result. Space is O(n times m) for the dp table plus O(n times m) recursion stack in worst case. This fits comfortably on any modern system.
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