Minimum Falling Path Sum

/*
 * Problem : Smallest falling path.
 * Input   : r, c and the rows.
 * Output  : The smallest sum.
 * Approach: Row by row table
 * Time    : O(r c)
 * Space   : O(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) {
        int cols = m[0].length;
        // Step 1: best[j] is the smallest sum of a path that ends at column j of the current row. The first row starts the paths.
        long[] best = new long[cols];
        for (int j = 0; j < cols; j++) {
            best[j] = m[0][j];
        }
        for (int i = 1; i < m.length; i++) {
            long[] next = new long[cols];
            for (int j = 0; j < cols; j++) {
                // Step 2: A path comes from the left, above or right cell of the row above. Take the smallest.
                long from = best[j];
                if (j > 0) {
                    from = Math.min(from, best[j - 1]);
                }
                if (j < cols - 1) {
                    from = Math.min(from, best[j + 1]);
                }
                next[j] = from + m[i][j];
            }
            best = next;
        }
        // Step 3: The path can end in any column of the last row.
        long answer = best[0];
        for (long value : best) {
            answer = Math.min(answer, value);
        }
        return answer;
    }

    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));
    }
}