Largest Square of Ones

/*
 * Problem : Biggest square of ones.
 * Input   : r and c, then the grid.
 * Output  : Side length.
 * Approach: Dynamic programming.
 * Time    : O(r * c)
 * Space   : O(r * c)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    // This method solves the task. It receives the input and returns the answer.
    static long solve(int[][] m) {
        // Step 1: side[i][j] is the side of the biggest square of ones that has its bottom-right corner at (i, j).
        int rows = m.length;
        int columns = m[0].length;
        int[][] side = new int[rows][columns];
        int best = 0;
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < columns; j++) {
                if (m[i][j] == 0) {
                    continue;
                }
                // Step 2: On the border the square has side 1. Inside, it is 1 plus the smallest of the up, left and up-left squares.
                if (i == 0 || j == 0) {
                    side[i][j] = 1;
                } else {
                    side[i][j] = 1 + Math.min(side[i - 1][j - 1], Math.min(side[i - 1][j], side[i][j - 1]));
                }
                best = Math.max(best, side[i][j]);
            }
        }
        return best;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int rows = scanner.nextInt();
        int cols = scanner.nextInt();
        int[][] m = new int[rows][cols];
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                m[i][j] = scanner.nextInt();
            }
        }
        System.out.println(solve(m));
    }
}