动态规划：最长公共子序列

import java.util.Scanner;

//最长公共子序列
public class LCS {
    public static void main(String[] args) {
        Scanner scanner=new Scanner(System.in);
        char[] x;
        char[] y;
        String stringX=scanner.nextLine();
        x=stringX.toCharArray();
        String stringY=scanner.nextLine();
        y=stringY.toCharArray();
        //c[i][j]记录Xi和Yj的最长公共子序列长度
        int[][] c=new int[x.length+1][y.length+1];
        //b[i][j]记录c[i][j]的值是由哪个子问题解到的
        int[][] b=new int[x.length+1][y.length+1];
        LCSLength(x, y, x.length, y.length, b,c);
        System.out.println(c[x.length][y.length]);
        printLCS(x.length, y.length, x, b);
    }

    private static void LCSLength(char[] x,char[]y,int m,int n,int[][] b,int[][]c){
        int i,j;
        for (i = 1; i <= m; i++) {
            c[i][0]=0;
        }
        for (j = 1; j <= n; j++) {
            c[0][j]=0;
        }
        for (i = 1; i <= m; i++) {
            for (j = 1; j <= n; j++) {
                if (x[i-1]==y[j-1]) {
                    c[i][j]=1+c[i-1][j-1];b[i][j]=1;
                }
                else if (c[i-1][j]>=c[i][j-1]) {
                    c[i][j]=c[i-1][j];
                    b[i][j]=2;
                }
                else {
                    c[i][j]=c[i][j-1];
                    b[i][j]=3;
                }
            }
        }
    }

    //打印最长子序列
    private static void printLCS(int i,int j,char[] x,int[][] b){
        if (i==0||j==0) return;
        if (b[i][j]==1) {
            printLCS(i-1, j-1, x, b);
            System.out.print(x[i-1]);
        }
        else if (b[i][j]==2) {
            printLCS(i-1, j, x, b);
        }
        else {
            printLCS(i, j-1, x, b);
        }
    }
}