DSA topic · Stage 4

Matrix & Grid Traversal interview preparation

Treat cells and legal moves as an implicit graph while controlling bounds, revisits, and layer state.

DSA prep Practice 6 questions

Concept

Grid questions make traversal invariants visible through islands, fills, spreading processes, and path constraints.

Complexity lens

A full traversal is O(rows × columns) time with up to O(rows × columns) visited, queue, or stack state.

Common mistakes

Checking bounds after indexing
Marking visited too late
Assuming rectangular input without clarification

Recognition

Decide from constraints, not labels.

These clues narrow the model. They do not replace an invariant or complexity check.

Recognition clues

Cells are nodes with local movement rules
Components, spread time, boundary reachability, or paths matter
Row/column shape and mutation policy affect visited state

Implementation options

DFS flood fill
BFS for layers or minimum unweighted moves
Multi-source BFS when several origins spread simultaneously

Interview behavior

State direction set and boundary predicate
Clarify whether the grid may be mutated
Convert rows × columns into V and local neighbors into E when explaining complexity

Patterns that operate on this topic

DFSEach active frame owns one node and the unfinished neighbors or child results needed before that frame can resolve.BFSWhen a node is first dequeued, its recorded layer is the minimum number of unweighted edges from the source set.2D DPdp[i][j] has a fixed meaning at the intersection of two prefixes/coordinates, and iteration follows its dependency directions.Binary SearchThe answer remains inside the declared interval, and each update strictly shrinks that interval.Frequency MapThe table contains exactly the information from the processed prefix that a future element may need.

Representative problems

6 current Matrix & Grid Traversal questions.

Exact active distribution: 1 easy, 4 medium, 1 hard. External records contain metadata and original guidance only.

External catalogUnverified
Number of Islands
Treat a grid as an implicit graph and mark each cell once.
Graphs Arrays Matrix & Grid Traversal DFS BFS
MediumFree / publicSolve problem
External catalogUnverified
Longest Increasing Path in a Matrix
Memoize an acyclic increasing traversal from each cell.
Graphs Dynamic Programming Arrays Matrix & Grid Traversal DFS 2D DP
HardFree / publicSolve problem
External catalogUnverified
Search a 2D Matrix
Tests mapping a conceptual sorted sequence onto two dimensions.
Binary Search Matrix & Grid Traversal Binary Search
MediumFree / publicSolve problem
External catalogUnverified
Flood Fill
Introduces a grid as an implicit graph with explicit visited-state choices.
Graphs Matrix & Grid Traversal Frequency Map
EasyFree / publicSolve problem
External catalogUnverified
Max Area of Island
Adds a returned aggregate to ordinary component traversal.
Graphs Matrix & Grid Traversal Frequency Map
MediumFree / publicSolve problem
External catalogUnverified
Rotting Oranges
Teaches layer-by-layer shortest transitions from several starting points.
Graphs Matrix & Grid Traversal Stacks & Queues BFS
MediumFree / publicSolve problem

Review state

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Question pages let you record local completion. Account status, confidence, notes, and a topic roll-up are shown only when private account persistence is available.

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Review prompts

Were ragged or empty grids possible?
Was visited marked before enqueue?
Did diagonal movement accidentally enter the model?

Prerequisites and next step

Recursion & Search

Explore decision trees systematically and prune invalid partial work.

Open the roadmap

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