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Treat the 2D grid as the data structure. In-place markers, layer-by-layer iteration, spiral traversal, transpose-then-reverse rotation, prefix sums, and staircase walks.

18 problems 4 Easy 8 Medium 6 Hard

2D grids as the primary data structure. Standard moves: 4-directional traversal, layer-by-layer iteration (spiral), transpose-then-reverse rotation, in-place marker mutation (first-row / first-col flag trick), and prefix sums for range queries. The grid itself often serves as the 'visited' set when in-place mutation is allowed.

Most graph algorithms (BFS, DFS, Dijkstra) port to grids directly — they're just dense implicit graphs.

When to reach for this pattern

  • Input is an m × n grid
  • Spiral traversal, rotation, reflection
  • Row / column zeroing or marking
  • Range-sum or range-update queries over a rectangle

Canonical template 

// 4-directional DFS template
int dr[4] = {1, -1, 0, 0}, dc[4] = {0, 0, 1, -1};
for (int k = 0; k < 4; ++k) {
    int nr = r + dr[k], nc = c + dc[k];
    if (nr < 0 || nr >= m || nc < 0 || nc >= n) continue;
    // process (nr, nc)
}

// rotate 90° clockwise: transpose then reverse rows
for (int i = 0; i < n; ++i)
    for (int j = i + 1; j < n; ++j)
        swap(M[i][j], M[j][i]);
for (auto& row : M) reverse(row.begin(), row.end());

C++ · adapt the names and types to your problem.

Common pitfalls

  • Forgetting bounds check before grid access — segfault or wrong result
  • Modifying the grid in-place during traversal without saving / restoring
  • Spiral boundaries: top / bottom / left / right need consistent inclusive/exclusive convention
  • Off-by-one on diagonal walks: top-right vs bottom-left vs (r + c == const) vs (r - c == const)

Related patterns

Graphs Backtracking Dynamic Programming

Problems (18)

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