动态规划：最长公共子序列

来源：互联网发布：techsmith软件编辑：程序博客网时间：2024/06/06 07:22
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);        }    }}
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