Longest Common Subsequence

/*
 * Problem : Find the LCS length.
 * Input   : Two words.
 * Output  : The length.
 * Approach: Fill a 2D table.
 * Time    : O(m * n)
 * Space   : O(m * n)
 * 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 int solve(String a, String b) {
        // Step 1: table[i][j] = the LCS length of the first i letters of a and the first j letters of b.
        int[][] table = new int[a.length() + 1][b.length() + 1];

        for (int i = 1; i <= a.length(); i++) {
            for (int j = 1; j <= b.length(); j++) {
                if (a.charAt(i - 1) == b.charAt(j - 1)) {
                    // Step 2: Equal letters extend the best answer of the shorter words by 1.
                    table[i][j] = table[i - 1][j - 1] + 1;
                } else {
                    // Step 3: Otherwise skip one letter from a or one letter from b, and keep the better result.
                    table[i][j] = Math.max(table[i - 1][j], table[i][j - 1]);
                }
            }
        }

        // Step 4: The last cell has the answer for the full words.
        return table[a.length()][b.length()];
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String a = scanner.next();
        String b = scanner.next();
        System.out.println(solve(a, b));
    }
}