Project Euler Problem 19: Counting Sundays

Problem

You are given the following information, but you may prefer to do some research for yourself.

• 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)?

Solution

Given the first day of the year and whether it's a leap year, the number of Sundays can be found quickly through a lookup.

      private static final int[] LEAP_YEAR_DAY = new int[7];  
      private static final int[] NONE_LEAP_YEAR_DAY = new int[7];  
      private static final int[] DAYS_IN_MONTH = {31,28,31,30,31,30,31,31,30,31,30}; //Jan - Nov   
      public static void main(String[] args) {  
           pattern(1900, NONE_LEAP_YEAR_DAY);  
           pattern(2000, LEAP_YEAR_DAY);  
           int firstDayOfYear = 1;  
           int totalSundays = 0;  
           for (int year=1901; year<=2000; year++){  
                firstDayOfYear = firstDayOfYear(firstDayOfYear, year-1);  
                totalSundays += numberSundays(firstDayOfYear, year);  
           }  
           System.out.print(totalSundays);  
      }  
      private static int firstDayOfYear(int previousYearFirstDay, int previousYear){  
           if (isLeapYear(previousYear)){  
                return (previousYearFirstDay + 366 % 7) % 7;  
           }  
           return (previousYearFirstDay + 365 % 7) % 7;  
      }  
      private static int numberSundays(int firstDay, int year){  
           int sundayIndex = (7 - firstDay) % 7;  
           return isLeapYear(year) ? LEAP_YEAR_DAY[sundayIndex] : NONE_LEAP_YEAR_DAY[sundayIndex];  
      }  
      private static void pattern(int year, int[] days) {  
           int nthDayInYear = 1; //1st Jan is the 1st day of the year  
           int firstDayOfMonth = 0; //1 is Monday, 0 being Sunday  
           days[firstDayOfMonth]++;   
           for (int i=0; i<DAYS_IN_MONTH.length; i++){  
                nthDayInYear += daysInMonth(i, year);  
                firstDayOfMonth = (nthDayInYear - 1) % 7;  
                days[firstDayOfMonth]++;  
           }  
      }  
      private static int daysInMonth(int i, int year) {  
           if (i != 1) { //Not Feb  
                return DAYS_IN_MONTH[i];  
           }  
           return isLeapYear(year) ? DAYS_IN_MONTH[i] + 1: DAYS_IN_MONTH[i];  
      }  
      private static boolean isLeapYear(int year) {  
           return (year % 100 != 0 && year % 4 ==0) || year % 400 == 0;  
      }  

Project Euler Problem 18 and 67: Maximum path sum

Problem

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3
7 4
2 4 6
8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below:

75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

Solution

Once again, don't use recursive prematurely!

This one requires working from bottom to top.

 private static final int ROW = 15;  
      private static final int[][] M = new int[ROW][ROW];  
      public static void main(String[] args) {  
           readFile();  
           for (int i=ROW-2; i >= 0; i--){  
                for (int j=0; j <= i; j++){  
                     M[i][j] = Math.max(M[i+1][j], M[i+1][j+1]) + M[i][j];  
                }  
           }  
           System.out.println(M[0][0]);       
      }  
      private static void readFile() {  
           File file = new File("Q18.txt");  
           try {  
                Scanner sc = new Scanner(file);  
                int i = 0;  
                while (sc.hasNextLine()) {  
                     int j = 0;  
                     Scanner lineSc = new Scanner(sc.nextLine());  
                     while (lineSc.hasNextInt()){  
                          M[i][j++]=lineSc.nextInt();       
                     }  
                     i++;  
                }  
                sc.close();  
           } catch (FileNotFoundException e) {  
                e.printStackTrace();  
           }  
      }