What does this recursive function mean? - mips

I've been tasked with implementing a recursive function in MIPS. This function is
function1(n) = n-5 (if n <= 3)
otherwise = 4*function1(n-1) - n*function1(n-3)
One of the test cases is if n = 6, then the result is 200.
How do you get 200 from entering 6 in this function? To me it looks like the answer should be 2. Is there something I am not understanding about recursion, or am I understanding the function wrong? I am so confused

You seem to be misunderstanding the function somewhere. Here are the steps I followed to arrive at 200:
function1(6) = 4*function1(5) - 6*function1(3) (by rule 2)
function1(5) = 4*function1(4) - 5*function1(2) (by rule 2)
function1(4) = 4*function1(3) - 4*function1(1) (by rule 2)
function1(3) = 3-5 = -2 (by rule 1)
function1(2) = 2-5 = -3 (by rule 1)
function1(1) = 1-5 = -4 (by rule 1)
Substituting back...
function1(4) = 4*-2 - 4*-4 = -8 - -16 = 8
function1(5) = 4*8 - 5*-3 = 32 - -15 = 47
function1(6) = 4*47 - 6*-2 = 188 - -12 = 200

Related

Reduce input to zero by using given variables

I hope you can help me with my request.
I have an integer input from a client. Lets say 250. The goal is to calculate the input to exactly 0 by only using 3 variables. x = 30, y = 50 and z = 100 and output how often i used each of them.
The given rules are:
I have to use as less of them as possible. means, first the z's then the y's then the x's. So i have to use as much as possible of the variables with greater values.
Im allowed to use a maximum of 3 of each of them.
I have to count how often i used each of them.
If a combination is not possible, lets say 70 ( 70 - y = 20, 70 - x - x = 10 ), give a message to the client, "Invalid input!".
Few examples:
Input = 250
Output:
z = 2
y = 1
####################
Input = 170
Output: Invalid input!
Because i can only calculate to zero by using 4 x's and 1 y. See rule 2.
Other solutions are not possible.
i.e. Input - z - y = 20 => error
Input - y - y - y = also 20 => error
####################
Input = 90
Output:
x = 3
####################
Input = 120
Output: Invalid input!
Input - z = 20 => error
Input - 50 - 50 = 20 => error
Input - x - x - x - x => See rule 2.
####################
and so on....
And how it could be extended if a further value is added to the 3 variables. i.e. 40
So if thats the case it should be somehowe dynamically.
I tried to explain that as much as possible. If you miss infos, just let me know.
Thank you.
dagogi

Big-O notation when the function has negative value

i need to proof that 2n^2 - 2n -7 = O(n^2), when the n is 1 or two i got negative value of f(n). i am not sure does the way i proof Big-O is correct.Your help and advice is highly appreciated.
f(n) = 2n^2 - 2n -7 = O(n^2) if c=2;
n=1->2(1)^2 - 2(1) -7 = -7 <= 2*(1)^2
n=2->2(2)^2 - 2(2) -7 = -3 <= 2*(2)^2
n=3->2(3)^2 - 2(3) -7 = 14 <= 2*(3)^2
The definition of Big-Oh has more to do with asymptotic behavior than local behavior. If your function went negative for increasing values of n, say it oscillated, there might be more of a concern. For this function, though, there is no problem: you are free to consider the function for all values greater than some n0 which you alone are allowed to choose. So, if the function going negative early on bothers you, write your proof such that those numbers aren't used. For example:
Base case: for n = 3, f(n) = 2*3*3 - 2*3 - 7 = 18 - 6 - 7 = 5 <= 9 * c = c * 3 * 3 = c * n^2. This is true provided that c >= 5/9.
Induction hypothesis: assume f(n) <= c * n^2 for all n starting at 3 up through k.
Induction step: we must show that f(k+1) <= c * (k+1)^2. We have f(k+1) = 2(k+1)^2 - 2(k+1) - 7 = 2k^2+4k+2 - 2k - 2 - 7 = 2k^2 + 2k - 7 < 2k^2 + 4k < 2k^2 + 4k + 2 = 2(k^2 + 2k + 1) = 2(k+1)^2, so the choice c = 2 works here.
In hindsight, it should be obvious that 2n^2 - 2n - 7 is always less than 2n^2 for positive increasing n.

Spawn Function in Corona SDK

Okay so I kind of am almost there but need a little push:
My dustbins spawn but there are a few to begin with like I want and then after about 30 seconds of the numbers of dustbins increasing there are 1000's all clumped together.. What can i do to alter my function so that its only ever a few at a time:
function spawnDustbin()
dustbin = {}
for i = 1,800 do
dustbin[i] = display.newImage("dustbin.png")
dustbin[i].xScale = 0.55
dustbin[i].yScale = 0.55
dustbin[i].y = 555
dustbin[i].x = (math.random(1000,1500) * i)
dustbin[i].speed = 4
physics.addBody( dustbin[i], "static", { friction=1.0, density=1.0, bounce=0, radius=30,} )
dustbin[i].enterFrame = moveDustbin
Runtime:addEventListener("enterFrame", dustbin[i])
end
end
and the movedustbin function simply moves the dustbin in the negative x direction:
function moveDustbin(self,event)
if self.x < -2560 then
self.x = 2560
else
self.x = self.x - val
end
end
First 20ish seconds:
http://i.stack.imgur.com/7iEeP.png
After 20 seconds:
http://i.stack.imgur.com/aae0D.png
Thank you very much
James
That "spawnDustbin" function above is spawning 800 dustbins every frame. That will really crush your performance, and I am pretty certain you don't want to create that many objects every frame.
You might want to do something like this:
local dustbin = {}
local i = 0
local function spawnDustbin()
i = i+1
dustbin[i] = display.newImage("dustbin.png")
dustbin[i].xScale = 0.55
dustbin[i].yScale = 0.55
dustbin[i].y = 555
dustbin[i].x = (math.random(1000,1500) * i)
dustbin[i].speed = 4
physics.addBody( dustbin[i], "static", { friction=1.0, density=1.0, bounce=0, radius=30,} )
dustbin[i].enterFrame = moveDustbin
Runtime:addEventListener("enterFrame", dustbin[i])
end
timer.performWithDelay(500, spawnDustbin, 10)
YMMV but that will spawn 10 dustbins in 5 seconds.

Convert decimal number to excel-header-like number

Locked. This question and its answers are locked because the question is off-topic but has historical significance. It is not currently accepting new answers or interactions.
0 = A
1 = B
...
25 = Z
26 = AA
27 = AB
...
701 = ZZ
702 = AAA
I cannot think of any solution that does not involve loop-bruteforce :-(
I expect a function/program, that accepts a decimal number and returns a string as a result.
Haskell, 78 57 50 43 chars
o=map(['A'..'Z']:)$[]:o
e=(!!)$o>>=sequence
Other entries aren't counting the driver, which adds another 40 chars:
main=interact$unlines.map(e.read).lines
A new approach, using a lazy, infinite list, and the power of Monads! And besides, using sequence makes me :), using infinite lists makes me :o
If you look carefully the excel representation is like base 26 number but not exactly same as base 26.
In Excel conversion Z + 1 = AA while in base-26 Z + 1 = BA
The algorithm is almost same as decimal to base-26 conversion with just once change.
In base-26, we do a recursive call by passing it the quotient, but here we pass it quotient-1:
function decimalToExcel(num)
// base condition of recursion.
if num < 26
print 'A' + num
else
quotient = num / 26;
reminder = num % 26;
// recursive calls.
decimalToExcel(quotient - 1);
decimalToExcel(reminder);
end-if
end-function
Java Implementation
Python, 44 chars
Oh c'mon, we can do better than lengths of 100+ :
X=lambda n:~n and X(n/26-1)+chr(65+n%26)or''
Testing:
>>> for i in 0, 1, 25, 26, 27, 700, 701, 702:
... print i,'=',X(i)
...
0 = A
1 = B
25 = Z
26 = AA
27 = AB
700 = ZY
701 = ZZ
702 = AAA
Since I am not sure what base you're converting from and what base you want (your title suggests one and your question the opposite), I'll cover both.
Algorithm for converting ZZ to 701
First recognize that we have a number encoded in base 26, where the "digits" are A..Z. Set a counter a to zero and start reading the number at the rightmost (least significant digit). Progressing from right to left, read each number and convert its "digit" to a decimal number. Multiply this by 26a and add this to the result. Increment a and process the next digit.
Algorithm for converting 701 to ZZ
We simply factor the number into powers of 26, much like we do when converting to binary. Simply take num%26, convert it to A..Z "digits" and append to the converted number (assuming it's a string), then integer-divide your number. Repeat until num is zero. After this, reverse the converted number string to have the most significant bit first.
Edit: As you point out, once two-digit numbers are reached we actually have base 27 for all non-least-significant bits. Simply apply the same algorithms here, incrementing any "constants" by one. Should work, but I haven't tried it myself.
Re-edit: For the ZZ->701 case, don't increment the base exponent. Do however keep in mind that A no longer is 0 (but 1) and so forth.
Explanation of why this is not a base 26 conversion
Let's start by looking at the real base 26 positional system. (Rather, look as base 4 since it's less numbers). The following is true (assuming A = 0):
A = AA = A * 4^1 + A * 4^0 = 0 * 4^1 + 0 * 4^0 = 0
B = AB = A * 4^1 + B * 4^0 = 0 * 4^1 + 1 * 4^0 = 1
C = AC = A * 4^1 + C * 4^0 = 0 * 4^1 + 2 * 4^0 = 2
D = AD = A * 4^1 + D * 4^0 = 0 * 4^1 + 3 * 4^0 = 3
BA = B * 4^0 + A * 4^0 = 1 * 4^1 + 0 * 4^0 = 4
And so forth... notice that AA is 0 rather than 4 as it would be in Excel notation. Hence, Excel notation is not base 26.
In Excel VBA ... the obvious choice :)
Sub a()
For Each O In Range("A1:AA1")
k = O.Address()
Debug.Print Mid(k, 2, Len(k) - 3); "="; O.Column - 1
Next
End Sub
Or for getting the column number in the first row of the WorkSheet (which make more sense, since we are in Excel ...)
Sub a()
For Each O In Range("A1:AA1")
O.Value = O.Column - 1
Next
End Sub
Or better yet: 56 chars
Sub a()
Set O = Range("A1:AA1")
O.Formula = "=Column()"
End Sub
Scala: 63 chars
def c(n:Int):String=(if(n<26)""else c(n/26-1))+(65+n%26).toChar
Prolog, 109 123 bytes
Convert from decimal number to Excel string:
c(D,E):- d(D,X),atom_codes(E,X).
d(D,[E]):-D<26,E is D+65,!.
d(D,[O|M]):-N is D//27,d(N,M),O is 65+D rem 26.
That code does not work for c(27, N), which yields N='BB'
This one works fine:
c(D,E):-c(D,26,[],X),atom_codes(E,X).
c(D,B,T,M):-(D<B->M-S=[O|T]-B;(S=26,N is D//S,c(N,27,[O|T],M))),O is 91-S+D rem B,!.
Tests:
?- c(0, N).
N = 'A'.
?- c(27, N).
N = 'AB'.
?- c(701, N).
N = 'ZZ'.
?- c(702, N).
N = 'AAA'
Converts from Excel string to decimal number (87 bytes):
x(E,D):-x(E,0,D).
x([C],X,N):-N is X+C-65,!.
x([C|T],X,N):-Y is (X+C-64)*26,x(T,Y,N).
F# : 166 137
let rec c x = if x < 26 then [(char) ((int 'A') + x)] else List.append (c (x/26-1)) (c (x%26))
let s x = new string (c x |> List.toArray)
PHP: At least 59 and 33 characters.
<?for($a=NUM+1;$a>=1;$a=$a/26)$c=chr(--$a%26+65).$c;echo$c;
Or the shortest version:
<?for($a=A;$i++<NUM;++$a);echo$a;
Using the following formula, you can figure out the last character in the string:
transform(int num)
return (char)num + 47; // Transform int to ascii alphabetic char. 47 might not be right.
char lastChar(int num)
{
return transform(num % 26);
}
Using this, we can make a recursive function (I don't think its brute force).
string getExcelHeader(int decimal)
{
if (decimal > 26)
return getExcelHeader(decimal / 26) + transform(decimal % 26);
else
return transform(decimal);
}
Or.. something like that. I'm really tired, maybe I should stop answering questions and go to bed :P

Code Golf: Calculate Orthodox Easter date

Locked. This question and its answers are locked because the question is off-topic but has historical significance. It is not currently accepting new answers or interactions.
The Challenge
Calculate the Date of the Greek Orthodox Easter (http://www.timeanddate.com/holidays/us/orthodox-easter-day) Sunday in a given Year (1900-2100) using the least amount of characters.
Input is just a year in the form '2010'. It's not relevant where you get it (Input, CommandLineArgs etc.) but it must be dynamic!
Output should be in the form day-month-year (say dd/mm/yyyy or d/m/yyyy)
Restrictions No standard functions, such as Mathematica's EasterSundayGreekOrthodox or PHP's easter_date(), which return the (not applicable gregorian) date automatic must be used!
Examples
2005 returns 1/5/2005
2006 returns 23/4/2006
2007 returns 8/4/2007
2008 returns 27/4/2008
2009 returns 19/4/2009
2010 returns 4/4/2010
2011 returns 24/4/2011
2012 returns 15/4/2012
2013 returns 5/5/2013
2014 returns 20/4/2014
2015 returns 12/4/2015
Code count includes input/output (i.e full program).
Edit:
I mean the Eastern Easter Date.
Reference: http://en.wikipedia.org/wiki/Computus
Python (101 140 132 115 chars)
y=input()
d=(y%19*19+15)%30
e=(y%4*2+y%7*4-d+34)%7+d+127
m=e/31
a=e%31+1+(m>4)
if a>30:a,m=1,5
print a,'/',m,'/',y
This one uses the Meeus Julian algorithm but since this one only works between 1900 and 2099, an implementation using Anonymous Gregorian algorithm is coming right up.
Edit: Now 2005 is properly handled. Thanks to Mark for pointing it out.
Edit 2: Better handling of some years, thanks for all the input!
Edit 3: Should work for all years in range. (Sorry for hijacking it Juan.)
PHP CLI, no easter_date(), 125 characters
Valid for dates from 13 March 1900 to 13 March 2100, now works for Easters that fall in May
Code:
<?=date("d/m/Y",mktime(0,0,0,floor(($b=($a=(19*(($y=$argv[1])%19)+15)%30)+(2*($y%4)+4*$y%7-$a+34)%7+114)/31),($b%31)+14,$y));
Invocation:
$ php codegolf.php 2010
$ php codegolf.php 2005
Output:
04/04/2010
01/05/2005
With whitespace:
<?=date("d/m/Y", mktime(0, 0, 0, floor(($b = ($a = (19 * (($y = $argv[1]) % 19) + 15) % 30) + (2 * ($y % 4) + 4 * $y % 7 - $a + 34) % 7 + 114) / 31), ($b % 31) + 14, $y));
This iteration is no longer readable thanks to PHP's handling of assignments. It's almost a functional language!
For completeness, here's the previous, 127 character solution that does not rely on short tags:
Code:
echo date("d/m/Y",mktime(0,0,0,floor(($b=($a=(19*(($y=$argv[1])%19)+15)%30)+(2*($y%4)+4*$y%7-$a+34)%7+114)/31),($b%31)+14,$y));
Invocation:
$ php -r 'echo date("d/m/Y",mktime(0,0,0,floor(($b=($a=(19*(($y=$argv[1])%19)+15)%30)+(2*($y%4)+4*$y%7-$a+34)%7+114)/31),($b%31)+14,$y));' 2010
$ php -r 'echo date("d/m/Y",mktime(0,0,0,floor(($b=($a=(19*(($y=$argv[1])%19)+15)%30)+(2*($y%4)+4*$y%7-$a+34)%7+114)/31),($b%31)+14,$y));' 2005
C#, 155 157 182 209 212 characters
class P{static void Main(string[]i){int y=int.Parse(i[0]),c=(y%19*19+15)%30,d=c+(y%4*2+y%7*4-c+34)%7+128;System.Console.Write(d%31+d/155+"/"+d/31+"/"+y);}}
Python 2.3, 97 characters
y=int(input())
c=(y%19*19+15)%30
d=c+(y%4*2+y%7*4-c+34)%7+128
print"%d/%d/%d"%(d%31+d/155,d/31,y)
This also uses the Meeus Julian algorithm (and should work for dates in May).
removed no longer necessary check for modern years and zero-padding in output
don't expect Easters in March anymore because there are none between 1800-2100
included Python 2.3 version (shortest so far)
Mathematica
<<Calendar`;a=Print[#3,"/",#2,"/",#]&##EasterSundayGreekOrthodox##&
Invoke with
a[2010]
Output
4/4/2010
Me too: I don't see the point in not using built-in functions.
Java - 252 196 190 chars
Update 1: The first algo was for Western Gregorian Easter. Fixed to Eastern Julian Easter now. Saved 56 chars :)
Update 2: Zero padding seem to not be required. Saved 4 chars.
class E{public static void main(String[]a){long y=new Long(a[0]),b=(y%19*19+15)%30,c=b+(y%4*2+y%7*4-b+34)%7+(y>1899&y<2100?128:115),m=c/31;System.out.printf("%d/%d/%d",c%31+(m<5?0:1),m,y);}}
With newlines
class E{
public static void main(String[]a){
long y=new Long(a[0]),
b=(y%19*19+15)%30,
c=b+(y%4*2+y%7*4-b+34)%7+(y>1899&y<2100?128:115),
m=c/31;
System.out.printf("%d/%d/%d",c%31+(m<5?0:1),m,y);
}
}
JavaScript (196 characters)
Using the Meeus Julian algorithm. This implementation assumes that a valid four-digit year was given.
y=~~prompt();d=(19*(y%19)+15)%30;x=d+(2*(y%4)+4*(y%7)-d+34)%7+114;m=~~(x/31);d=x%31+1;if(y>1899&&y<2100){d+=13;if(m==3&&d>31){d-=31;m++}if(m==4&&d>30){d-=30;m++}}alert((d<10?"0"+d:d)+"/0"+m+"/"+y)
Delphi 377 335 317 characters
Single line:
var y,c,n,i,j,m:integer;begin Val(ParamStr(1),y,n);c:=y div 100;n:=y-19*(y div 19);i:=c-c div 4-(c-((c-17)div 25))div 3+19*n+15;i:=i-30*(i div 30);i:=i-(i div 28 )*(1-(i div 28)*(29 div(i+1))*((21 -n)div 11));j:=y+y div 4 +i+2-c+c div 4;j:=j-7*(j div 7);m:=3+(i-j+40 )div 44;Write(i-j+28-31*(m div 4),'/',m,'/',y)end.
Formatted:
var
y,c,n,i,j,m:integer;
begin
Val(ParamStr(1),y,n);
c:=y div 100;
n:=y-19*(y div 19);
i:=c-c div 4-(c-((c-17)div 25))div 3+19*n+15;
i:=i-30*(i div 30);
i:=i-(i div 28 )*(1-(i div 28)*(29 div(i+1))*((21 -n)div 11));
j:=y+y div 4 +i+2-c+c div 4;j:=j-7*(j div 7);
m:=3+(i-j+40 )div 44;
Write(i-j+28-31*(m div 4),'/',m,'/',y)
end.
Tcl
Eastern Easter
(116 chars)
puts [expr 1+[incr d [expr ([set y $argv]%4*2+$y%7*4-[
set d [expr ($y%19*19+15)%30]]+34)%7+123]]%30]/[expr $d/30]/$y
Uses the Meeus algorithm. Takes the year as a command line argument, produces Eastern easter. Could be a one-liner, but it's slightly more readable when split...
Western Easter
(220 chars before splitting over lines)
interp alias {} tcl::mathfunc::s {} set;puts [expr [incr 3 [expr {
s(2,(s(4,$argv)%100/4*2-s(3,(19*s(0,$4%19)+s(1,$4/100)-$1/4-($1-($1+8)/25+46)
/3)%30)+$1%4*2-$4%4+4)%7)-($0+11*$3+22*$2)/451*7+114}]]%31+1]/[expr $3/31]/$4
Uses the Anonymous algorithm.
COBOL, 1262 chars
WORKING-STORAGE SECTION.
01 V-YEAR PIC S9(04) VALUE 2010.
01 V-DAY PIC S9(02) VALUE ZERO.
01 V-EASTERDAY PIC S9(04) VALUE ZERO.
01 V-CENTURY PIC S9(02) VALUE ZERO.
01 V-GOLDEN PIC S9(04) VALUE ZERO.
01 V-GREGORIAN PIC S9(04) VALUE ZERO.
01 V-CLAVIAN PIC S9(04) VALUE ZERO.
01 V-FACTOR PIC S9(06) VALUE ZERO.
01 V-EPACT PIC S9(06) VALUE ZERO.
PROCEDURE DIVISION
XX-CALCULATE EASTERDAY.
COMPUTE V-CENTURY = (V-YEAR / 100) + 1
COMPUTE V-GOLDEN= FUNCTION MOD(V-YEAR, 19) + 1
COMPUTE V-GREGORIAN = (V-CENTURY * 3) / 4 - 12
COMPUTE V-CLAVIAN
= (V-CENTURY * 8 + 5) / 25 - 5 - V-GREGORIAN
COMPUTE V-FACTOR
= (V-YEAR * 5) / 4 - V-GREGORIAN - 10
COMPUTE V-EPACT
= FUNCTION MOD((V-GOLDEN * 11 + 20 + V-CLAVIAN), 30)
IF V-EPACT = 24
ADD 1 TO V-EPACT
ELSE
IF V-EPACT = 25
IF V-GOLDEN > 11
ADD 1 TO V-EPACT
END-IF
END-IF
END-IF
COMPUTE V-DAY = 44 - V-EPACT
IF V-DAY < 21
ADD 30 TO V-DAY
END-IF
COMPUTE V-DAY
= V-DAY + 7 - (FUNCTION MOD((V-DAY + V-FACTOR), 7))
IF V-DAY <= 31
ADD 300 TO V-DAY GIVING V-EASTERDAY
ELSE
SUBTRACT 31 FROM V-DAY
ADD 400 TO V-DAY GIVING V-EASTERDAY
END-IF
.
XX-EXIT.
EXIT.
Note: Not mine, but I like it
EDIT: I added a char count with spaces but I don't know how spacing works in COBOL so I didn't change anything from original. ~vlad003
UPDATE: I've found where the OP got this code: http://www.tek-tips.com/viewthread.cfm?qid=31746&page=112. I'm just putting this here because the author deserves it. ~vlad003
C, 128 121 98 characters
Back to Meeus' algorithm. Computing the day in Julian, but adjusting for Gregorian (this still seems naive to me, but I cannot find a shorter alternative).
main(y,v){int d=(y%19*19+15)%30;d+=(y%4*2+y%7*4-d+34)%7+128;printf("%d/%d/%d",d%31+d/155,d/31,y);}
I have not found a case where floor(d/31) would actually be needed. Also, to account for dates in May, the m in Meeus' algorithm must be at least 5, therefore the DoM is greater than 154, hence the division.
The year is supplied as the number of program invocation arguments plus one, ie. for 1996 you must provide 1995 arguments. The range of ARG_MAX on modern systems is more than enough for this.
PS. I see Gabe has come to the same implementation in Python 2.3, surpassing me by one character. Aw. :(
PPS. Anybody looking at a tabular method for 1800-2099?
Edit - Shortened Gabe's answer to 88 characters:
y=input()
d=(y%19*19+15)%30
d+=(y%4*2+y%7*4-d+34)%7+128
print"%d/%d/%d"%(d%31+d/155,d/31,y)
BASIC, 973 chars
Sub EasterDate (d, m, y)
Dim FirstDig, Remain19, temp 'intermediate results
Dim tA, tB, tC, tD, tE 'table A to E results
FirstDig = y \ 100 'first 2 digits of year
Remain19 = y Mod 19 'remainder of year / 19
' calculate PFM date
temp = (FirstDig - 15) \ 2 + 202 - 11 * Remain19
Select Case FirstDig
Case 21, 24, 25, 27 To 32, 34, 35, 38
temp = temp - 1
Case 33, 36, 37, 39, 40
temp = temp - 2
End Select
temp = temp Mod 30
tA = temp + 21
If temp = 29 Then tA = tA - 1
If (temp = 28 And Remain19 > 10) Then tA = tA - 1
'find the next Sunday
tB = (tA - 19) Mod 7
tC = (40 - FirstDig) Mod 4
If tC = 3 Then tC = tC + 1
If tC > 1 Then tC = tC + 1
temp = y Mod 100
tD = (temp + temp \ 4) Mod 7
tE = ((20 - tB - tC - tD) Mod 7) + 1
d = tA + tE
'return the date
If d > 31 Then
d = d - 31
m = 4
Else
m = 3
End If
End Sub
Credit: Astronomical Society of South Australia
EDIT: I added a char count but I think many spaces could be removed; I don't know BASIC so I didn't make any changes to the code. ~vlad003
I'm not going to implement it, but I'd like to see one where the code e-mails the Pope, scans any answer that comes back for a date, and returns that.
Admittedly, the calling process may be blocked for a while.
Javascript 125 characters
This will handle years 1900 - 2199. Some of the other implementations cannot handle the year 2100 correctly.
y=prompt();k=(y%19*19+15)%30;e=(y%4*2+y%7*4-k+34)%7+k+127;m=~~(e/31);d=e%31+m-4+(y>2099);alert((d+=d<30||++m-34)+"/"+m+"/"+y)
Ungolfed..ish
// get the year to check.
y=prompt();
// do something crazy.
k=(y%19*19+15)%30;
// do some more crazy...
e=(y%4*2+y%7*4-k+34)%7+k+127;
// estimate the month. p.s. The "~~" is like Math.floor
m=~~(e/31);
// e % 31 => get the day
d=e%31;
if(m>4){
d += 1;
}
if(y > 2099){
d += 1;
}
// if d is less than 30 days add 1
if(d<30){
d += 1;
}
// otherwise, change month to May
// and adjusts the days to match up with May.
// e.g., 32nd of April is 2nd of May
else{
m += 1;
d = m - 34 + d;
}
// alert the result!
alert(d + "/" + m + "/" + y);
A fix for dates up to 2399.
I'm sure there is a way to algorithmically calculate dates beyond this but I don't want to figure it out.
y=prompt();k=(y%19*19+15)%30;e=(y%4*2+y%7*4-k+34)%7+k+127;m=~~(e/31);d=e%31+m-4+(y<2200?0:~~((y-2000)/100));alert((d+=d<30||++m-34)+"/"+m+"/"+y)
'VB .Net implementation of:
'http://aa.usno.navy.mil/faq/docs/easter.php
Dim y As Integer = 2010
Dim c, d, i, j, k, l, m, n As Integer
c = y \ 100
n = y - 19 * (y \ 19)
k = (c - 17) \ 25
i = c - c \ 4 - (c - k) \ 3 + 19 * n + 15
i = i - 30 * (i \ 30)
i = i - (i \ 28) * (1 - (i \ 28) * (29 \ (i + 1)) * ((21 - n) \ 11))
j = y + y \ 4 + i + 2 - c + c \ 4
j = j - 7 * (j \ 7)
l = i - j
m = 3 + (l + 40) \ 44
d = l + 28 - 31 * (m \ 4)
Easter = DateSerial(y, m, d)