蓝桥日记②2018第九届省赛（软件类）JavaA组★答案解析

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【蓝桥日记②】2018第九届省赛（软件类）JavaA组🏅答案解析

文章目录

- 【蓝桥日记②】2018第九届省赛（软件类）JavaA组🏅答案解析

题目链接：第九届蓝桥杯大赛个人赛省赛（软件类）Java大学A组

官网题库中搜索相应题目

1、分数

考点：等比数列求和

等差数列求和公式
$S_n = \\fracn(a_1+a_n)2=na_1+\\fracn(n-1)d2,n ∈ N^*$
等比数列求和公式
$a_n=a_1q^n-1 \\\\ S_n=\\frac1-q^n1-q, q\\neq1$

方法一：Java大整数运算

package nineSession;
import java.math.BigInteger;

/*** 2017第九届  1、分数 ***/
public class test1 
    public static void main(String[] args) 
        // 等比数列通项和 S = a1(1 - q^n) / (1 - q)
        // 将a1 = 1, q = 1 / 2, n = 20 代入化解
        BigInteger e = BigInteger.TWO;  // BigInteger.valueOf(2)
        BigInteger a = e.pow(20).subtract(BigInteger.ONE);
        BigInteger b = e.pow(19);
        BigInteger g = a.gcd(b);
        a.divide(g);
        b.divide(g);
        System.out.println(a + "/" + b);

方法二：位运算

package nineSession;

/*** 2017第九届  1、分数 ***/
public class test1_3 
    private static long gcd(long a, long b) 
        return b == 0 ? a : gcd(b, a % b);
    

    public static void main(String[] args) 
        long a = (1 << 20) - 1;
        long b = (1 << 19);
        long g = gcd(a, b);
        System.out.println(a / g + "/" + b / g);

方法三：快速幂+最大公约数

package nineSession;

/*** 2017第九届  1、分数 ***/
public class test1_2 
    private static long gcd(long a, long b) 
        return b == 0 ? a : gcd(b, a % b);
    

    private static long fastPow(long e, int q) 
        long res = 1;
        while (q > 0) 
            if ((q & 1) == 1) res = res * e;
            e = e * e;
            q >>= 1;
        
        return res;
    

    public static void main(String[] args) 
        long a = fastPow(2, 20) - 1;
        long b = fastPow(2, 19);
        long g = gcd(a, b);
        a /= g;
        b /= g;
        System.out.println(a + "/" + b);

答案：1048575/524288

2、星期一

package nineSession;

/*** 2017第九届  2、星期一 ***/
public class test2 
    private static boolean isLeap(int y) 
        return y % 400 == 0 || (y % 4 == 0 && y % 100 != 0);
    

    public static void main(String[] args) 
        int t = -6; // 2000-12-31 为星期日
        for (int i = 1901; i <= 2000; i++) 
            t += isLeap(i) ? 366 : 365;
        
        int res = 0;
        for (int i = t; i > 0; i -= 7) res += 1;
        System.out.println(res);

答案：5217

3、复数幂

考点：BigInteger

package nineSession;

import java.math.BigInteger;

/*** 2017第九届  3、复数幂 ***/
public class test3 
    public static void main(String[] args) 
        // (a + bi)(x + yi) = ax - by + (ay + bx)i
        BigInteger a = BigInteger.valueOf(2);
        BigInteger b = BigInteger.valueOf(3);
        BigInteger x = BigInteger.valueOf(2);
        BigInteger y = BigInteger.valueOf(3);
        for (int i = 1; i < 123456; i++) 
            BigInteger a1 = a.multiply(x).subtract(b.multiply(y));
            BigInteger b1 = a.multiply(y).add(b.multiply(x));
            a = a1;
            b = b1;
        
        String sign = b.compareTo(BigInteger.ZERO) > 0 ? "+" : "";
        System.out.println(a + sign + b + "i");

答案：太长了~

4、方格计数

考点：计算点到圆心距离是否小于半径

package nineSession;

/*** 2017第九届  4、方格计数 ***/
public class test4 
    public static void main(String[] args) 
        long res = 0, range = 50000 * 50000L;
        for (int i = 1; i < 50000; i++) 
            for (int j = 1; j < 50000; j++) 
                if ((long)i * i + (long)j * j <= range) res += 4;
            
        
        System.out.println(res);

答案：7853781044

5、打印图形

考点：递归

package nineSession;

/*** 2017第九届  5、打印图形 ***/
public class test5 
    static void show(byte[][] buf) 
        for (int i = 0; i < buf.length; i++) 
            for (int j = 0; j < buf[i].length; j++) 
                System.out.print(buf[i][j] == 0 ? ' ' : 'o');
            
            System.out.println();
        
    

    static void draw(byte[][] buf, int x, int y, int size) 
        if (size == 1) 
            buf[y][x] = 1;
            return;
        
        int n = size / 3;
        draw(buf, x, y, n);
        draw(buf, x - n, y, n);
        draw(buf, x + n, y, n);
        draw(buf, x, y - n, n);
        draw(buf, x, y + n, n);
    

    public static void main(String[] args) 
        final int N = 3;
        int t = 1;
        for (int i = 0; i < N; i++) t *= 3;

        byte[][] buf = new byte[t][t];
        draw(buf, t / 2, t / 2, t);
        show(buf);

答案：size / 3

6、航班时间

考点：时间函数+字符串处理

package nineSession;
import java.text.ParseException;
import java.text.SimpleDateFormat;
import java.util.Date;
import java.util.Scanner;

/*** 2017第九届  6.航班时间 ***/
public class test6 
    public static void main(String[] args) throws ParseException 
        Scanner sc = new Scanner(System.in);
        int T = sc.nextInt();
        sc.nextLine();
        String[] lines = new String[T * 2];
        for (int i = 0; i < T * 2; i++) 
            lines[i] = sc.nextLine();
        
        sc.close();

        for (int i = 0; i < T; i++) 
            long time1 = getTime(lines[i * 2]);
            long time2 = getTime(lines[i * 2 + 1]);
            long t = (time1 + time2) / 2;
            System.out.printf("%02d:%02d:%02d\\n", t / 3600, t / 60 % 60, t % 60);
        
    

    private static long getTime(String line) throws ParseException 
        String[] split = line.split(" ");
        SimpleDateFormat format = new SimpleDateFormat("HH:mm:ss");
        Date t1 = format.parse(split[0]);
        Date t2 = format.parse(split[1]);
        long d = 0l;
        if (split.length == 3) 
            d = (long)(split[2].charAt(2) - '0');
        
        return d * 24 * 3600 + t2.getTime() / 1000 - t1.getTime() / 1000;

7、三体攻击

方法一：暴力模拟（超时 3/4）

package nineSession;
import java.util.Scanner;

/*** 2017第九届  7.三体攻击 ***/
public class test7 
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