最长公共子序列问题

题目描述：

给出两个字符串A B，求A与B的最长公共子序列（子序列不要求是连续的）。
比如两个串为：

abcicba
abdkscab

ab是两个串的子序列，abc也是，abca也是，其中abca是这两个字符串最长的子序列。

输入

第1行：字符串A
第2行：字符串B
(A,B的长度 <= 1000)

输出

输出最长的子序列，如果有多个，随意输出1个。

输入示例


abcicba
abdkscab


输出示例

abca

import java.util.Scanner;

public class LCS {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        char[] a = scanner.next().toCharArray();
        char[] b = scanner.next().toCharArray();
        int n1 = a.length;
        int n2 = b.length;
        if (n1 == 0 || n2 == 0) {
            System.out.println(0);
            return ;
        }
        int n = Math.max(n1, n2);
        int[][] arr = new int[n + 1][n + 1];
        int[][] bb = new int[n+1][n+1];
        StringBuilder stringBuilder = new StringBuilder();
        for (int i = 0; i <= n1; i++)
            arr[i][0] = 0;
        for (int i = 0; i <= n2; i++)
            arr[0][i] = 0;
        for (int i = 1; i <= n1; i++) {
            for (int j = 1; j <= n2; j++) {
                if (a[i - 1] == b[j - 1]) {
                    arr[i][j] = arr[i - 1][j - 1] + 1;
                    bb[i][j] = 0;
                }
                else if (arr[i-1][j] >= arr[i][j-1]){
                    arr[i][j] = arr[i-1][j];
                    bb[i][j] = 1;
                } else {
                    arr[i][j] = arr[i][j - 1];
                    bb[i][j] = 2;
                }
            }
        }
        lcs(bb, a, n1, n2, stringBuilder);
        System.out.println(stringBuilder.toString());
    }

    public static void lcs(int[][] b, char[] a, int i, int j, StringBuilder stringBuilder) {
        if (i == 0 || j == 0)
            return ;
        if (b[i][j] == 0) {
            lcs(b, a, i - 1, j - 1, stringBuilder);
            stringBuilder.append(a[i-1]);
        } else if (b[i][j] == 1) {
            lcs(b, a, i-1, j, stringBuilder);
        } else
            lcs(b, a, i, j-1, stringBuilder);
    }
}