Largest All One Square in Java

// Largest All One Square in Java
//
// PURPOSE
// Each all-one square ending at a cell extends the smallest neighboring square from above,
// left, and upper-left.
//
// METHOD
// Use a single padded row and retain the previous diagonal. A zero cell resets its entry; a
// one cell adds one to the minimum of three neighbors.
//
// COMPLEXITY
// O(rows * cols) time, O(cols) auxiliary space.
//
// CONTRACT
// Flattened 0/1 matrix; rows,cols>=0. Returns SIDE LENGTH, not area.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 2.
// Run: javac AlgorithmExample.java && java AlgorithmExample
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class AlgorithmExample {
    static void alg_require(boolean valid) { if (!valid) throw new IllegalArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int largest_square(int[] grid, int rows, int cols) {
        java.util.Objects.requireNonNull(grid, "grid");
        alg_require((grid.length == Math.multiplyExact(rows, cols)));
        alg_require(((rows >= 0) && (cols >= 0) && (rows <= 1000000) && (cols <= 1000000)));
        int[] dp = new int[alg_size(Math.addExact(cols, 1))];
        int r = 0;
        int c = 0;
        int diagonal = 0;
        int old = 0;
        int best = 0;
        while ((r < rows)) {
            diagonal = 0;
            c = 1;
            while ((c <= cols)) {
                old = dp[c];
                if ((grid[Math.subtractExact(Math.addExact(Math.multiplyExact(r, cols), c), 1)] == 1)) {
                    dp[c] = Math.addExact(1, Math.min(dp[c], Math.min(dp[Math.subtractExact(c, 1)], diagonal)));
                    best = Math.max(best, dp[c]);
                } else {
                    dp[c] = 0;
                }
                diagonal = old;
                c = Math.addExact(c, 1);
            }
            r = Math.addExact(r, 1);
        }
        return best;
    }

    public static void main(String[] args) {
        int[] grid = new int[] {1, 1, 0, 1, 1, 1, 0, 1, 1};
        int rows = 3;
        int cols = 3;
        int result = largest_square(grid, rows, cols);
        System.out.println(result);
    }
}