The Largest Submatrix With Rearrangements coding problem asks you to find the area of the largest submatrix consisting entirely of 1s in a given binary grid. The unique constraint is that you are allowed to rearrange the columns of the matrix in any order you want. This flexibility means that 1s that were originally in different columns can be brought together to form a wide, contiguous block of 1s.
This problem is frequently seen in Samsung and Google interviews because it requires a combination of grid processing and greedy optimization. It tests whether a candidate can simplify a seemingly complex "rearrangement" problem into a row-by-row sorting task. It evaluates your ability to use precomputation (calculating heights of 1s) and sorting to achieve an efficient solution.
This problem utilizes the Matrix and Sorting interview pattern. First, transform the matrix so that each cell (r, c) contains the number of consecutive 1s ending at that cell from above (the "height"). Then, for each row, treat these heights as bar heights in a histogram. Since you can rearrange columns, you simply sort the heights in the current row in descending order. The area of a potential submatrix ending at this row with width k is then height[k-1] * k.
Binary Matrix: [[1, 0, 1], [1, 1, 0], [1, 1, 1]]
A common error is trying to use the "Largest Rectangle in Histogram" algorithm without sorting. Because columns can be rearranged, the bars don't need to stay in their original relative positions; sorting is the key greedy step. Another mistake is failing to correctly update the heights row-by-row, which can lead to O(N²) calculation for each cell.
In "Matrix, Sorting, Greedy interview pattern" problems, always look for ways to process the data row-by-row or column-by-column. If the problem allows "rearrangement," it almost always implies that sorting or a priority queue will be involved in the optimal solution.
