Meta·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

May 2026Remote

Summary

Meta SWE interview with a graph/DP problem that looked straightforward on the surface but had a follow-up that made me rethink my whole approach. The recursion depth angle was something I hadn't prepped for specifically.

Questions Asked (2)

Given an m x n integer matrix, find the length of the longest path of strictly increasing values where movement is restricted to up, down, left, and right. Design an efficient algorithm and walk through its time and space complexity.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I went straight to DFS with memoization, which is the right call, but I fumbled explaining why the memoization was valid here.

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AI HintsAI Generated

Suggested Approach

Use DFS with memoization to compute the longest increasing path starting from each cell, caching results to avoid redundant work. Then, iterate over all cells to find the maximum path length, ensuring O(m*n) time complexity.

Pro tip: Emphasize that the problem is a DAG and that memoization is key to efficiency; also mention that you can optimize space by using a 2D array for memoization and that recursion depth is bounded by m*n.

1. Clarify and Define

Restate the problem: find the longest strictly increasing path in a matrix with 4-directional movement. Confirm assumptions like no wrap-around and that paths can start anywhere.

2. Design the Algorithm

Use DFS with memoization: for each cell, recursively explore neighbors with larger values, caching the longest path length from that cell. Initialize memo array with 0.

3. Analyze Complexity

Time complexity is O(m*n) because each cell is visited once and its result cached. Space complexity is O(m*n) for memoization and recursion stack.

4. Walk Through an Example

Trace a small matrix (e.g., 3x3) to demonstrate how memoization avoids recomputation and correctly computes the longest path.

5. Discuss Trade-offs and Optimizations

Mention alternative approaches like topological sort (also O(m*n)) and compare; discuss iterative vs recursive DFS and potential stack overflow for large matrices.

Key Points to Mention

The problem can be modeled as a directed acyclic graph (DAG) where edges go from smaller to larger values.
Memoization ensures each cell's longest path is computed only once, achieving O(m*n) time.
Space complexity includes O(m*n) for memoization and O(m*n) worst-case recursion stack.
Strictly increasing condition means no cycles, so no need for visited set beyond memoization.
Edge cases: empty matrix, single row/column, all equal values (answer 1).
Potential optimization: use iterative topological sort to avoid recursion depth issues.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.

Follow-up: for very large matrices where deep recursion could cause a stack overflow, how would you redesign the solution to be iterative or otherwise avoid blowing the call stack?

Algorithms & Data StructuresSystem Design

Author's notes

This one tripped me up more than it should have.

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AI HintsAI Generated

Suggested Approach

Acknowledge the stack overflow risk and propose converting the recursive algorithm to an iterative one using an explicit stack or queue. Explain how the iterative version preserves the same logic while controlling memory usage, and discuss trade-offs like increased code complexity and potential performance differences.

Pro tip: Mention that you can also increase the recursion limit or use tail-call optimization if the language supports it, but emphasize that an explicit stack is more portable and predictable. This shows you consider practical constraints and language-specific features.

1. Identify the recursion pattern

Determine whether the recursion is depth-first (e.g., DFS) or breadth-first (e.g., BFS) and what data structure can replace the call stack.

2. Choose an explicit data structure

Select a stack for DFS-like traversal or a queue for BFS-like traversal to simulate the recursive calls iteratively.

3. Convert the algorithm

Rewrite the recursive function as a loop that pushes initial state onto the data structure and processes elements until it's empty, handling base cases and state updates.

4. Analyze complexity and trade-offs

Compare time and space complexity of iterative vs. recursive versions, noting that iterative may use more heap memory but avoids stack overflow.

5. Consider optimizations

Discuss further optimizations like tail recursion elimination, increasing stack size, or using an explicit stack with manual memory management if needed.

Key Points to Mention

Stack overflow occurs due to limited call stack size in deep recursion.
Explicit stack/queue simulates recursion and uses heap memory instead of call stack.
Iterative solutions often have similar time complexity but may have higher constant factors.
Trade-offs: code readability, memory usage, and potential for manual error.
Language-specific features: tail-call optimization, recursion depth limits, or generators.
For very large matrices, consider memory-efficient traversal like iterative deepening or in-place marking.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.