Day of week

[Ryan McGuire]

Your assignment, should you choose to accept it, is to come up with the Day Of The Week calculation that is easiest to perform mentally. The algorithm has to work for for any date from Jan 1, 1900 to Dec 31, 2099. (Two centuries ought to be enough.) The final result of the calculation must come out so that a 0 represents Sunday, 1 Monday, ... 6 Saturday.


The exact fitness calulation will be this:

 2 points for each constant that has to be memorized 
   (if the series of constants is some otherwise well-known number, then
   that can count as a single constant.  e.g. If the constants are 1, 4, 9, 
   and 2, then they can be consolidated into a single constant 1492, when 
   Columbus sailed to America.  Use some good faith judgement on what 
   counts as "well-known".)
 2 point for each addition or substraction of one- or two- digit numbers
 3 points for each addition or subtration of three- or four-digit numbers
 4 points for each integer division or multiplication operation
 3 points for a MOD 4 calculation
 5 points for a MOD 7 calculation

As you can see allowance was made for the fact that x mod 4 is easier to calculate in your head than x mod 7.


Let's see an example algorithm/calculation (March 2, 2005)

 4 points  Divide the year by four:                           2005 / 4 = 501
 3         Add the year:                                   501 + 2005 = 2506
24         Add the appropriate month constant from 
           this table:  
           Jan=5, Feb=1, Mar=1, Apr=4, May=6, Jun=2,
           Jul=4, Aug=0, Sep=3, Oct=5, Nov=1, Dec=3          2506 + 1 = 2507
 3         If the year MOD 4 is 0 and the month is           2509 - 0 = 2507
           Jan or Feb, subtract one.
 3         Add the day:                                      2509 + 2 = 2509
 5         MOD that by 7.                                     2509 MOD 7 = 3
--------                                                    ----------------
42 points                                                   3 is a Wednesday

Can I cut down that 24 points for 12 constants? Hmmm... 5, 1, 1, 4, 6, 2, 4, 0, 3, 5, 1, 3. I don't see anything.

Surely, there is an algorithm that scores fewer than 42 points (and still comes out with the right answer).


Ryan
[ March 02, 2005: Message edited by: Ryan McGuire ]

[David Harkness]

Originally posted by Ryan McGuire:
Surely, there is an algorithm that scores fewer than 42 points

Forget the algorithm -- you've just found the answer to life, the universe, and everything!
[ March 02, 2005: Message edited by: David Harkness ]

[Mitch Ikeson]

But it scores < not = 42.

But he is near the answer.

[Eric Pascarello]

I personally would just type this into the address bar:

javascript:alert(new Date(prompt('The Date in question?')).getDay());

Would your algo. account for leap year? To lazy to test!

Eric

[Ryan McGuire]

Originally posted by Eric Pascarello:
I personally would just type this into the address bar:

javascript:alert(new Date(prompt('The Date in question?')).getDay());

Would your algo. account for leap year? To lazy to test!

Eric

Very nice if you're near a computer. Notice, however, that I'm going for easy to memorize/perform in one's head. One might infer that I don't plan on running this on a compueter.

The divide by four in the first step is what handles leap years.

Ryan

[David O'Meara]

Can I cut down that 24 points for 12 constants? Hmmm... 5, 1, 1, 4, 6, 2, 4, 0, 3, 5, 1, 3. I don't see anything.

Not exactly in the rules, but why not call it 511462403513 (ie one constant ) and define the maths to pop the M'th digit? What are the 'points' costs of abitrary div, mod, power, log functions?

[edit - yeah yeah, i read it a bit closer ]
[ March 05, 2005: Message edited by: David O'Meara ]

[Ryan McGuire]

Originally posted by Ryan McGuire:

...

The exact fitness calulation will be this:
...

2 things:

Any MOD operation that's really easy counts the same as a MOD 4. I would say that MOD 2, 4, 5, 10, 20, 40, 50, 100 all fit in this class. Maybe MOD 3 and 30 fit in here too. I'd have to say MOD 7 and 12 don't.

What may be obvious is that I'm looking for a DayOfWeek calculation that's easy to do in one's head. The "fitness calculation" score was an attempt to characterize "easy to do in head". If you can make an argument that you've found an improvement that makes the calculation easier despite having a higher score, I'd love to see it.

Ryan

[Sonny Pondrom]

  
points
32005 - 1900 = 105  year since beginning
4105/4       =  26  leap days (integer)
3       105 + 26    =  131 extra lunar + leap days 
24      131 + 3     =  134  correct for month-1
3       134 + 2     =  136  day of month 
5       mod(136,7)  =   3  =   wednesday
42
 
jan3
feb3
mar6
apr8
may11
jun13
jul16
aug19
sep21
oct24
nov26
dec29 
 
Since I could do no better I stopped.    :(   
 

[ankur rathi]

Ryan McGuire wrote:Your assignment, should you choose to accept it, is to come up with the Day Of The Week calculation that is easiest to perform mentally. The algorithm has to work for for any date from Jan 1, 1900 to Dec 31, 2099. (Two centuries ought to be enough.) The final result of the calculation must come out so that a 0 represents Sunday, 1 Monday, ... 6 Saturday.


The exact fitness calulation will be this:

 2 points for each constant that has to be memorized 
   (if the series of constants is some otherwise well-known number, then
   that can count as a single constant.  e.g. If the constants are 1, 4, 9, 
   and 2, then they can be consolidated into a single constant 1492, when 
   Columbus sailed to America.  Use some good faith judgement on what 
   counts as "well-known".)
 2 point for each addition or substraction of one- or two- digit numbers
 3 points for each addition or subtration of three- or four-digit numbers
 4 points for each integer division or multiplication operation
 3 points for a MOD 4 calculation
 5 points for a MOD 7 calculation

As you can see allowance was made for the fact that x mod 4 is easier to calculate in your head than x mod 7.


Let's see an example algorithm/calculation (March 2, 2005)

 4 points  Divide the year by four:                           2005 / 4 = 501
 3         Add the year:                                   501 + 2005 = 2506
24         Add the appropriate month constant from 
           this table:  
           Jan=5, Feb=1, Mar=1, Apr=4, May=6, Jun=2,
           Jul=4, Aug=0, Sep=3, Oct=5, Nov=1, Dec=3          2506 + 1 = 2507
 3         If the year MOD 4 is 0 and the month is           2509 - 0 = 2507
           Jan or Feb, subtract one.
 3         Add the day:                                      2509 + 2 = 2509
 5         MOD that by 7.                                     2509 MOD 7 = 3
--------                                                    ----------------
42 points                                                   3 is a Wednesday

Can I cut down that 24 points for 12 constants? Hmmm... 5, 1, 1, 4, 6, 2, 4, 0, 3, 5, 1, 3. I don't see anything.

Surely, there is an algorithm that scores fewer than 42 points (and still comes out with the right answer).


Ryan
[ March 02, 2005: Message edited by: Ryan McGuire ]

A doubt in 3rd line. 24 points are for remembering 12 constants but adding will also accumulate 3 more points. Right?

[ankur rathi]

March 2, 2005

    
1. Year MOD 100 : 2005 % 100 = 5 : how many points you'll give for MOD 100? It's easy, IMO.
2. Divide result of 1 by 4 : 5 / 4 = 1 : 4 Points
3. Add result of 1 & 2 : 5 + 1 = 6 : 2 Points
4. Add result of 3 & Month Code : 6 + 2 = 8 : 24 + 2 Points
5. Add result of 4 & Date : 8 + 2 = 10 : 2 Points
6. Divide result of 5 by 7 : 10 / 7 = 3 : 4 Points

3 is Wednesday

   
Month Code:

Jan	Feb	Mar	Apr	May	Jun	Jul	Ago	Sept	Oct	Nov	Dec
6	2	2	5	0	3	5	1	4	6	2	4

   
1 = Monday, 2 = Tuesday, 3 = Wednesday, etc.

Total points = 40, if consider MOD 100 for 2 points.

No better than yours, this will not work for leap years, this will only work for 21st century (2000s).

Reference: http://www.terra.es/personal2/grimmer/#Monthcodes

[Pankaj Rathod]

Method to calulate day of week.

(works for year from 1900) (takes care of leap years)

Example date: 16-Feb-2009
...
...

Edit: The method posted was wrong. Realised the mistake.

[Pankaj Rathod]