Top 10 Multi-dimensional array problems for FAANG interview

Multi-dimensional arrays (2D arrays / matrices) are extremely common in FAANG interviews, often combined with matrix traversal, dynamic programming, or simulation. Here's a curated list of top 10 multi-dimensional array problems:

Top 10 Multi-Dimensional Array Problems for FAANG

1. Number of Islands

• Problem: Count the number of islands in a 2D grid of '1's (land) and '0's (water).
• Concept: DFS/BFS on matrix cells, mark visited.

2. Max Area of Island

• Problem: Find the size of the largest island in a grid.
• Concept: DFS/BFS to explore connected components, track max area.

3. Rotate Image (Matrix)

• Problem: Rotate an n x n matrix 90° clockwise in place.
• Concept: Transpose + reverse rows (or reverse columns + transpose).

4. Spiral Matrix / Spiral Order

• Problem: Return elements of a matrix in spiral order.
• Concept: Use four pointers (top, bottom, left, right) to traverse layers.

5. Set Matrix Zeroes

• Problem: If an element is 0, set its entire row and column to 0.
• Concept: Use flags or mark first row/column, then update matrix in place.

6. Word Search

• Problem: Check if a word exists in a grid, moving horizontally or vertically (or diagonally in variants).
• Concept: Backtracking DFS from every cell.

7. Search in 2D Matrix

• Problem: Matrix sorted row-wise and/or column-wise, search for target efficiently.
• Concept: Binary search or start from top-right/bottom-left for O(m + n) solution.

8. Minimum Path Sum

• Problem: Find a path from top-left to bottom-right with minimum sum in a grid.
• Concept: Dynamic Programming (DP) with dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j].

9. Rotate or Flip Submatrices

• Problem: Rotate or flip portions of a matrix, sometimes in-place.
• Concept: Layered iteration for submatrices, often used in image processing questions.

10. Maximal Rectangle / Largest Square in Matrix

• Problem: Find the largest rectangle/square of 1s in a 2D binary matrix.
• Concept: Treat each row as histogram → use stack-based largest rectangle in histogram algorithm.

⚡ Tips for Multi-Dimensional Array Problems

1. Always track boundaries (row and column limits).
2. Visited tracking is essential in DFS/BFS for islands, word search, etc.
3. For in-place modifications, be careful with overwriting data (sometimes mark with a sentinel value).
4. Recognize patterns that reduce 2D to 1D (like histogram for maximal rectangle).
5. Practice both iterative and recursive approaches, especially backtracking for word search or paths.