Largest Equal Squares with No Shared Cells

# Largest Equal Squares with No Shared Cells You are given an `m`-by-`n` binary matrix `mat`. A cell is usable when it contains `1` and unusable when it contains `0`. Choose two square submatrices with the same positive integer side length `k`. Every cell of both squares must be usable, and the squares must not share any cell. Return the largest possible area of each square, `k * k`. If no pair exists, return `0`. ### Function `int maxArea(vector<vector<int>>& mat)` ### Example 1 **Input:** `mat = [[1, 1, 0, 1, 1], [1, 1, 0, 1, 1]]` **Output:** `4` **Explanation:** Choose the square with top-left corner `(0, 0)`, covering rows `0..1` and columns `0..1`, and the square with top-left corner `(0, 3)`, covering rows `0..1` and columns `3..4`. Both are all-ones squares of side `2`, and their cell sets are disjoint. A larger side length cannot fit in the two-row matrix. ### Example 2 **Input:** `mat = [[1, 1], [1, 1]]` **Output:** `1` **Explanation:** There is only one side-`2` square, so two such squares cannot be chosen. Two different usable cells form two disjoint side-`1` squares, each of area `1`. ### Constraints - `mat.length == m`, and each row has length `n`. - `1 <= m, n <= 500` - Every matrix entry is either `0` or `1`. ### Clarifications - Squares are aligned with the matrix rows and columns. A square starting at `(r, c)` covers rows `r..r + k - 1` and columns `c..c + k - 1`, inclusively. - Touching along a boundary or at a corner is allowed if no matrix cell belongs to both squares. - The two squares must have equal side length; return one square's area, not their combined area. - You must choose two squares. One usable cell alone is insufficient. ### What a Strong Answer Covers - Verifying that every covered cell is usable. - Enforcing equal side lengths and cell-disjointness, including boundary-touching cases. - Maximizing the per-square area and handling matrices with fewer than two usable cells.