I've built a function in q such that I can see how many Sunday's fall on the 1st of the month between two dates
\W 1 f3:{[sd;ed] count distinct `week$(sd + til 1 + ed - sd) where (`dd$distinct `week$sd + til 1 + ed - sd)=01}
How can I edit with to work with pre 2000 dates? Can I put a modulus around the negative dates? Or will that redender my function incorrect?
You can also try this:
q) f:{sum 1=mod[`date$a[1] + til 1+(-). a:(0;1<`dd$x)+`month$(y;x);7]}
q) f[2018.01.01;2018.12.31] / 2
q) f[1998.01.02;1999.12.31] / 4
Related
Having an infinite sequence s = 1234567891011...
Let's find the number at the n position (n <= 10^18)
EX: n = 12 => 1; n = 15 => 2
import Foundation
func findNumber(n: Int) -> Character {
var i = 1
var z = ""
while i < n + 1 {
z.append(String(i))
i += 1
}
print(z)
return z[z.index(z.startIndex, offsetBy: n-1)]
}
print(findNumber(n: 12))
That's my code but when I find the number at 100.000th position, it returns an error, I thought I appended too many i to z string.
Can anyone help me, in swift language?
The problem we have here looks fairly straight forward. Take a list of all the number 1-infinity and concatenate them into a string. Then find the nth digit. Straight forward problem to understand. The issue that you are seeing though is that we do not have an infinite amount of memory nor time to be able to do this reasonably in a computer program. So we must find an alternative way around this that does not just add the numbers onto a string and then find the nth digit.
The first thing we can say is that we know what the entire list is. It will always be the same. So can we use any properties of this list to help us?
Let's call the input number n. This is the position of the digit that we want to find. Let's call the output digit d.
Well, first off, let's look at some examples.
We know all the single digit numbers are just in the same position as the number itself.
So, for n<10 ... d = n
What about for two digit numbers?
Well, we know that 10 starts at position 10. (Because there are 9 single digit numbers before it). 9 + 1 = 10
11 starts at position 12. Again, 9 single digits + one 2 digit number before it. 9 + 2 + 1 = 12
So how about, say... 25? Well that has 9 single digit numbers and 15 two digit numbers before it. So 25 starts at 9*1 + 15*2 + 1 = 40 (+ 1 as the sum gets us to the end of 24 not the start of 25).
So... 99 starts at? 9*1 + 89*2 + 1 = 188.
The we do the same for the three digit numbers...
100... 9*1 + 90*2 + 1 = 190
300... 9*1 + 90*2 + 199*3 + 1 = 787
1000...? 9*1 + 90*2 + 900*3 + 1 = 2890
OK... so now I'm seeing a pattern here that seems to need to know the number of digits in each number. Well... I can get the number of digits in a number by rounding up the log(base 10) of that number.
rounding up log base 10 of 5 = 1
rounding up log base 10 of 23 = 2
rounding up log base 10 of 99 = 2
rounding up log base 10 of 627 = 3
OK... so I think I need something like...
// in pseudo code
let lengthOfNumber = getLengthOfNumber(n)
var result = 0
for each i from 0 to lengthOfNumber - 1 {
result += 9 * 10^i * (i + 1) // this give 9*1 + 90*2 + 900*3 + ...
}
let remainder = n - 10^(lengthOfNumber - 1) // these have not been added in the loop above
result += remainder * lengthOfNumber
So, in the above pseudo code you can give it any number and it will return the position in the list that that number starts on.
This isn't the exact same as the problem you are trying to solve. And I don't want to solve it for you.
This is just a leg up on how I would go about solving it. Hopefully, this will give you some guidance on how you can take this further and solve the problem that you are trying to solve.
Is it possible for all calculations in the expression for numbers in a power to be prevented? Perhaps by pre-processing the expression or adding tellsimp rules? Or some other way?
For example, to
distrib (10 ^ 10 * (x + 1));
which produces:
1000000000 x + 1000000000
instead issued:
10 ^ 10 * x + 10 ^ 10
And similarly
factor (10 ^ 10 * x + 10 ^ 10);
returned:
10 ^ 10 * (x + 1);
Just as
factor(200);
2^3*5^2
represents power of numbers, only permanently?
Interesting question, although I don't see a good solution. Here's something I tried as an experiment, which is to display integers in factored form. I am working with Maxima 5.44.0 + SBCL.
(%i1) :lisp (defun integer-formatter (x) ($factor x))
INTEGER-FORMATTER
(%i1) :lisp (setf (get 'integer 'formatter) 'integer-formatter)
INTEGER-FORMATTER
(%i1) (x + 1000)^3;
3 3 3
(%o1) (x + 2 5 )
(%i2) 10^10*(x + 1);
2 5 2 5
(%o2) (2 5 ) (x + 1)
This is only a modification of the display; the internal representation is just a single integer.
(%i3) :lisp $%
((MTIMES SIMP) 10000000000 ((MPLUS SIMP) 1 $X))
That seems kind of clumsy, since e.g. 2^(2*5)*5^(2*5) isn't really more comprehensible than 10000000000.
A separate question is whether the arithmetic on 10^10 could be suppressed, so it actually stays as 10^10 and isn't represented internally as 10000000000. I'm pretty sure that would be difficult. Unfortunately Maxima is not too good with retracting identities which are applied, particularly with the built-in identities which are applied to perform arithmetic and other operations.
I am struggling to write a nprev function in KDB; xprev function returns the nth element but I need all the prev n elements relative to the current element.
q)t:([] i:1+til 26; s:.Q.a)
q)update xp:xprev[3;]s,p:prev s from t
Any help is greatly appreciated.
You can achieve the desired result by applying prev repeatedly and flipping the result
q)n:3
q)select flip 1_prev\[n;s] from t
s
-----
" "
"a "
"ba "
"cba"
"dcb"
"edc"
..
If n is much smaller than the rows count, this will be faster than some of the more straightforward solutions.
The xprev function basically looks like this :
xprev1:{y til[count y]-x} //readable xprev
We can tweak it to get all n elements
nprev:{y til[count y]-\:1+til x}
using nprev in the query
q)update np: nprev[3;s] , xp1:xprev1[3;s] , xp: xprev[3;s], p:prev[s] from t
i s np xp1 xp p
-------------------
1 a " "
2 b "a " a
3 c "ba " b
4 d "cba" a a c
5 e "dcb" b b d
6 f "edc" c c e
k equivalent of nprev
k)nprev:{$[0h>#y;'`rank;y(!#y)-\:1+!x]}
and similarly nnext would look like
k)nnext:{$[0h>#y;'`rank;y(!#y)+\:1+!x]}
I have a variable with a date table that looks like this
* table:
[day]
* number: 15
[year]
* number: 2015
[month]
* number: 2
How do I get the days between the current date and the date above? Many thanks!
You can use os.time() to convert your table to seconds and get the current time and then use os.difftime() to compute the difference. see Lua Wiki for more details.
reference = os.time{day=15, year=2015, month=2}
daysfrom = os.difftime(os.time(), reference) / (24 * 60 * 60) -- seconds in a day
wholedays = math.floor(daysfrom)
print(wholedays) -- today it prints "1"
as #barnes53 pointed out could be off by one day for a few seconds so it's not ideal, but it may be good enough for your needs.
You can use the algorithms gathered here:
chrono-Compatible Low-Level Date Algorithms
The algorithms are shown using C++, but they can be easily implemented in Lua if you like, or you can implement them in C or C++ and then just provide Lua bindings.
The basic idea using these algorithms is to compute a day number for the two dates and then just subtract them to give you the number of days.
--[[
http://howardhinnant.github.io/date_algorithms.html
Returns number of days since civil 1970-01-01. Negative values indicate
days prior to 1970-01-01.
Preconditions: y-m-d represents a date in the civil (Gregorian) calendar
m is in [1, 12]
d is in [1, last_day_of_month(y, m)]
y is "approximately" in
[numeric_limits<Int>::min()/366, numeric_limits<Int>::max()/366]
Exact range of validity is:
[civil_from_days(numeric_limits<Int>::min()),
civil_from_days(numeric_limits<Int>::max()-719468)]
]]
function days_from_civil(y, m, d)
if m <= 2 then
y = y - 1
m = m + 9
else
m = m - 3
end
local era = math.floor(y/400)
local yoe = y - era * 400 -- [0, 399]
local doy = math.modf((153*m + 2)/5) + d-1 -- [0, 365]
local doe = yoe * 365 + math.modf(yoe/4) - math.modf(yoe/100) + doy -- [0, 146096]
return era * 146097 + doe - 719468
end
local reference_date = {year=2001, month = 1, day = 1}
local date = os.date("*t")
local reference_days = days_from_civil(reference_date.year, reference_date.month, reference_date.day)
local days = days_from_civil(date.year, date.month, date.day)
print(string.format("Today is %d days into the 21st century.",days-reference_days))
os.time (under Windows, at least) is limited to years from 1970 and up. If, for example, you need a general solution to also find ages in days for people born before 1970, this won't work. You can use a julian date conversion and subtract between the two numbers (today and your target date).
A sample julian date function that will work for practically any date AD is given below (Lua v5.3 because of // but you could adapt to earlier versions):
local
function div(n,d)
local a, b = 1, 1
if n < 0 then a = -1 end
if d < 0 then b = -1 end
return a * b * (math.abs(n) // math.abs(d))
end
--------------------------------------------------------------------------------
-- Convert a YYMMDD date to Julian since 1/1/1900 (negative answer possible)
--------------------------------------------------------------------------------
function julian(year, month, day)
local temp
if (year < 0) or (month < 1) or (month > 12)
or (day < 1) or (day > 31) then
return
end
temp = div(month - 14, 12)
return (
day - 32075 +
div(1461 * (year + 4800 + temp), 4) +
div(367 * (month - 2 - temp * 12), 12) -
div(3 * div(year + 4900 + temp, 100), 4)
) - 2415021
end
Being new to crystal, I am unable to figure out how to compute rows 3 and 4 below.
Rows 1 and 2 are simple percentages of the sum of the data.
Row 3 is a computed value (see below.)
Row 4 is a sum of the data points (NOT a percentage as in row 1 and row 2)
Can someone give me some pointers on how to generate the display as below.
My data:
2010/01/01 A 10
2010/01/01 B 20
2010/01/01 C 30
2010/02/01 A 40
2010/02/01 B 50
2010/02/01 C 60
2010/03/01 A 70
2010/03/01 B 80
2010/03/01 C 90
I want to display
2010/01/01 2010/02/01 2010/03/01
========== ========== ==========
[ B/(A + B + C) ] 20/60 50/150 80/240 <=== percentage of sum
[ C/(A + B + C) ] 30/60 60/150 90/240 <=== percentage of sum
[ 1 - A/(A + B + C) ] 1 - 10/60 1 - 40/150 1 - 70/240 <=== computed
[ (A + B + C) ] 60 150 250 <=== sum
Assuming you are using a SQL data source, I suggest deriving each of the output rows' values (ie. [B/(A + B + C)], [C/(A + B + C)], [1 - A/(A + B + C)] and [(A + B + C)]) per date in the SQL query, then using Crystal's crosstab feature to pivot them into the output format desired.
Crystal's crosstabs aren't particularly suited to deriving different calculations on different rows of output.