How to convert number into string in agda? - string

I need to write something to convert number into string with agda. I found someone asked the way to transfer string into agda before.
Agda: parse a string with numbers
I thinked about use it backwards,
row-to-stringh : (m : ℕ) → string
row-to-stringh 0 = "0"
row-to-stringh 1 = "1"
row-to-stringh 2 = "2"
row-to-stringh 3 = "3"
row-to-stringh 4 = "4"
row-to-stringh 5 = "5"
row-to-stringh 6 = "6"
row-to-stringh 7 = "7"
row-to-stringh 8 = "8"
row-to-stringh 9 = "9"
row-to-stringh _ = ""
but it not good enough. when the number is greater than 9, it will just convert it into "", instead of "(that number)". Can someone help me with this?

If you don't want to implement this function yourself, there's a show function in the standard library.
If you want to write it yourself: the usual way of converting a number into a string is to extract the digits by repeatedly dividing with a remainder. For example (remainders are written in parens):
7214 / 10 = 721 (4)
721 / 10 = 72 (1)
72 / 10 = 7 (2)
7 / 10 = 0 (7)
You then just collect the remainders into list, reverse it and convert the digits to chars. It might be tempting to try this in Agda as well, however, you'll run into problems with termination checker.
Firstly, you'll have to convince it that divMod (that is, division with remainder - modulus) terminates. You can just hardcode the divisor into the function and convincing the termination checker becomes easy.
The hard part is showing that repeatedly dividing the number by 10 actually terminates. This will most likely involve some rather complex tricks (such as well founded recursion).
If you want to know how it's done this way, take a look at the implementation linked above. Anyways, there's a bit less efficient but much simpler way of doing this.
Let's represent digits by a list of natural numbers.
Digits = List ℕ
We would like to write a function addOne, that (as the name suggests) adds one to a number represented by a list of digits, that is:
addOne : Digits → Digits
For this, we'll use the primitive pen & paper method: add one to the least significant digit; if the result is less than 10, we are done; if it isn't, write 0 and carry the 1 to the next digit. So, here's our carry:
data Carry : Set where
+0 : Carry
+1 : Carry
And here's the function that performs the addition - the second Carry argument can be thought of as a carry from the addition of previous two digits.
ripple-carry : Digits → Carry → Digits
ripple-carry ns +0 = ?
ripple-carry [] +1 = ?
ripple-carry (n ∷ ns) +1 with suc n ≤? 9
... | yes _ = ?
... | no _ = ?
The actual implementation is an exercise - use the description given above. Just note that we store digits in reverse order (this allows for more efficient and easier implementation). For example, 123 is represented by 3 ∷ 2 ∷ 1 ∷ [] and 0 by [].
We can recover the addOne function:
addOne : Digits → Digits
addOne n = ripple-carry n +1
The rest is just plumbing.
toDigits : ℕ → Digits
toDigits zero = []
toDigits (suc n) = addOne (toDigits n)
show : ℕ → String
show 0 = "0"
show n = (fromList ∘ map convert ∘ reverse ∘ toDigits) n
where
convert : ℕ → Char
convert 0 = '0'
convert 1 = '1'
convert 2 = '2'
convert 3 = '3'
convert 4 = '4'
convert 5 = '5'
convert 6 = '6'
convert 7 = '7'
convert 8 = '8'
convert 9 = '9'
convert _ = ' ' -- Never happens.
Used modules:
open import Data.Char
open import Data.List
open import Data.Nat
open import Data.String
open import Function
open import Relation.Nullary
I did some testing and it turns out that this method is actually fairly effective (especially when compared to the function from standard library).
The algorithm presented above needs to access O(n) digits (addOne needs to access only one digit in 90% of cases, two digits in 9%, three in 0.9%, etc) for a given number n. Unless we have some faster primitive operations (such as _+_ using Haskell's Integer behind the scenes), this is about the fastest we can get - we are working with unary numbers after all.
Standard library uses repeated division mentioned above, which is also (unless my math is wrong) O(n). However, this does not count handling of proofs, which adds enormous overhead, slowing it down to halt. Let's do a comparison:
open import Data.Nat
open import Data.Nat.Show
open import Function
open import IO
main = (run ∘ putStrLn ∘ show) n
And here are times for the compiled code (using C-c C-x C-c in Emacs). show from standard library:
n time
———————————————
1000 410 ms
2000 2690 ms
3000 8640 ms
If we use show as defined above, we get:
n time
———————————————
100000 26 ms
200000 41 ms
300000 65 ms

Related

Printf text and return value of a method call

Disclaimer: I am a total newb to haskell, but I can't find the answer. Maybe I am searching in the wrong way or it is so basic that nobody even asks that.
Here is what I try to do:
import Text.Printf
factorial n = if n < 2 then 1 else n * factorial (n-1)
main = do
let input = 22
printf "Some text... %d! = %d" input (factorial input)
But that doesn't work, a bunch of errors appear. Can you give me a quick hint, what I am doing wrong?
the only input is of ambiguous type in your code.
import Text.Printf
factorial n = if n < 2 then 1 else n * factorial (n-1)
main = do
let input = 22::Integer
printf "Some text... %d! = %d" input (factorial input)
return ()
The problem is that the compiler cannot infer the type of input. To do, you would need to provide it explicitly:
import Text.Printf
factorial n = if n < 2 then 1 else n * factorial (n-1)
main = do
let input = 22 :: Integer
printf "Some text... %d! = %d" input (factorial input)
Note that Integer willl work for very large results, whereas Int won't, quoting Haskell Wikibook:
"Integer" is an arbitrary precision type: it will hold any number no
matter how big, up to the limit of your machine's memory…. This means
you never have arithmetic overflows. On the other hand it also means
your arithmetic is relatively slow. Lisp users may recognise the
"bignum" type here.
"Int" is the more common 32 or 64 bit integer. Implementations vary,
although it is guaranteed to be at least 30 bits.

How do I convert a 4 digit number into individual digits?

I need to write logic to break down a 4 digit number into individual digits.
On a reply here at SO to a question regarding 3 digits, someone gave the math below:
int first = 321/100;
int second = (321/10)-first*10;
int third = (321/1)-first*100-second*10;
Can someone help me?
Thank you in advance!
Well, using the sample you found, we can quite easily infer a code for you.
The first line says int first = 321/100;, which returns 3 (integer division is the euclidian one). 3 is indeed the first integer in 321 so that's a good thing. However, we have a 4 digit number, let's try replacing 100 with 1000:
int first = 4321/1000;
This does return 4 !
Let's try adapting the rest of your code (plus I put your four digit number in the variable entry).
int entry = 4321;
int first = entry/1000;
int second = entry/100 - first*10;
int third = entry/10 - first*100 - second*10;
int fourth = entry - first*1000 - second*100 - third*10;
second will be entry/100 (43) minus first*10 (40), so we're okay.
third is then 432 - 400 - 30 which turns to 2. This also works till fourth.
For more-than-four digits, you may want to use a for-loop and maybe some modulos though.
This snip of code counts the number of digits input from the user
then breaks down the digits one by one:
PRINT "Enter value";
INPUT V#
X# = V#
DO
IF V# < 1 THEN
EXIT DO
END IF
D = D + 1
V# = INT(V#) / 10
LOOP
PRINT "Digits:"; D
FOR L = D - 1 TO 0 STEP -1
M = INT(X# / 10 ^ L)
PRINT M;
X# = X# - M * 10 ^ L
NEXT
END

Extract LSB bit from a Byte in python

I have a byte in variable 'DATA'. I want to extract the LSB bit out of it and print it.
I'm very new to python, I found many articles with complex bitwise addition logic and all which was very tough to understand.
I'm looking for a simple logic like we do with the strings eg DATA[7:1]
Please help me out...
Is your "byte" an int? If so, just take bitwise AND (&) with 1 (or, if you want to be more explicit, the binary literal 0b1) to get the least significant bit.
>>> x = 14
>>> x & 1
0
>>> x = 15
>>> x & 1
1
Is your "byte" a bytes object? If so, just index into it and take bitwise AND.
>>> y = bytes([14, 15])
>>> y[0] & 1
0
>>> y[1] & 1
1
Simplest and probably fastest:
least_significant_bit_of_x = x & -x
You can find more tricks here: https://www.informit.com/articles/article.aspx?p=1959565
Although the go-to reference for bitwise "black magic" is Knuth's "The Art of Computer Programming, vol. 1".
Right shift by the number n and take the last bit by and 1
num >> n &1

algorithm/code in R to find pattern from any position in a string

I want to find the pattern from any position in any given string such that the pattern repeats for a threshold number of times at least.
For example for the string "a0cc0vaaaabaaaabaaaabaa00bvw" the pattern should come out to be "aaaab". Another example: for the string "ff00f0f0f0f0f0f0f0f0000" the pattern should be "0f".
In both cases threshold has been taken as 3 i.e. the pattern should be repeated for at least 3 times.
If someone can suggest an optimized method in R for finding a solution to this problem, please do share with me. Currently I am achieving this by using 3 nested loops, and it's taking a lot of time.
Thanks!
Use regular expressions, which are made for this type of stuff. There may be more optimized ways of doing it, but in terms of easy to write code, it's hard to beat. The data:
vec <- c("a0cc0vaaaabaaaabaaaabaa00bvw","ff00f0f0f0f0f0f0f0f0000")
The function that does the matching:
find_rep_path <- function(vec, reps) {
regexp <- paste0(c("(.+)", rep("\\1", reps - 1L)), collapse="")
match <- regmatches(vec, regexpr(regexp, vec, perl=T))
substr(match, 1, nchar(match) / reps)
}
And some tests:
sapply(vec, find_rep_path, reps=3L)
# a0cc0vaaaabaaaabaaaabaa00bvw ff00f0f0f0f0f0f0f0f0000
# "aaaab" "0f0f"
sapply(vec, find_rep_path, reps=5L)
# $a0cc0vaaaabaaaabaaaabaa00bvw
# character(0)
#
# $ff00f0f0f0f0f0f0f0f0000
# [1] "0f"
Note that with threshold as 3, the actual longest pattern for the second string is 0f0f, not 0f (reverts to 0f at threshold 5). In order to do this, I use back references (\\1), and repeat these as many time as necessary to reach threshold. I need to then substr the result because annoyingly base R doesn't have an easy way to get just the captured sub expressions when using perl compatible regular expressions. There is probably a not too hard way to do this, but the substr approach works well in this example.
Also, as per the discussion in #G. Grothendieck's answer, here is the version with the cap on length of pattern, which is just adding the limit argument and the slight modification of the regexp.
find_rep_path <- function(vec, reps, limit) {
regexp <- paste0(c("(.{1,", limit,"})", rep("\\1", reps - 1L)), collapse="")
match <- regmatches(vec, regexpr(regexp, vec, perl=T))
substr(match, 1, nchar(match) / reps)
}
sapply(vec, find_rep_path, reps=3L, limit=3L)
# a0cc0vaaaabaaaabaaaabaa00bvw ff00f0f0f0f0f0f0f0f0000
# "a" "0f"
find.string finds substring of maximum length subject to (1) substring must be repeated consecutively at least th times and (2) substring length must be no longer than len.
reps <- function(s, n) paste(rep(s, n), collapse = "") # repeat s n times
find.string <- function(string, th = 3, len = floor(nchar(string)/th)) {
for(k in len:1) {
pat <- paste0("(.{", k, "})", reps("\\1", th-1))
r <- regexpr(pat, string, perl = TRUE)
if (attr(r, "capture.length") > 0) break
}
if (r > 0) substring(string, r, r + attr(r, "capture.length")-1) else ""
}
and here are some tests. The last test processes the entire text of James Joyce's Ulysses in 1.4 seconds on my laptop:
> find.string("a0cc0vaaaabaaaabaaaabaa00bvw")
[1] "aaaab"
> find.string("ff00f0f0f0f0f0f0f0f0000")
[1] "0f0f"
>
> joyce <- readLines("http://www.gutenberg.org/files/4300/4300-8.txt")
> joycec <- paste(joyce, collapse = " ")
> system.time(result <- find.string2(joycec, len = 25))
user system elapsed
1.36 0.00 1.39
> result
[1] " Hoopsa boyaboy hoopsa!"
ADDED
Although I developed my answer before having seen BrodieG's, as he points out they are very similar to each other. I have added some features of his to the above to get the solution below and tried the tests again. Unfortunately when I added the variation of his code the James Joyce example no longer works although it does work on the other two examples shown. The problem seems to be in adding the len constraint to the code and may represent a fundamental advantage of the code above (i.e. it can handle such a constraint and such constraints may be essential for very long strings).
find.string2 <- function(string, th = 3, len = floor(nchar(string)/th)) {
pat <- paste0(c("(.", "{1,", len, "})", rep("\\1", th-1)), collapse = "")
r <- regexpr(pat, string, perl = TRUE)
ifelse(r > 0, substring(string, r, r + attr(r, "capture.length")-1), "")
}
> find.string2("a0cc0vaaaabaaaabaaaabaa00bvw")
[1] "aaaab"
> find.string2("ff00f0f0f0f0f0f0f0f0000")
[1] "0f0f"
> system.time(result <- find.string2(joycec, len = 25))
user system elapsed
0 0 0
> result
[1] "w"
REVISED The James Joyce test that was supposed to be testing find.string2 was actually using find.string. This is now fixed.
Not optimized (even it is fast) function , but I think it is more R way to do this.
Get all patterns of certains length > threshold : vectorized using mapply and substr
Get the occurrence of these patterns and extract the one with maximum occurrence : vectorized using str_locate_all.
Repeat 1-2 this for all lengths and tkae the one with maximum occurrence.
Here my code. I am creating 2 functions ( steps 1-2) and step 3:
library(stringr)
ss = "ff00f0f0f0f0f0f0f0f0000"
ss <- "a0cc0vaaaabaaaabaaaabaa00bvw"
find_pattern_length <-
function(length=1,ss){
patt = mapply(function(x,y) substr(ss,x,y),
1:(nchar(ss)-length),
(length+1):nchar(ss))
res = str_locate_all(ss,unique(patt))
ll = unlist(lapply(res,length))
list(patt = patt[which.max(ll)],
rep = max(ll))
}
get_pattern_threshold <-
function(ss,threshold =3 ){
res <-
sapply(seq(threshold,nchar(ss)),find_pattern_length,ss=ss)
res[,which.max(res['rep',])]
}
some tests:
get_pattern_threshold('ff00f0f0f0f0f0f0f0f0000',5)
$patt
[1] "0f0f0"
$rep
[1] 6
> get_pattern_threshold('ff00f0f0f0f0f0f0f0f0000',2)
$patt
[1] "f0"
$rep
[1] 18
Since you want at least three repetitions, there is a nice O(n^2) approach.
For each possible pattern length d cut string into parts of length d. In case of d=5 it would be:
a0cc0
vaaaa
baaaa
baaaa
baa00
bvw
Now look at each pairs of subsequent strings A[k] and A[k+1]. If they are equal then there is a pattern of at least two repetitions. Then go further (k+2, k+3) and so on. Finally you also check if suffix of A[k-1] and prefix of A[k+n] fit (where k+n is the first string that doesn't match).
Repeat it for each d starting from some upper bound (at most n/3).
You have n/3 possible lengths, then n/d strings of length d to check for each d. It should give complexity O(n (n/d) d)= O(n^2).
Maybe not optimal but I found this cutting idea quite neat ;)
For a bounded pattern (i.e not huge) it's best I think to just create all possible substrings first and then count them. This is if the sub-patterns can overlap. If not change the step fun in the loop.
pat="a0cc0vaaaabaaaabaaaabaa00bvw"
len=nchar(pat)
thr=3
reps=floor(len/2)
# all poss strings up to half length of pattern
library(stringr)
pat=str_split(pat, "")[[1]][-1]
str.vec=vector()
for(win in 2:reps)
{
str.vec= c(str.vec, rollapply(data=pat,width=win,FUN=paste0, collapse=""))
}
# the max length string repeated more than 3 times
tbl=table(str.vec)
tbl=tbl[tbl>=3]
tbl[which.max(nchar(names(tbl)))]
aaaabaa
3
NB Whilst I'm lazy and append/grow the str.vec here in a loop, for a larger problem I'm pretty sure the actual length of str.vec is predetermined by the length of the pattern if you care to work it out.
Here is my solution, it's not optimized (build vector with patterns <- c() ; pattern <- c(patterns, x) for example) and can be improve but simpler than yours, I think.
I can't understand which pattern exactly should (I just return the max) be returned but you can adjust the code to what you want exactly.
str <- "a0cc0vaaaabaaaabaaaabaa00bvw"
findPatternMax <- function(str){
nb <- nchar(str):1
length.patt <- rev(nb)
patterns <- c()
for (i in 1:length(nb)){
for (j in 1:nb[i]){
patterns <- c(patterns, substr(str, j, j+(length.patt[i]-1)))
}
}
patt.max <- names(which(table(patterns) == max(table(patterns))))
return(patt.max)
}
findPatternMax(str)
> findPatternMax(str)
[1] "a"
EDIT :
Maybe you want the returned pattern have a min length ?
then you can add a nchar.patt parameter for example :
nchar.patt <- 2 #For a pattern of 2 char min
nb <- nb[length.patt >= nchar.patt]
length.patt <- length.patt[length.patt >= nchar.patt]

Haskell flag pattern writing function?

I really need help in writing this function in Haskell, I don't even know where to start. Here are the specs:
Define a function flagpattern that takes a positive Int value greater than or equal to five and returns a String that can be displayed as the following `flag' pattern of dimension n, e.g.
Main> putStr (flagpattern 7)
#######
## ##
# # # #
# # #
# # # #
## ##
#######
Assuming you want a "X" enclosed in 4 lines, you need to write a function that given a coordinate (x,y) returns what character should be at that position:
coordinate n x y = if i == 0 then 'X' else ' '
(This version outputs only the leftmost X'es, modify it, remember indices start with 0)
Now you want them nicely arranged in a matrix, use a list comprehension, described in the linked text.
You should start from your problem definition:
main :: IO ()
main = putStr . flagPattern $ 7
Then, you should ask yourself about how much dots flag has:
flagPattern :: Int -> String
flagPattern = magic $ [1..numberOfDots]
Then, (hard) part of magic function should decide for each dot whether it is   or #:
partOfMagic ...
| ... = "#" -- or maybe even "#\n" in some cases?
| otherwise = " "
Then, you can concatenate parts into one string and get the answer.
Start with the type signature.
flagpattern :: Int -> String
Now break the problem into subproblems. For example, suppose I told you to produce row 2 of a size 7 flag pattern. You would write:
XX XX
Or row 3 of a size 7 flag pattern would be
X X X X
So suppose we had a function that could produce a given row. Then we'd have
flagpattern :: Int -> String
flagpattern size = unlines (??? flagrow ???)
flagrow :: Int -> Int -> String
flagrow row size = ???
unlines takes a list of Strings and turns it into a single String with newlines between each element of the list. See if you can define flagrow, and get it working correctly for any given row and size. Then see if you can use flagrow to define flagpattern.

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