Is Find the Minimum Area to Cover All Ones II easy or hard?

Find the Minimum Area to Cover All Ones II is classified as a Hard problem. The difficulty comes from reasoning about how three rectangles can partition the grid and ensuring every possible configuration is evaluated efficiently.

Find the Minimum Area to Cover All Ones II Python/Java solution

Python, Java, C++, and JavaScript solutions typically iterate over possible horizontal and vertical cuts of the grid. For each partition configuration, the algorithm calculates the bounding rectangle of 1s inside each section and sums their areas to track the minimum total.

How to solve Find the Minimum Area to Cover All Ones II in O(n)?

A true O(n) solution is not typical because the algorithm must examine multiple ways to split the grid into three rectangles. Efficient implementations instead use structured enumeration with precomputed bounding boxes, leading to roughly O(m^2 * n^2) complexity while still remaining fast for the problem constraints.

What is the best approach for Find the Minimum Area to Cover All Ones II?

The most practical solution enumerates horizontal and vertical partitions that divide the grid into three rectangles, then computes the bounding box of 1s inside each region. With prefix or cached computations, the solution runs around O(m^2 * n^2). This approach balances clarity and efficiency and is commonly used in competitive programming solutions.

Is Find the Minimum Area to Cover All Ones II asked at Google/Amazon/Meta?

Problems involving grid partitioning, rectangle covering, and bounding box optimization appear frequently in interviews at large tech companies such as Google, Amazon, and Meta. Variants of this question test matrix reasoning, enumeration strategies, and optimization across multiple regions.

What data structure is used in Find the Minimum Area to Cover All Ones II?

The main data structure is a 2D grid or matrix representing the binary values. Efficient solutions often add prefix arrays or cached bounding box calculations to quickly determine the smallest rectangle covering all 1s in a submatrix.

What is the time complexity of Find the Minimum Area to Cover All Ones II?

Most accepted solutions run in about O(m^2 * n^2) time by enumerating grid partitions and computing the minimal bounding rectangle for each region. Space complexity is usually O(1) to O(m*n) depending on whether prefix information or memoization tables are used.

3197. Find the Minimum Area to Cover All Ones II - Practice Online

You are given a 2D binary array grid. You need to find 3 non-overlapping rectangles having non-zero areas with horizontal and vertical sides such that all the 1's in grid lie inside these rectangles.

Return the minimum possible sum of the area of these rectangles.

Note that the rectangles are allowed to touch.

Example 1:

Input: grid = [[1,0,1],[1,1,1]]

Output: 5

Explanation:

The 1's at (0, 0) and (1, 0) are covered by a rectangle of area 2.
The 1's at (0, 2) and (1, 2) are covered by a rectangle of area 2.
The 1 at (1, 1) is covered by a rectangle of area 1.

Example 2:

Input: grid = [[1,0,1,0],[0,1,0,1]]

Output: 5

Explanation:

The 1's at (0, 0) and (0, 2) are covered by a rectangle of area 3.
The 1 at (1, 1) is covered by a rectangle of area 1.
The 1 at (1, 3) is covered by a rectangle of area 1.

Constraints:

1 <= grid.length, grid[i].length <= 30
grid[i][j] is either 0 or 1.
The input is generated such that there are at least three 1's in grid.