思路：

        1、取出年月日  
        2、判断月份是否合法
        3、判断日期是否合法 

import java.util.Scanner;

public class Demo1 {

	public static void main(String[] args) {
		Scanner sca = new Scanner(System.in);
		System.out.println("请输入日期字符串：");
		String date = sca.next();
		//分别取出年月日
		int year = Integer.parseInt("" + date.charAt(0) + date.charAt(1) + date.charAt(2) + date.charAt(3));
		int month = Integer.parseInt("" + date.charAt(5) + date.charAt(6));
		int day = Integer.parseInt("" + date.charAt(8) + date.charAt(9));
		boolean flag = true;
		if(month < 1 || month > 12) {
			flag = false;
			}else{
				if(month == 1 || month == 3 || month == 5 || month == 7 || month == 8 || month == 10 || month == 12) {
				if(day >= 1 && day <= 31) {
					flag = true;
				}else{
					flag = false;
				}
			}else if(month == 4 || month == 6 || month == 9 || month == 11) {
				if(day >= 1 && day <= 30) {
					flag = true;
				}else{
					flag = false;
				}
			}else{
				if(year % 400 == 0 || year % 4 == 0 && year % 100 != 0) {
					if(day >= 1 && day <= 29) {
						flag = true;
					}else{
						flag = false;
					}
				}else{
					if(day >= 1 && day <= 28) {
						flag = true;
					}else{
						flag = false;
					}
				}
			}
		}
		if(flag) {
			System.out.println("合法日期");
		}else{
			System.out.println("非法日期");
		}
	}
}