Find the Minimum Area to Cover All Ones I - Video Solutions

Problem Overview: You are given a binary grid and need the smallest axis-aligned rectangle that covers every cell containing 1. The rectangle must include all rows and columns where a 1 appears, and the result is the area of that rectangle.

Approach 1: Brute Force Rectangle Search (O(m³ * n³) time, O(1) space)

The brute force idea checks every possible rectangle in the grid and verifies whether it covers all the 1 cells. You iterate over all pairs of top/bottom rows and left/right columns, then scan the rectangle to confirm whether every 1 lies inside it. This method uses nested loops over the grid dimensions and repeated validation scans. It works but quickly becomes impractical as the grid grows. This approach mainly demonstrates the baseline reasoning before optimizing with better observations about the distribution of 1s in the matrix.

Approach 2: Coordinate Compression / Bounding Box (O(m * n) time, O(1) space)

The key observation: the smallest rectangle covering all 1s is defined by the extreme coordinates where 1 appears. While scanning the grid once, track four values: minRow, maxRow, minCol, and maxCol. Each time you encounter a 1, update these boundaries. After the scan, the rectangle height is maxRow - minRow + 1 and the width is maxCol - minCol + 1. Multiplying them gives the minimum area. The idea resembles coordinate compression because you reduce the relevant search space to the coordinates containing 1. This single pass solution leverages simple iteration over the array-based grid and avoids storing extra structures.

Recommended for interviews: Interviewers expect the bounding box scan. It shows you can translate a spatial constraint into tracked boundaries while iterating through a grid. Mentioning the brute force rectangle enumeration shows you understand the naive search space, but recognizing that only the extreme coordinates matter demonstrates stronger algorithmic thinking.