Square but not cube
From Rosetta Code
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Show the first 30 positive integers which are squares but not cubes of such integers.
Optionally, show also the first 3 positive integers which are both squares and cubes - and mark them as such.
Contents
ALGOL 68[edit]
Avoids computing cube roots.
BEGIN
# list the first 30 numbers that are squares but not cubes and also #
# show the numbers that are both squares and cubes #
INT count := 0;
INT c := 1;
INT c3 := 1;
FOR s WHILE count < 30 DO
INT sq = s * s;
WHILE c3 < sq DO
c +:= 1;
c3 := c * c * c
OD;
print( ( whole( sq, -5 ) ) );
IF c3 = sq THEN
# the square is also a cube #
print( ( " is also the cube of ", whole( c, -5 ) ) )
ELSE
# square only #
count +:= 1
FI;
print( ( newline ) )
OD
END
- Output:
1 is also the cube of 1
4
9
16
25
36
49
64 is also the cube of 4
81
100
121
144
169
196
225
256
289
324
361
400
441
484
529
576
625
676
729 is also the cube of 9
784
841
900
961
1024
1089
AppleScript[edit]
on run
script listing
on |λ|(x)
set sqr to x * x
set strSquare to sqr as text
if isCube(sqr) then
strSquare & " (also cube)"
else
strSquare
end if
end |λ|
end script
unlines(map(listing, ¬
enumFromTo(1, 33)))
end run
-- isCube :: Int -> Bool
on isCube(x)
x = (round (x ^ (1 / 3))) ^ 3
end isCube
-- GENERIC FUNCTIONS -------------------------------------------------
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set lst to {}
repeat with i from m to n
set end of lst to i
end repeat
return lst
else
return {}
end if
end enumFromTo
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- unlines :: [String] -> String
on unlines(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set str to xs as text
set my text item delimiters to dlm
str
end unlines
- Output:
1 (also cube) 4 9 16 25 36 49 64 (also cube) 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 (also cube) 784 841 900 961 1024 1089
AWK[edit]
# syntax: GAWK -f SQUARE_BUT_NOT_CUBE.AWK
BEGIN {
while (n < 30) {
sqpow = ++square ^ 2
if (is_cube(sqpow) == 0) {
n++
printf("%4d\n",sqpow)
}
else {
printf("%4d is square and cube\n",sqpow)
}
}
exit(0)
}
function is_cube(x, i) {
for (i=1; i<=x; i++) {
if (i ^ 3 == x) {
return(1)
}
}
return(0)
}
- Output:
1 is square and cube 4 9 16 25 36 49 64 is square and cube 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 is square and cube 784 841 900 961 1024 1089
C[edit]
#include <stdio.h>
#include <math.h>
int main() {
int n = 1, count = 0, sq, cr;
for ( ; count < 30; ++n) {
sq = n * n;
cr = (int)cbrt((double)sq);
if (cr * cr * cr != sq) {
count++;
printf("%d\n", sq);
}
else {
printf("%d is square and cube\n", sq);
}
}
return 0;
}
- Output:
Same as Ring example.
F#[edit]
let rec fN n g φ=if φ<31 then match compare(n*n)(g*g*g) with | -1->printfn "%d"(n*n);fN(n+1) g (φ+1)
| 0->printfn "%d cube and square"(n*n);fN(n+1)(g+1)φ
| 1->fN n (g+1) φ
fN 1 1 1
- Output:
1 cube and square 4 9 16 25 36 49 64 cube and square 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 cube and square 784 841 900 961 1024 1089
Factor[edit]
USING: combinators interpolate io kernel prettyprint math
math.functions math.order pair-rocket ;
IN: rosetta-code.square-but-not-cube
: fn ( s c n -- s' c' n' )
dup 31 < [
2over [ sq ] [ 3 ^ ] bi* <=> {
+lt+ => [ [ dup sq . 1 + ] 2dip 1 + fn ]
+eq+ => [ [ dup sq [I ${} cube and squareI] nl 1 + ] [ 1 + ] [ ] tri* fn ]
+gt+ => [ [ 1 + ] dip fn ]
} case
] when ;
1 1 1 fn 3drop
- Output:
1 cube and square 4 9 16 25 36 49 64 cube and square 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 cube and square 784 841 900 961 1024 1089
Go[edit]
package main
import (
"fmt"
"math"
)
func main() {
for n, count := 1, 0; count < 30; n++ {
sq := n * n
cr := int(math.Cbrt(float64(sq)))
if cr*cr*cr != sq {
count++
fmt.Println(sq)
} else {
fmt.Println(sq, "is square and cube")
}
}
}
- Output:
1 is square and cube 4 9 16 25 36 49 64 is square and cube 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 is square and cube 784 841 900 961 1024 1089
Haskell[edit]
import Data.List (partition, sortBy)
import Control.Monad (join)
import Data.Ord (comparing)
isCube :: Int -> Bool
isCube n = n == round (fromIntegral n ** (1 / 3)) ^ 3
both, only :: [Int]
(both, only) = partition isCube $ join (*) <$> [1 ..]
-- TEST -----------------------------------------------------------
main :: IO ()
main =
(putStrLn . unlines) $
uncurry ((++) . show) <$>
sortBy
(comparing fst)
((flip (,) " (also cube)" <$> take 3 both) ++ (flip (,) "" <$> take 30 only))
Or simply
import Control.Monad (join)
cubeRoot :: Int -> Int
cubeRoot = round . (** (1 / 3)) . fromIntegral
isCube :: Int -> Bool
isCube = (==) <*> ((^ 3) . cubeRoot)
-- TEST ---------------------------------------------
main :: IO ()
main =
(putStrLn . unlines) $
(\x ->
show x ++
if isCube x
then concat [" (also cube of ", show (cubeRoot x), ")"]
else []) <$>
take 33 (join (*) <$> [1 ..])
Or, if we prefer a finite series to an infinite one
import Control.Applicative (liftA2)
isCube :: Int -> Bool
isCube = (==) <*> ((^ 3) . round . (** (1 / 3)) . fromIntegral)
squares :: Int -> Int -> [Int]
squares m n = (>>= id) (*) <$> [m .. n]
-- TEST ------------------------------------------------------------
main :: IO ()
main = (putStrLn . unlines) $ liftA2 (++) show label <$> squares 1 33
label :: Int -> String
label n
| isCube n = " (also cube)"
| otherwise = ""
- Output:
1 (also cube) 4 9 16 25 36 49 64 (also cube) 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 (also cube) 784 841 900 961 1024 1089
JavaScript[edit]
(() => {
'use strict';
const main = () =>
unlines(map(
x => x.toString() + (
isCube(x) ? (
` (cube of ${cubeRootInt(x)} and square of ${
Math.pow(x, 1/2)
})`
) : ''
),
map(x => x * x, enumFromTo(1, 33))
));
// isCube :: Int -> Bool
const isCube = n =>
n === Math.pow(cubeRootInt(n), 3);
// cubeRootInt :: Int -> Int
const cubeRootInt = n => Math.round(Math.pow(n, 1 / 3));
// GENERIC FUNCTIONS ----------------------------------
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = (m, n) =>
m <= n ? iterateUntil(
x => n <= x,
x => 1 + x,
m
) : [];
// iterateUntil :: (a -> Bool) -> (a -> a) -> a -> [a]
const iterateUntil = (p, f, x) => {
const vs = [x];
let h = x;
while (!p(h))(h = f(h), vs.push(h));
return vs;
};
// map :: (a -> b) -> [a] -> [b]
const map = (f, xs) => xs.map(f);
// unlines :: [String] -> String
const unlines = xs => xs.join('\n');
// MAIN ---
return main();
})();
- Output:
1 (cube of 1 and square of 1) 4 9 16 25 36 49 64 (cube of 4 and square of 8) 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 (cube of 9 and square of 27) 784 841 900 961 1024 1089
Kotlin[edit]
// Version 1.2.60
fun main(args: Array<String>) {
var n = 1
var count = 0
while (count < 30) {
val sq = n * n
val cr = Math.cbrt(sq.toDouble()).toInt()
if (cr * cr * cr != sq) {
count++
println(sq)
}
else {
println("$sq is square and cube")
}
n++
}
}
- Output:
Same as Ring example.
Pascal[edit]
Only using addition :-)
program SquareButNotCube;
var
sqN,
sqDelta,
SqNum,
cbN,
cbDelta1,
cbDelta2,
CbNum,
CountSqNotCb,
CountSqAndCb : NativeUint;
begin
CountSqNotCb := 0;
CountSqAndCb := 0;
SqNum := 0;
CbNum := 0;
cbN := 0;
sqN := 0;
sqDelta := 1;
cbDelta1 := 0;
cbDelta2 := 1;
repeat
inc(sqN);
inc(sqNum,sqDelta);
inc(sqDelta,2);
IF sqNum>cbNum then
Begin
inc(cbN);
cbNum := cbNum+cbDelta2;
inc(cbDelta1,6);// 0,6,12,18...
inc(cbDelta2,cbDelta1);//1,7,19,35...
end;
IF sqNum <> cbNUm then
Begin
writeln(sqNum :25);
inc(CountSqNotCb);
end
else
Begin
writeln(sqNum:25,sqN:10,'*',sqN,' = ',cbN,'*',cbN,'*',cbN);
inc(CountSqANDCb);
end;
until CountSqNotCb >= 30;//sqrt(High(NativeUint));
writeln(CountSqANDCb,' where numbers are square and cube ');
end.
- Output:
1 1*1 = 1*1*1
4
9
16
25
36
49
64 8*8 = 4*4*4
81
100
121
144
169
196
225
256
289
324
361
400
441
484
529
576
625
676
729 27*27 = 9*9*9
784
841
900
961
1024
1089
3 where numbers are square and cube
// there are 1625 numbers which are square and cube < High(Uint64)
//18412815093994140625 4291015625*4291015625 = 2640625*2640625*2640625
Perl[edit]
Hash[edit]
Use a hash to track state (and avoid floating-point math).
while ($cnt < 30) {
$n++;
$h{$n**2}++;
$h{$n**3}--;
$cnt++ if $h{$n**2} > 0;
}
print "First 30 positive integers that are a square but not a cube:\n";
print "$_ " for sort { $a <=> $b } grep { $h{$_} == 1 } keys %h;
print "\n\nFirst 3 positive integers that are both a square and a cube:\n";
print "$_ " for sort { $a <=> $b } grep { $h{$_} == 0 } keys %h;
- Output:
First 30 positive integers that are a square but not a cube: 4 9 16 25 36 49 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 784 841 900 961 1024 1089 First 3 positive integers that are both a square and a cube: 1 64 729
Generators[edit]
A more general approach involving generators/closures to implement 'lazy' lists as in the Perl 6 example. Using ideas and code from the very similar Generator exponential task. Output is the same as previous.
# return an anonymous subroutine that generates stream of specified powers
sub gen_pow {
my $m = shift;
my $e = 1;
return sub { return $e++ ** $m; };
}
# return an anonymous subroutine generator that filters output from supplied generators g1 and g2
sub gen_filter {
my($g1, $g2) = @_;
my $v1;
my $v2 = $g2->();
return sub {
while (1) {
$v1 = $g1->();
$v2 = $g2->() while $v1 > $v2;
return $v1 unless $v1 == $v2;
}
};
}
my $pow2 = gen_pow(2);
my $pow3 = gen_pow(3);
my $squares_without_cubes = gen_filter($pow2, $pow3);
print "First 30 positive integers that are a square but not a cube:\n";
print $squares_without_cubes->() . ' ' for 1..30;
my $pow6 = gen_pow(6);
print "\n\nFirst 3 positive integers that are both a square and a cube:\n";
print $pow6->() . ' ' for 1..3;
Perl 6[edit]
my @square-and-cube = map { .⁶ }, 1..Inf;
my @square-but-not-cube = (1..Inf).map({ .² }).grep({ $_ ∉ @square-and-cube[^@square-and-cube.first: * > $_, :k]});
put "First 30 positive integers that are a square but not a cube: \n", @square-but-not-cube[^30];
put "\nFirst 15 positive integers that are both a square and a cube: \n", @square-and-cube[^15];
- Output:
First 30 positive integers that are a square but not a cube: 4 9 16 25 36 49 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 784 841 900 961 1024 1089 First 15 positive integers that are both a square and a cube: 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 2985984 4826809 7529536 11390625
Python[edit]
# nonCubeSquares :: Int -> [(Int, Bool)]
def nonCubeSquares(n):
upto = enumFromTo(1)
ns = upto(n)
setCubes = set(x ** 3 for x in ns)
ms = upto(n + len(set(x * x for x in ns).intersection(
setCubes
)))
return list(tuple([x * x, x in setCubes]) for x in ms)
# squareListing :: [(Int, Bool)] -> [String]
def squareListing(xs):
justifyIdx = justifyRight(len(str(1 + len(xs))))(' ')
justifySqr = justifyRight(1 + len(str(xs[-1][0])))(' ')
return list(
'(' + str(1 + idx) + '^2 = ' + str(n) +
' = ' + str(round(n ** (1 / 3))) + '^3)' if bln else (
justifyIdx(1 + idx) + ' ->' +
justifySqr(n)
)
for idx, (n, bln) in enumerate(xs)
)
def main():
print(
unlines(
squareListing(
nonCubeSquares(30)
)
)
)
# GENERIC ------------------------------------------------------------------
# enumFromTo :: Int -> Int -> [Int]
def enumFromTo(m):
return lambda n: list(range(m, 1 + n))
# justifyRight :: Int -> Char -> String -> String
def justifyRight(n):
return lambda cFiller: lambda a: (
((n * cFiller) + str(a))[-n:]
)
# unlines :: [String] -> String
def unlines(xs):
return '\n'.join(xs)
main()
- Output:
(1^2 = 1 = 1^3) 2 -> 4 3 -> 9 4 -> 16 5 -> 25 6 -> 36 7 -> 49 (8^2 = 64 = 4^3) 9 -> 81 10 -> 100 11 -> 121 12 -> 144 13 -> 169 14 -> 196 15 -> 225 16 -> 256 17 -> 289 18 -> 324 19 -> 361 20 -> 400 21 -> 441 22 -> 484 23 -> 529 24 -> 576 25 -> 625 26 -> 676 (27^2 = 729 = 9^3) 28 -> 784 29 -> 841 30 -> 900 31 -> 961 32 -> 1024 33 -> 1089
REXX[edit]
Programming note: line 11 could've been written as:
sq= j**2; cube= j**3 /*compute the square of J and the cube.*/
It would've been slightly easier to read, but a bit slower to compute.
/*REXX pgm shows N ints>0 that are squares and not cubes, & which are squares and cubes.*/
parse arg N . /*obtain optional argument from the CL.*/
if N=='' | N=="," then N=30 /*Not specified? Then use the default.*/
w= length(N) + 3 /*W: used for aligning output columns.*/
say ' count ' /*display the 1st line of the title. */
say ' ───────' /* " " 2nd " " " " */
@@= 'is a square and' /*a text literal used for the displays.*/
$.= 0; @.= 0 /*arrays for computed: squares; cubes.*/
#=0 /*count (integer): squares & not cubes.*/
do j=1 until #==N /*loop 'til enough " " " " */
sq= j*j; cube= sq*j /*compute the square of J and the cube.*/
$.sq= 1; @.cube= 1 /*populate square array; pop cube array*/
if $.j then do; z= @.j /*if J is a square, then get value. */
if \@.j then #= #+1 /*bump counter of squares and not cubes*/
if @.z then _= right(j, 3*w) @@ "a cube"
else _= right(#': ' right(j, w), 3*w) @@ " not a cube"
say _
end
end /*j*/ /*stick a fork in it, we're all done. */
- output when using the default input:
count
───────
1 is a square and a cube
1: 4 is a square and not a cube
2: 9 is a square and not a cube
3: 16 is a square and not a cube
4: 25 is a square and not a cube
5: 36 is a square and not a cube
6: 49 is a square and not a cube
64 is a square and a cube
7: 81 is a square and not a cube
8: 100 is a square and not a cube
9: 121 is a square and not a cube
10: 144 is a square and not a cube
11: 169 is a square and not a cube
12: 196 is a square and not a cube
13: 225 is a square and not a cube
14: 256 is a square and not a cube
15: 289 is a square and not a cube
16: 324 is a square and not a cube
17: 361 is a square and not a cube
18: 400 is a square and not a cube
19: 441 is a square and not a cube
20: 484 is a square and not a cube
21: 529 is a square and not a cube
22: 576 is a square and not a cube
23: 625 is a square and not a cube
24: 676 is a square and not a cube
729 is a square and a cube
25: 784 is a square and not a cube
26: 841 is a square and not a cube
27: 900 is a square and not a cube
28: 961 is a square and not a cube
29: 1024 is a square and not a cube
30: 1089 is a square and not a cube
Ring[edit]
# Project : Square but not cube
limit = 30
num = 0
sq = 0
while num < limit
sq = sq + 1
sqpow = pow(sq,2)
flag = iscube(sqpow)
if flag = 0
num = num + 1
see sqpow + nl
else
see "" + sqpow + " is square and cube" + nl
ok
end
func iscube(cube)
for n = 1 to cube
if pow(n,3) = cube
return 1
ok
next
return 0
Output:
1 is square and cube 4 9 16 25 36 49 64 is square and cube 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 is square and cube 784 841 900 961 1024 1089
Sidef[edit]
var square_and_cube = Enumerator({|f|
1..Inf -> each {|n| f(n**6) }
})
var square_but_not_cube = Enumerator({|f|
1..Inf -> lazy.map {|n| n**2 }.grep {|n| !n.is_power(3) }.each {|n| f(n) }
})
say "First 30 positive integers that are a square but not a cube:"
say square_but_not_cube.first(30).join(' ')
say "First 15 positive integers that are both a square and a cube:"
say square_and_cube.first(15).join(' ')
- Output:
First 30 positive integers that are a square but not a cube: 4 9 16 25 36 49 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 784 841 900 961 1024 1089 First 15 positive integers that are both a square and a cube: 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 2985984 4826809 7529536 11390625
zkl[edit]
println("First 30 positive integers that are a square but not a cube:");
squareButNotCube:=(1).walker(*).tweak(fcn(n){
sq,cr := n*n, sq.toFloat().pow(1.0/3).round(); // cube root(64)<4
if(sq==cr*cr*cr) Void.Skip else sq
});
squareButNotCube.walk(30).concat(",").println("\n");
println("First 15 positive integers that are both a square and a cube:");
println((1).walker(*).tweak((1).pow.unbind().fp1(6)).walk(15));
- Output:
First 30 positive integers that are a square but not a cube: 4,9,16,25,36,49,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,784,841,900,961,1024,1089 First 15 positive integers that are both a square and a cube: L(1,64,729,4096,15625,46656,117649,262144,531441,1000000,1771561,2985984,4826809,7529536,11390625
