Coprimes
p and q are coprimes if they have no common factors other than 1.
Let input: [21,15],[17,23],[36,12],[18,29],[60,15]
- Task
APL
<lang apl>(⊢(/⍨)1=∨/¨) (21 15)(17 23)(36 12)(18 29)(60 15)</lang>
- Output:
┌─────┬─────┐ │17 23│18 29│ └─────┴─────┘
AppleScript
<lang applescript>on hcf(a, b)
repeat until (b = 0)
set x to a
set a to b
set b to x mod b
end repeat
if (a < 0) then return -a
return a
end hcf
local input, coprimes, thisPair, p, q set input to {{21, 15}, {17, 23}, {36, 12}, {18, 29}, {60, 15}} set coprimes to {} repeat with thisPair in input
set {p, q} to thisPair
if (hcf(p, q) is 1) then set end of coprimes to thisPair's contents
end repeat return coprimes</lang>
- Output:
<lang applescript>{{17, 23}, {18, 29}}</lang>
or, composing a definition and test from more general functions:
<lang applescript>------------------------- COPRIME ------------------------
-- coprime :: Int -> Int -> Bool on coprime(a, b)
1 = gcd(a, b)
end coprime
TEST -------------------------
on run
script test
on |λ|(xy)
set {x, y} to xy
coprime(x, y)
end |λ|
end script
filter(test, ¬
{[21, 15], [17, 23], [36, 12], [18, 29], [60, 15]})
end run
GENERIC ------------------------
-- abs :: Num -> Num on abs(x)
-- Absolute value.
if 0 > x then
-x
else
x
end if
end abs
-- filter :: (a -> Bool) -> [a] -> [a]
on filter(p, xs)
tell mReturn(p)
set lst to {}
set lng to length of xs
repeat with i from 1 to lng
set v to item i of xs
if |λ|(v, i, xs) then set end of lst to v
end repeat
lst
end tell
end filter
-- gcd :: Int -> Int -> Int
on gcd(a, b)
set x to abs(a)
set y to abs(b)
repeat until y = 0
if x > y then
set x to x - y
else
set y to y - x
end if
end repeat
return x
end gcd
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper.
if script is class of f then
f
else
script
property |λ| : f
end script
end if
end mReturn</lang>
- Output:
{{17, 23}, {18, 29}}
Factor
<lang factor>USING: io kernel math prettyprint sequences ;
- coprime? ( seq -- ? ) [ ] [ simple-gcd ] map-reduce 1 = ;
{
{ 21 15 }
{ 17 23 }
{ 36 12 }
{ 18 29 }
{ 60 15 }
{ 21 22 25 31 143 }
} [ dup pprint coprime? [ " Coprime" write ] when nl ] each</lang>
- Output:
{ 21 15 }
{ 17 23 } Coprime
{ 36 12 }
{ 18 29 } Coprime
{ 60 15 }
{ 21 22 25 31 143 } Coprime
Go
Uses the same observation as the Wren entry. <lang go>package main
import (
"fmt" "rcu"
)
func main() {
pairs := [][2]int{{21, 15}, {17, 23}, {36, 12}, {18, 29}, {60, 15}}
fmt.Println("The following pairs of numbers are coprime:")
for _, pair := range pairs {
if rcu.Gcd(pair[0], pair[1]) == 1 {
fmt.Println(pair)
}
}
}</lang>
- Output:
The following pairs of numbers are coprime: [17 23] [18 29]
Haskell
<lang haskell>------------------------- COPRIMES -----------------------
coprime :: Integral a => a -> a -> Bool coprime a b = 1 == gcd a b
TEST -------------------------
main :: IO () main =
print $
filter
((1 ==) . uncurry gcd)
[ (21, 15),
(17, 23),
(36, 12),
(18, 29),
(60, 15)
]</lang>
- Output:
[(17,23),(18,29)]
Julia
<lang julia>filter(p -> gcd(p...) == 1, [[21,15],[17,23],[36,12],[18,29],[60,15],[21,22,25,31,143]])
</lang>
- Output:
3-element Vector{Vector{Int64}}:
[17, 23] [18, 29] [21, 22, 25, 31, 143]
Phix
function gcd1(sequence s) return gcd(s)=1 end function ?filter({{21,15},{17,23},{36,12},{18,29},{60,15}},gcd1)
- Output:
{{17,23},{18,29}}
A longer set/element such as {21,22,25,30,143} would also be shown as coprime, since it is, albeit not pairwise coprime - for the latter you would need something like:
function pairwise_coprime(sequence s) for i=1 to length(s)-1 do for j=i+1 to length(s) do if gcd(s[i],s[j])!=1 then return false end if end for end for return true end function ?filter({{21,15},{17,23},{36,12},{18,29},{60,15},{21, 22, 25, 31, 143}},pairwise_coprime)
Output is the same as the above, because this excludes the {21, 22, 25, 31, 143}, since both 22 and 143 are divisible by 11.
Python
<lang python>Coprimes
from math import gcd
- coprime :: Int -> Int -> Bool
def coprime(a, b):
True if a and b are coprime. return 1 == gcd(a, b)
- ------------------------- TEST -------------------------
- main :: IO ()
def main():
List of pairs filtered for coprimes
print([
xy for xy in [
(21, 15), (17, 23), (36, 12),
(18, 29), (60, 15)
]
if coprime(*xy)
])
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
[(17, 23), (18, 29)]
Raku
How do you determine if numbers are co-prime? Check to see if the Greatest common divisor is equal to one. Since we're duplicating tasks willy-nilly, lift code from that task, (or in this case, just use the builtin).
<lang perl6>say .raku, ( [gcd] |$_ ) == 1 ?? ' Coprime' !! for [21,15],[17,23],[36,12],[18,29],[60,15],[21,22,25,31,143]</lang>
[21, 15] [17, 23] Coprime [36, 12] [18, 29] Coprime [60, 15] [21, 22, 25, 31, 143] Coprime
REXX
<lang rexx>/*REXX prgm tests number sequences (min. of two #'s, separated by a commas) if comprime.*/ parse arg @ /*obtain optional arguments from the CL*/ if @= | @=="," then @= '21,15 17,23 36,12 18,29 60,15 21,22,25,143 -2,0 0,-3'
do j=1 for words(@); say /*process each of the sets of numbers. */
stuff= translate( word(@, j), , ',') /*change commas (,) to blanks for GCD.*/
cofactor= gcd(stuff) /*get Greatest Common Divisor of #'s.*/
if cofactor==1 then say stuff " ─────── are coprime ───────"
else say stuff " have a cofactor of: " cofactor
end /*j*/
exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ gcd: procedure; parse arg $ /*╔═══════════════════════════════════╗*/
do #=2 for arg()-1; $= $ arg(#) /*║This GCD handles multiple arguments║*/
end /*#*/ /*║ & multiple numbers per argument, &║*/
parse var $ x z . /*║negative numbers and non-integers. ║*/
if x=0 then x= z; x= abs(x) /*╚═══════════════════════════════════╝*/
do j=2 to words($); y= abs( word($, j) ); if y=0 then iterate
do until _==0; _= x // y; x= y; y= _
end /*until*/
end /*j*/
return x</lang>
- output when using the default inputs:
21,15 have a cofactor of: 3 17,23 ─────── are coprime ─────── 36,12 have a cofactor of: 12 18,29 ─────── are coprime ─────── 60,15 have a cofactor of: 15 21,22,25,143 ─────── are coprime ─────── -2,0 have a cofactor of: 2 0,-3 have a cofactor of: 3
Ring
<lang ring> see "working..." + nl row = 0 Coprimes = [[21,15],[17,23],[36,12],[18,29],[60,15]] input = "input: [21,15],[17,23],[36,12],[18,29],[60,15]" see input + nl see "Coprimes are:" + nl
lncpr = len(Coprimes) for n = 1 to lncpr
flag = 1
if Coprimes[n][1] < Coprimes[n][2]
min = Coprimes[n][1]
else
min = Coprimes[n][2]
ok
for m = 2 to min
if Coprimes[n][1]%m = 0 and Coprimes[n][2]%m = 0
flag = 0
exit
ok
next
if flag = 1
row = row + 1
see "" + Coprimes[n][1] + " " + Coprimes[n][2] + nl
ok
next
see "Found " + row + " coprimes" + nl see "done..." + nl </lang>
- Output:
working... input: [21,15],[17,23],[36,12],[18,29],[60,15] Coprimes are: 17 23 18 29 Found 2 coprimes done...
Wren
Two numbers are coprime if their GCD is 1. <lang ecmascript>import "/math" for Int
var pairs = [[21,15],[17,23],[36,12],[18,29],[60,15]] System.print("The following pairs of numbers are coprime:") for (pair in pairs) if (Int.gcd(pair[0], pair[1]) == 1) System.print(pair)</lang>
- Output:
The following pairs of numbers are coprime: [17, 23] [18, 29]