Clarify the problem first: define the grid (obstacles, movement directions) and what 'reachability' means (e.g., from a start to all cells, or between all pairs). Then choose a DP formulation that builds reachability incrementally, such as propagating reachable states row by row or using BFS/DFS with memoization, and analyze time/space complexity.
Pro tip: Explicitly state your assumptions about movement (4-directional vs 8-directional) and obstacles, and mention that for all-pairs reachability, Floyd-Warshall on the grid graph or repeated BFS may be more appropriate than a simple DP. This shows you understand the problem's nuances and can adapt your approach.
Ask about grid size, obstacles, allowed moves (4 or 8 directions), and whether reachability is from a single source or between all pairs. Confirm if the grid is static or dynamic.
Decide on a state that captures reachability, e.g., dp[i][j] = true if cell (i,j) is reachable from the start. For all-pairs, consider dp[i][j][k][l] or a transitive closure approach.
Set base cases (e.g., start cell is reachable). Define transitions based on allowed moves and obstacles, ensuring you handle boundaries and blocked cells.
Determine if the DP can be computed in a single pass (e.g., row-major for right/down moves) or requires iterative relaxation (e.g., Bellman-Ford style) for arbitrary directions. Consider using BFS/DFS with memoization if cycles exist.
State time and space complexity. For large grids, discuss optimizations like using bitsets, rolling arrays, or early termination. Mention trade-offs between DP and graph search.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The interviewer opened by calling it easy, which immediately made me tense up more than any hard problem would.
First, present a clear brute-force solution for matrix traversal, then systematically optimize it by analyzing memory access patterns, cache behavior, and instruction-level parallelism. Focus on micro-optimizations like loop ordering, blocking, and reducing branch mispredictions, while explaining the trade-offs.
Pro tip: Demonstrate awareness that asymptotic complexity is not the only factor in performance; mention specific hardware details like cache line size and prefetching to show depth. Also, be prepared to discuss how you would measure and validate improvements using profiling tools.
Ask questions to understand the matrix dimensions, traversal order, memory layout, and performance goals. Confirm whether the matrix is stored in row-major or column-major order.
Write a straightforward nested loop traversal, analyze its time and space complexity, and identify potential inefficiencies.
Discuss cache locality, loop interchange, blocking, and vectorization. Explain how each can improve performance without changing asymptotic complexity.
Show code for optimized traversal (e.g., loop reordering for row-major access) and reason about expected speedup. Mention profiling to validate.
Address when micro-optimizations are worth it, potential downsides like code complexity, and how to decide based on profiling data.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.