Largest Rectangular Sub-matrix whose Sum is 0

In this video, we explore the problem of finding the area of the largest submatrix in a 2D matrix where the sum is equal to zero. The task is to identify the submatrix with the largest area where the sum of its elements is zero. The naive approach iterates through all possible submatrices using four nested loops and calculates their sums to check if it’s equal to zero. However, this method is inefficient for larger matrices, so we explore an optimized solution using prefix sums.

The optimized approach uses prefix sums and dynamic programming to reduce the time complexity to O(n^3). We iterate over pairs of rows and compute the column-wise cumulative sum in a temporary array. The length of the longest subarray with a zero sum in this temporary array helps us find the width of the largest 0-sum submatrix. The area of this submatrix is updated and maximized as we proceed through the matrix. This approach significantly improves the performance compared to the naive method.

For more details, please go through - Largest Submatrix With Sum 0