In-between fractions

Question

In-between fractions

The challenge:

You will need to create code that takes atleast 3 inputs; 2 integers and "a fraction representation" - whichever type suits your language for representing the fraction increments) ie. If you choose string the input would be "1/4" or you could choose 2 extra integer inputs or a tuple or w/e.

Input can be anywhere reasonable (STDIN, function arguments, from a file, etc.), and so can output (STDOUT, function return value, to a file, etc.)

Rules:

1. The input "fraction" will always be a valid fraction, less than 1; example "1/4"
2. The second input integer will always have a higher value than the first integer. I.E the first input integer will always have a lower value than the second.
3. The input integers can be negative.
4. Outputted fractions should be reduced as much as possible (simplified)

The code will need to output every "fraction step" between the 2 numbers in increments of the input fraction.

The code should be a program or function as stated here

Example 1:

Input: -2,3,"1/2"

Output:

 -2
 -3/2 
 -1 
 -1/2 
  0 
  1/2 
  1 
  3/2  
  2 
  5/2 
  3

Example 2:

Input: 1,2,"2/3"

Output:

1
5/3
2

or

1
4/3
2

Note: Counting can start from either direction (thank you @Mego)

This is code-golf, so the shortest answer in bytes wins.

Answer 1

Octave, 34 30 bytes

@(a,b,c)rats(union([a:c:b],b))

Now takes the fraction as a numeric expression rather than separate numerator and denominator.

Sample on ideone

Answer 2

Mathematica, 16 bytes

Range@##⋃{#2}&

An unnamed function that takes two integers and a rational number and returns a list of numbers, e.g.:

Range@##⋃{#2}&[-2, 3, 1/2]
(* {-2, -(3/2), -1, -(1/2), 0, 1/2, 1, 3/2, 2, 5/2, 3} *)

Mathematica's Range does exactly what the challenge asks, except that it omits the upper bound if the difference between lower and upper bound isn't exactly a multiple of the step size. Therefore we take the Union (using ⋃) with the list containing only the upper bound which ensures that it appears exactly once. Note that Union will sort the result but we want it sorted anyway, since the step size is always positive. Also since we're working with rationals, they're automatically reduced as much as possible.

Answer 3

T-SQL 2012+, 831 535 477 270 246 240 219 bytes

Please note this is a one liner - sql doesn't have build in function to reduce the fraction. May not be the best language for this type of question. It is human readable(kind of - compared to some of the other languages).

DECLARE @f INT=-5,@t INT=3,@n INT=3,@ INT=8;

WITH C as(SELECT
top((@t*@-@f*@)/@n+1)ROW_NUMBER()OVER(ORDER BY @)M
FROM sys.messages)SELECT(SELECT
IIF(V%@=0,LEFT(V/@,9),CONCAT(V/MAX(M),'/',ABS(@)/MAX(M)))FROM c
WHERE V%M=0AND @%M=0)FROM(SELECT
@f*@+@n*~-M V FROM c)k

Try it online

Answer 4

Python 2, 81 bytes

from fractions import*
a,b,c=map(Fraction,input())
while a<b:print a;a+=c
print b

Try it online

Answer 5

Ruby, 32 54 48 bytes

->a,b,c{(a..b).step(c){|x|p x%1>0?x:x.to_i};p b}

This solution is based on Mego's Python answer and assumes that c will always be a Rational, Ruby's fraction format. Try it online!

Edit: Fixed a bug where integers weren't presented like integers. -6 bytes thanks to Not That Charles and MegaTom.

The functions are called in this way:

> f=->a,b,c{(a..b).step(c){|x|p x%1>0?x:x.to_i};p b}
> f[1,4,Rational(2,3)]
1
(5/3)
(7/3)
3
(11/3)
4

Answer 6

Haskell, 31 26 bytes

f a b c=min[b]$a:f(a+c)b c

Lazy evaluation FTW! Demo:

*Main> import Data.Ratio
*Main Data.Ratio> f (-2) 3 (1%2)
[(-2) % 1,(-3) % 2,(-1) % 1,(-1) % 2,0 % 1,1 % 2,1 % 1,3 % 2,2 % 1,5 % 2,3 % 1]
*Main Data.Ratio> f 1 2 (2%3)
[1 % 1,5 % 3,2 % 1]

(I was initially tempted by Haskell’s [a,a+c..b] notation, but it has some quirks that necessitate something like f a b c|l<-[a,a+c..b-c/2]=l++[b|last l<b] for 41 bytes or f a b c=[x|x<-[a,a+c..],x<b]++[b] for 33.)

Answer 7

MATL, 16 15 bytes

3$:3Gvu9X10ZGZD

This may fail for very large denominators. I hope output format is acceptable.

Try it online!

3$:    % take three inputs and generate range
3G     % push third input again
v      % vertically concatenate. Gives vertical array as output 
u      % get unique elements (i.e. remove the last one if it is repeated)
9X1    % predefined literal 'rat'
0ZG    % set rational format
ZD     % display using that format

Answer 8

Matlab with Symbolic Toolbox / Octave with SymPy, 27 bytes

Thanks to @sanchises for pointing out an error, now corrected

@(a,b,c)sym(union(a:c:b,b))

This is an anonymous function. To call it, assign it to a variable or use ans.

Example:

>> @(a,b,c)sym(union(a:c:b,b))
ans = 
    @(a,b,c)sym(union(a:c:b,b))
>> ans(-2,3,1/2)
ans =
[ -2, -3/2, -1, -1/2, 0, 1/2, 1, 3/2, 2, 5/2, 3]

Answer 9

Julia, 14 bytes

f(a,b,c)=a:c:b

This is similar to the Mathematica answer, except that Julia's ranges are already in the desired format, so it is even shorter. Also returns a collection of numbers. Example output:

11-element StepRange{Rational{Int64},Rational{Int64}}:
 -3//1,-5//2,-2//1,-3//2,-1//1,-1//2,0//1,1//2,1//1,3//2,2//1

Note that the integers are displayed with 1 in the denominator, and a double-slash is used for fractions. To get the output exactly as defined in the question requires some more code:

f(a,b,c)=map(x->println(x.num,x.den<2?"":"/$(x.den)"),a:c:b)

Answer 10

Javascript, 108 90 86  81 bytes

(a,b,n,d)=>{var s="";for(a=a*d;a<b*d;a+=n)s+=(a%d?a+"/"+d:a/d)+" ";s+=b;return s}

An anonymous function. After assignment to a named variable with white space:

var f=(a,b,n,d)=>
{ var s="";
  for(a=a*d; a<b*d; a+=n)
    s+= (a%d ? a + "/" + d : a/d) + " ";
  s+=b;
  return s
}

Test examples:

console.log(f(1,2,1,8)); //writes:
1 9/8 10/8 11/8 12/8 13/8 14/8 15/8 2

console.log(f(-3,3,4,7)); // writes:
-3 -17/7 -13/7 -9/7 -5/7 -1/7 3/7 1 11/7 15/7 19/7 3 

An imperative approach using javascript, no recursion, library or functional programming.

Answer 11

Pyret, 56 bytes

{(b,e,n,d):link(e,map(_ / d,range(b * d, e * d))).sort()}

Takes in beginning (b), end (e), numerator (n), and denominator (d). Creates a range of integers, divides those through and appends the end to the list (by linking and then sorting).

Answer 12

Smalltalk – 89 bytes

For once Smalltalk is almost competitive!

Number extend[p:e q:i[|h|self to:e by:i do:[:x|h:=x. x printNl].h=e ifFalse:[e printNl]]]

Call like this:

> 2 p:5 q:1/2
2
5/2
3
7/2
4
9/2
5

> 1 p:2 q:2/3
1
5/3
2

Answer 13

R - 71 bytes

Assumes you have already installed the MASS package

f=function(x,y,z)MASS::fractions(union(seq(x,y,eval(parse(text=z))),y))

> f(1, 2, '1/3')
[1]   1 4/3 5/3   2
> f(2, 5, '1/2')
[1]   2 5/2   3 7/2   4 9/2   5