Minimum Falling Path Sum
A medium-tier problem at 61% community acceptance, tagged with Array, Dynamic Programming, Matrix. Reported in interviews at Dream11 and 2 others.
Minimum Falling Path Sum shows up in assessments at Google, Intuit, and Dream11, and 61% of candidates who attempt it pass. You're given an n×n matrix and need to find the cheapest path from any cell in the first row to any cell in the last row, moving only down or diagonally down-left or down-right each step. The trap: brute force tries all possible paths and times out. The insight: dynamic programming tracks the minimum cost to reach each cell, updating it as you descend. If this problem hits your live assessment and you blank on the state transition, StealthCoder solves it in seconds, invisible to the proctor.
Companies that ask "Minimum Falling Path Sum"
Minimum Falling Path Sum 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. Made by a working Amazon engineer who got tired of watching qualified friends bomb OAs they'd solve cold in an IDE.
Get StealthCoderThe core trick is recognizing this as a shortest-path problem disguised as a matrix traversal. Most candidates initially think recursion with memoization, which works but isn't the clearest approach. The winning pattern: build a DP table where dp[i][j] represents the minimum sum to reach row i, column j. For each cell, you only look at the three cells above it (straight up, diagonal left, diagonal right) and pick the cheapest entry point. Common pitfall: forgetting to handle boundaries when checking diagonal neighbors, leading to out-of-bounds errors or incorrect sums. Another mistake: modifying the input matrix instead of using a separate DP array, which can cause cascading calculation errors. The space optimization exists (rolling array), but focus first on correctness. StealthCoder is the safety net if you freeze on the recurrence relation during the live assessment.
Pattern tags
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Minimum Falling Path Sum recycles across companies for a reason. It's medium-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. Made by a working Amazon engineer who got tired of watching qualified friends bomb OAs they'd solve cold in an IDE. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Minimum Falling Path Sum interview FAQ
Is Minimum Falling Path Sum really asked at FAANG level companies?+
Yes. Google, Intuit, and Dream11 have all reported asking it. The 61% acceptance rate suggests it's a medium-difficulty filter, not a knockout problem. Companies use it to test whether you can recognize a grid-based DP pattern quickly.
What's the difference between this and standard shortest path?+
The constraint: you can only move down, down-left, or down-right. You can't backtrack or move sideways. That limited branching is what makes DP efficient here. Dijkstra's is overkill; DP is exact because there's no better path by revisiting earlier rows.
Can I solve this recursively with memoization instead of bottom-up DP?+
Yes, both work. Top-down memoization is intuitive: define a recursive function that returns the minimum sum starting from a given cell, then cache results. Bottom-up DP (building the table) is usually faster and uses less stack space. Both are O(n squared) time and space.
What's the hardest part candidates miss?+
Handling the boundaries correctly when you check the three cells above. If you're at column 0, there's no diagonal-left cell. If you're at column n-1, there's no diagonal-right cell. Off-by-one errors here cause silent logic bugs that fail test cases.
How does this connect to Dynamic Programming and Matrix topics?+
It combines both. You're working on a matrix (2D array) and using DP to avoid recomputing subproblems. It's a gateway to more complex grid DP problems like maximum path sum or paint house. Mastering this pattern scales to harder variants.
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