COSC 1315 Fundamentals of Programming

COSC 1315 - Fundamentals of Programming
Allan Kochis

We want to write a program that inputs a month day and year and tells us what day of the week it is.

Valid Year
Our year must be greater than 1752 since our calendar changed. So 1752 is an anomaly and before that we would need a different algorithm. For the curious here is what the calendar for 1752 looked like:

                               1752
 
       January               February                 March
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
          1  2  3  4                      1    1  2  3  4  5  6  7
 5  6  7  8  9 10 11    2  3  4  5  6  7  8    8  9 10 11 12 13 14
12 13 14 15 16 17 18    9 10 11 12 13 14 15   15 16 17 18 19 20 21
19 20 21 22 23 24 25   16 17 18 19 20 21 22   22 23 24 25 26 27 28
26 27 28 29 30 31      23 24 25 26 27 28 29   29 30 31
 
        April                   May                   June
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
          1  2  3  4                   1  2       1  2  3  4  5  6
 5  6  7  8  9 10 11    3  4  5  6  7  8  9    7  8  9 10 11 12 13
12 13 14 15 16 17 18   10 11 12 13 14 15 16   14 15 16 17 18 19 20
19 20 21 22 23 24 25   17 18 19 20 21 22 23   21 22 23 24 25 26 27
26 27 28 29 30         24 25 26 27 28 29 30   28 29 30
                       31
        July                  August                September
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
          1  2  3  4                      1          1  2 14 15 16
 5  6  7  8  9 10 11    2  3  4  5  6  7  8   17 18 19 20 21 22 23
12 13 14 15 16 17 18    9 10 11 12 13 14 15   24 25 26 27 28 29 30
19 20 21 22 23 24 25   16 17 18 19 20 21 22
26 27 28 29 30 31      23 24 25 26 27 28 29
                       30 31
       October               November               December
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
 1  2  3  4  5  6  7             1  2  3  4                   1  2
 8  9 10 11 12 13 14    5  6  7  8  9 10 11    3  4  5  6  7  8  9
15 16 17 18 19 20 21   12 13 14 15 16 17 18   10 11 12 13 14 15 16
22 23 24 25 26 27 28   19 20 21 22 23 24 25   17 18 19 20 21 22 23
29 30 31               26 27 28 29 30         24 25 26 27 28 29 30
                                              31

Valid Month
Between 1 and 12.
Valid Day
Between 1 and the maximum for that month.
So 1..31 for January, March, May, July, August, October and December.
1..30 for April, June, September and November
February is either 1 .. 28 or 29 depending if it is a leap year.
Leap Year
A year that is divisible by 4. But it it is divisible by 100, it must be divisible by 400. So

year divisible
by 4 divisible
by 100 divisible
by 400 Leap
2006 No - - No
2004 Yes No - Yes
1900 Yes Yes No No
2000 Yes Yes Yes Yes

If we invert the year divisible by 100 test it looks like a logical or condition. so our test looks like:

year Y%4 ==0 Y%100 > 0 Y%400 == 0 Leap
2006 F - - F
2004 T T - T
1900 T F F F
2000 T F T T
Zeller's Congruence.
To calculate the day of the week for a given date, Zeller's congruence can be applied. A date is expressed as follows:
- "m" month number, with January and February taken as months 11 and 12 of the preceding year. Then March is 1, April is 2.. December is 10.
- "k" day of the month
- "C" The century
- "D" The year in the century.
- "f" The day of the week where 0 = Sunday, 1 = Monday ... 6 = Saturday
The congruence is

f={[2.6m-0.2]+k+D+[D/4]+[C/4]-2C} mod 7

[] denotes the greatest integer in.

year	divisible by 4	divisible by 100	divisible by 400	Leap
2006	No	-	-	No
2004	Yes	No	-	Yes
1900	Yes	Yes	No	No
2000	Yes	Yes	Yes	Yes

year	Y%4 ==0	Y%100 > 0	Y%400 == 0	Leap
2006	F	-	-	F
2004	T	T	-	T
1900	T	F	F	F
2000	T	F	T	T

IPO

Input	Processing	Output
Month Day Year	Processing Items Valid boolean set to true if date is valid. maxDays in a month m,k,C,D,f from Zeller's Congruence. Algorithm: Start Get Month Get Day Get Year If Month is invalid print error message set Valid date to false EndIf If Year is invalid Print error message set Valid date to false EndIf If Month is Jan, Mar, May, Jul, Aug, Oct, Dec set maxDays to 31 Else If Month is Apr, Jun, Sep, Nov set maxDays to 30 Else If Month is Feb If Year is a Leap Year set maxDays to 29 Else set MaxDays to 28 EndIf Else set maxDays to 1 EndIf If Day is not between 1 and maxDays Print Error Message set Valid date to False EndIf If Valid date is true Compute Day of week using Zeller congruence Print Day of week. Endif Stop	Day of Week

Input

Processing

Output

Month
Day
Year

Processing Items
  Valid boolean set to true if date is valid.
  maxDays in a month
  m,k,C,D,f from Zeller's Congruence.
 

Algorithm:
 
Start
  Get Month
  Get Day
  Get Year
 
  If Month is invalid
     print error message
     set Valid date to false
  EndIf
 
  If Year is invalid
     Print error message
     set Valid date to false
  EndIf
 
  If Month is Jan, Mar, May, Jul, Aug, Oct, Dec
     set maxDays to 31
  Else If Month is Apr, Jun, Sep, Nov
          set maxDays to 30
  Else If Month is Feb
          If Year is a Leap Year
             set maxDays to 29
          Else
             set MaxDays to 28
          EndIf
  Else
     set maxDays to 1
  EndIf
 
  If Day is not between 1 and maxDays
     Print Error Message
     set Valid date to False
  EndIf
 
  If Valid date is true
     Compute Day of week
        using Zeller congruence
     Print Day of week.
   Endif
 
Stop

Day of Week

C++ code

//
// what day of the week is it?
//
#include <iostream>
 
using namespace std;
int main()
{
    int   iMonth, iDay, iYear;  //  input
    bool  bValid=true;          //  valid input flag
    int   iMaxdays;             //  Days in month
    //
    //  variables for Zellers
    //
    int m,k,C,D,f;  //  as in the write up
 
    //
    //  get input
    //
    cout << "Please enter the Month :";
    cin  >> iMonth;
    cout << "Enter the day of the month :";
    cin  >> iDay;
    cout << "Finally enter the year : "; 
    cin  >> iYear;
    //
    //  validate the input
    //
    if(iMonth < 1 || iMonth > 12) {
              cout << "Invalid Month " <<endl;
              cout << " Must be 1..12" <<endl;
              bValid=false;
    }
    if(iYear < 1753 ) {
             cout << "Invalid year " <<endl;
             cout << "must be greater than 1753 " << endl;
             bValid=false;
    }
    switch(iMonth) {
        case  1:
        case  3:
        case  5:
        case  7:
        case  8:
        case 10:
        case 12:    iMaxdays=31;
                    break;
        case  4:
        case  6:
        case  9:
        case 11:    iMaxdays=30;
                    break;
        case  2:    if(iYear%4 == 0 &&
                    (iYear%100 >0 || iYear%400 == 0))
                         iMaxdays=29;
                     else iMaxdays=28;
                     break;
        default:    iMaxdays=1;            
    }
    if(iDay < 1 || iDay > iMaxdays) {
            cout << "Invalid day of Month " << endl;
            cout << "For month " << iMonth
                 << " must be 1 .. " << iMaxdays << endl;
             bValid=false;
    }
    //
    // Zeller's congruence
    //
    if(bValid) {
       m=iMonth-2;
       k=iDay;
       D=iYear;
       if(m <=0) {
           m+=12;
           D--;
       }
       C=D/100;
       D%=100;
       f=((int)(2.6*m-0.2) + k + D + D/4 + C/4 - 2*C) % 7;
       if(f < 0 ) f+=7;   // % to mod fix
       switch(f) {
          case 0 : cout << "Sunday"    << endl; break;
          case 1 : cout << "Monday"    << endl; break;        
          case 2 : cout << "Tuesday"   << endl; break;       
          case 3 : cout << "Wednesday" << endl; break;
          case 4 : cout << "Thursday"  << endl; break;
          case 5 : cout << "Friday"    << endl; break;
          case 6 : cout << "Saturday"  << endl; break;
       }
    }
      
   
    system("pause");
    return(0);
}

Test cases

Please enter the Month :9
Enter the day of the month :27
Finally enter the year : 2006
Wednesday
Press any key to continue . . .

Please enter the Month :12
Enter the day of the month :7
Finally enter the year : 1941
Sunday
Press any key to continue . . .

Please enter the Month :9
Enter the day of the month :11
Finally enter the year : 2001
Tuesday
Press any key to continue . . .

Please enter the Month :2
Enter the day of the month :29
Finally enter the year : 2006
Invalid day of Month
For month 2 must be 1 .. 28
Press any key to continue . . .

Please enter the Month :13
Enter the day of the month :23
Finally enter the year : 1624
Invalid Month
 Must be 1..12
Invalid year
must be greater than 1753
Invalid day of Month
For month 13 must be 1 .. 1
Press any key to continue . . .