下面是两行代码片段，使用Java 1.8 Time API满足您的需求。

LocalDate localDate = LocalDate.of(Integer.valueOf(year),Integer.valueOf(month),Integer.valueOf(day));
String dayOfWeek = String.valueOf(localDate.getDayOfWeek());

import java.text.SimpleDateFormat;
import java.util.Scanner;

class DayFromDate {

    public static void main(String args[]) {

        System.out.println("Enter the date(dd/mm/yyyy):");
        Scanner scan = new Scanner(System.in);
        String Date = scan.nextLine();

        try {
            boolean dateValid = dateValidate(Date);

            if(dateValid == true) {
                SimpleDateFormat df = new SimpleDateFormat( "dd/MM/yy" );  
                java.util.Date date = df.parse( Date );   
                df.applyPattern( "EEE" );  
                String day= df.format( date ); 

                if(day.compareTo("Sat") == 0 || day.compareTo("Sun") == 0) {
                    System.out.println(day + ": Weekend");
                } else {
                    System.out.println(day + ": Weekday");
                }
            } else {
                System.out.println("Invalid Date!!!");
            }
        } catch(Exception e) {
            System.out.println("Invalid Date Formats!!!");
        }
     }

    static public boolean dateValidate(String d) {

        String dateArray[] = d.split("/");
        int day = Integer.parseInt(dateArray[0]);
        int month = Integer.parseInt(dateArray[1]);
        int year = Integer.parseInt(dateArray[2]);
        System.out.print(day + "\n" + month + "\n" + year + "\n");
        boolean leapYear = false;

        if((year % 4 == 0) && (year % 100 != 0) || (year % 400 == 0)) {
            leapYear = true;
        }

        if(year > 2099 || year < 1900)
            return false;

        if(month < 13) {
            if(month == 1 || month == 3 || month == 5 || month == 7 || month == 8 || month == 10 || month == 12) {
                if(day > 31)
                    return false;
            } else if(month == 4 || month == 6 || month == 9 || month == 11) {
                if(day > 30)
                    return false;
            } else if(leapYear == true && month == 2) {
                if(day > 29)
                    return false;
            } else if(leapYear == false && month == 2) {
                if(day > 28)
                    return false;
            }

            return true;    
        } else return false;
    }
}

通过使用java.util.scanner包给用户输入日期、月和年来查找星期几的程序:

import java.util.Scanner;

public class Calender {
    public static String getDay(String day, String month, String year) {

        int ym, yp, d, ay, a = 0;
        int by = 20;
        int[] y = new int[]{6, 4, 2, 0};
        int[] m = new int []{0, 3, 3, 6, 1, 4, 6, 2, 5, 0, 3, 5};

        String[] wd = {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"};

        int gd = Integer.parseInt(day);
        int gm = Integer.parseInt(month);
        int gy = Integer.parseInt(year);

        ym = gy % 100;
        yp = ym / 4;
        ay = gy / 100;

        while (ay != by) {
            by = by + 1;
            a = a + 1;

            if(a == 4) {
                a = 0;
            }
        }

        if ((ym % 4 == 0) && (gm == 2)) {
            d = (gd + m[gm - 1] + ym + yp + y[a] - 1) % 7;
        } else
            d = (gd + m[gm - 1] + ym + yp + y[a]) % 7;

        return wd[d];
    }

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);

        String day = in.next();
        String month = in.next();
        String year = in.next();

        System.out.println(getDay(day, month, year));
    }
}

为今天找一个日期，然后从中找出一个星期。

    LocalDate d = java.time.LocalDate.now();
    System.out.println(java.time.LocalDate.now()); 
    
    Calendar c = Calendar.getInstance();
    int dayOfWeek = c.get(Calendar.DAY_OF_WEEK);
    System.out.println(dayOfWeek);

public class TryDateFormats {
    public static void main(String[] args) throws ParseException {
        String month = "08";
        String day = "05";
        String year = "2015";
        String inputDateStr = String.format("%s/%s/%s", day, month, year);
        Date inputDate = new SimpleDateFormat("dd/MM/yyyy").parse(inputDateStr);
        Calendar calendar = Calendar.getInstance();
        calendar.setTime(inputDate);
        String dayOfWeek = calendar.getDisplayName(Calendar.DAY_OF_WEEK, Calendar.LONG, Locale.US).toUpperCase();
        System.out.println(dayOfWeek);
    }
}

添加了另一种完全符合OP要求的方法，而不使用最新的内置方法:

public static String getDay(String inputDate) {
    String dayOfWeek = null;
    String[] days = new String[]{"Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"};

    try {
        SimpleDateFormat format1 = new SimpleDateFormat("dd/MM/yyyy");
        Date dt1 = format1.parse(inputDate);
        dayOfWeek = days[dt1.getDay() - 1];
    } catch(Exception e) {
        System.out.println(e);
    }

    return dayOfWeek;
}