数论模运算如何计算调整

Question

我不确定我的解决方案是否合理 (ans. 171) - Project Euler Q.19 因为我很难理解模块化算法并且不确定我的方法是否正确或不是...我在尝试获得将 0 作为键而不是 1 到星期一以在散列 table 中引用的等价性时遇到了麻烦。问题是；

1 Jan 1900 was a Monday.

Thirty days has September, April, June and November. All the rest have thirty-one, Saving February alone, which has twenty-eight, rain
or shine. And on leap years, twenty-nine.

A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.

How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?

所以我所做的是从 1 开始计算天数总和（参考散列 table 中的天数）并在找到星期天的总和后减去 1，因为按 0 计算总和会导致问题天数可被 3 和 6 整除（3：星期三，6:Sunday）。我怎么能通过使用 0 作为星期一的参考来做到这一点？

import java.util.*;

public class p19 {

    public static void main(String[] args) {

        Hashtable<Integer, String> days = new Hashtable<Integer, String>();
        days.put(1, "Monday");
        days.put(2, "Tuesday");
        days.put(3, "Wednesday");
        days.put(4, "Thursday");
        days.put(5, "Friday");
        days.put(6, "Saturday");
        days.put(7, "Sunday");

        Hashtable<Integer, String> months = new Hashtable<Integer, String>();
        months.put(1, "January");
        months.put(2, "February");
        months.put(3, "March");
        months.put(4, "April");
        months.put(5, "May");
        months.put(6, "June");
        months.put(7, "July");
        months.put(8, "August");
        months.put(9, "September");
        months.put(10, "October");
        months.put(11, "November");
        months.put(12, "December");

        int min, max;
        min = 1900;
        max = 2000;

        String[][] arr = new String[12 * (max - min + 1)][];

        // Total days starts at 1 to make modular arithmetic easier when accounting for days 
        // (i.e., 1 Monday, 2 Tuesday, etc.) and since the first day, hence, 0th day on 1 Jan 1900 is Monday.
        for (int year = min, index = 0, totalDays = 1; year <= max; year++) {

            for (int month = 1; month <= 12; month++, index++) {

                arr[index] = new String[numberOfDays(month,year)];

                int sum = 1;

                System.out.println(months.get(new Integer(month)) + " " + year);

                for (int day = 1; day <= numberOfDays(month, year); day++, totalDays++) {

                    if (totalDays % 7 == 0) {

                        arr[index][day - 1] = days.get(new Integer((totalDays % 7 + 7) % 365));                         
                    }
                    else {

                        arr[index][day - 1] = days.get(new Integer((totalDays % 7) % 365));                         
                    }

                    if (sum > 7) {

                        System.out.println();

                        sum = 1;
                    }

                    System.out.print(totalDays + ":= " + arr[index][day - 1] + ", " + day + " | ");

                    sum++;
                }

                System.out.println("\n");
            }
        }

        int count = 0;

        for (int i = 1; i < arr.length; i++) {

            if (arr[i][0] == "Sunday") {

                count++;
            }
        }
        // Subtract 1 from count since the total days were overstated by 1 before inititallizing array
        System.out.println("Number of Sundays that fell on the first of the month from: 1/Jan/1901 - 31/Dec/2000: " + (count - 1));
    }

    public static int numberOfDays (int month, int year) {

        int days = 0;

        switch (month) {
            case 7: 
            case 4: 
            case 6: 
            case 11:
                days = 30;
                break;
            case 2:
                if (isLeapYear(year)) {
                    days = 29;
                }
                else {
                    days = 28;
                }
                break;
            default: days = 31;
                break;   
        }

        return days;
    }

    public static boolean isLeapYear(int year) {

        return (year % 4 == 0 && year % 100 != 0) || (year % 400 == 0);
    }
}

Answer 1

您的 daysInMonth 检查不正确 - 结果一定是正确的：

switch (month) {
    case 4:
    case 6:
    case 9:
    case 11:
        days = 30;
        break;

程序的其余部分可以简化 - 请注意，起始年份也必须更正，dow 代表 DayOfWeek：

public static void main (String[] args) {

    int count = 0;
    // dow = 2, since 1.1.1901 was a Thuesday (2)
    for (int year = 1901, dow = 2; year <= 2000; ++year)
    {
        for (int month = 1; month <= 12; ++month)
        {
            if (dow == 0) {
                // System.out.println ("Date: " + year + "-" + month);
                ++count;
            }
            dow = (dow + numberOfDays (month, year)) % 7;
        }
    }
    System.out.println ("Number of Sundays that fell on the first of the month from: 1/Jan/1901 - 31/Dec/2000: " + count);
}

数论模运算如何计算调整

Number theory modular arithmetic how to account for adjustments

java

math

number-theory

modular-arithmetic