Find the Minimum Area to Cover All Ones I

Find the Minimum Area to Cover All Ones I

What is this problem about?

The Find the Minimum Area to Cover All Ones I coding problem presents a 2D binary grid where 1s represent points of interest. Your task is to find the smallest possible axis-aligned rectangle that contains all the 1s in the grid. The area of this rectangle is defined as $(maxRow - minRow + 1) imes (maxCol - minCol + 1)$.

Why is this asked in interviews?

Companies like Microsoft and Amazon ask this question to test your ability to perform efficient grid traversals and identify spatial boundaries. It evaluation whether you can find the minimum and maximum coordinates of a set of points in $O(N imes M)$ time. It’s a foundational Matrix interview pattern that mirrors tasks like cropping an image or finding the bounding box of a detected object in computer vision.

Algorithmic pattern used

This problem uses Coordinate Boundary Tracking.

1. Initialize minR, minC to infinity and maxR, maxC to -1.
2. Iterate through every cell $(r, c)$ in the grid.
3. If grid[r][c] == 1:
   • Update minR = min(minR, r)
   • Update maxR = max(maxR, r)
   • Update minC = min(minC, c)
   • Update maxC = max(maxC, c)
4. Calculate and return the area using the updated bounds.

Example explanation

Grid:

0 0 0
0 1 1
0 1 0

1. Points at (1,1), (1,2), (2,1).
2. minR = 1, maxR = 2. Height = $2-1+1 = 2$.
3. minC = 1, maxC = 2. Width = $2-1+1 = 2$. Area = $2 imes 2 = 4$.

Common mistakes candidates make

• Wrong Area Formula: Using (max - min) instead of (max - min + 1), which ignores the inclusive nature of the cells.
• Inefficient Search: Trying to use BFS or DFS when a simple nested loop scan is sufficient and more direct.
• Empty Grid: Not handling the case where there are no 1s in the grid (area should be 0).

Interview preparation tip

When finding a "Bounding Box," you only need the extreme indices. Don't worry about the connections between the points; just focus on the smallest/largest $X$ and $Y$ coordinates independently.