Array, Grid, And Prefix/Suffix Reasoning

What's being tested

These problems check grid traversal with correct neighbor indexing and boundary handling, plus prefix/suffix reasoning to combine left/right or above/below summaries efficiently. Interviewers probe whether you convert a local condition into a global O(m*n) or O(n) plan and handle edge cases cleanly.

Patterns & templates

• Neighbor iteration for grids — iterate dx/dy = {(0,1),(0,-1),(1,0),(-1,0)} and check 0<=r<m, 0<=c<n; overall O(m*n) time.

• Sentinel padding (add one-cell border) to simplify boundary logic and avoid repeated index checks when comparing neighbors.

• Prefix / suffix arrays: precompute prefix_max/prefix_min and suffix_max/suffix_min to evaluate removing any contiguous block in O(1) per candidate.

• Sliding window / two-pointer for contiguous subarray constraints — maintain window invariants and update aggregates in amortized O(1) per move.

• Prefix sums for range sums and constant-time queries: build pref[i] = sum(a[0..i-1]) so range sum is pref[r]-pref[l].

• Deques / monotonic queue for maintaining running min/max over windows in O(n) time when removal affects order.

• Space-time tradeoffs: O(n) auxiliary arrays are acceptable up to millions; beyond memory limits, stream and compress summaries.

Common pitfalls

Pitfall: Off-by-one errors when computing suffix indices — always define whether prefix/suffix is inclusive/exclusive and test on length-1 arrays.

Pitfall: Forgetting to recompute global min/max after removing a block — combine prefix and suffix extremes, don't just use local neighbors.