Replace me by the sum of my cyclic successors!

Question

I have a simple challenge for you this time. Given an array of positive integers A (or the equivalent in your language), replace each entry A_i with the sum of the next A_i elements of A, cycling back from the beginning if there are not enough items.

As usual, you can compete in any programming language and can take input and provide output through any standard method and in any reasonable format, while taking note that these loopholes are forbidden by default. You may optionally take the size of A as input too. This is code-golf, so the shortest submission (in bytes) for every language wins.

Examples / Test Cases

Given [1,3,4,5], your code should output [3,10,13,14], because 1 is replaced by 3, 3 is replaced by 4+5+1=10 (notice how it wrapped back from the start), 4 by 5+1+3+4=13 and 5 by 1+3+4+5+1=14.

Given [3,2,1,9], your program should produce [12,10,9,33], because we substitute 3 with 2+1+9=12, 2 with 1+9=10, 1 with 9 and 9 with 3+2+1+9+3+2+1+9+3=33 (notice how we wrapped back from the start more than once).

Some more test cases for you to choose from:

[4,3,2,1]                       -> [10,7,5,4]
[3,2,1,9]                       -> [12,10,9,33]
[1,3,4,5]                       -> [3,10,13,14]
[4,4,3,2,2]                     -> [11,11,8,6,8]
[3,5,3,2,1]                     -> [10,14,6,4,3]
[3,2,4,3,2,1,1]                 -> [9,7,7,4,2,1,3]
[7,8,6,5,4,3,2,1,5]             -> [29,33,20,15,11,8,6,5,30]
[28,2,4,2,3,2,3,4,5,3]          -> [137,6,10,5,9,7,12,38,39,34]
[1,2,3,4,5,4,3,2,1,2,3,4,3,2,1] -> [2,7,13,14,12,8,5,3,2,7,9,7,4,2,1]

Answer 1

MATL, 10 9 bytes

"G@:X@+)s

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	% implicit input
"	% for loop, iterate over the input array 
G	% push input x
@	% push for loop index, x[i]
:	% range, push [1,...,x[i]]
X@	% push for loop index, i
+	% sum, so stack holds [i+1,...,i+x[i]]
)	% index, modularly, so gets the cyclic successors
s	% sum cyclic successors, leaving the sum on the stack
	% implicit end of for loop
	% implicit output of stack

Answer 2

Jelly, 6 bytes

ṙJṁS¥"

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Answer 3

Python, 55 bytes

lambda a:[sum((-~v*a)[i:i+v])for i,v in enumerate(a,1)]

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Answer 4

J, 33 bytes

[:({.+/@{.}.)"1 i.@#|."{($~>./*#)

ungolfed

[: ({. +/@{. }.)"1 i.@# |."0 _ ($~ (>./ * #))

explanation

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Answer 5

C (gcc), 86 85 bytes

• Saved a byte thanks to Jakob.

C(y,c,l,i,k)int*y;{for(l=~0;++l<c;printf("%d,",k))for(k=i=0;i++<y[l];k+=y[(l+i)%c]);}

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Answer 6

Haskell, 50 47 44 bytes

zipWith((sum.).take)<*>scanr(:)[].tail.cycle

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                    -- <*> in function context is Haskell's S combinator, i.e.
                    --     (zipWith ... <*> scanr ...) arg
                    -- resovles to
                    --     zipWith ... arg (scanr ... arg)
zipWith             -- so we zip
                    --   the input list and
 scanr(:)[]         --   the tails (tails of [1,2,3] are [[1,2,3],[2,3],[3],[]])
      tail          --   of the tail of
          cycle     --   and infinite cycle of the input list
                    -- with the function
 (sum.).take        --   take that many elements given by the element
                    --   of the input list from the list given by the inits
                    --   and sum it   

Answer 7

05AB1E, 8 7 bytes

εL¾+èO¼

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Explanation

ε        # apply to each element x of the input
 L       # push range [1 ... x]
  ¾+     # add counter to each (initially 0)
    è    # cyclically index into input with each
     O   # sum
      ¼  # increment counter

Answer 8

K4 / K (oK), 20 19 bytes

Solution:

+/'x#'1_(1+2##x)#x:

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Examples:

q)k)+/'x#'1_(1+2##x)#x:1 3 4 5
3 10 13 14
q)k)+/'x#'1_(1+2##x)#x:4 3 2 1
10 7 5 4
q)k)+/'x#'1_(1+2##x)#x:3 2 4 3 2 1 1
9 7 7 4 2 1 3
q)k)+/'x#'1_(1+2##x)#x:1 2 3 4 5 4 3 2 1 2 3 4 3 2 1
2 7 13 14 12 8 5 3 2 7 9 7 4 2 1

Explanation:

Reshape input, drop first, take x length of each, sum up.

+/'x#'1_(1+2##x)#x: / the solution
                 x: / store input as x
                #   / reshape
        (      )    / do this together
             #x     / count x
           2#       / duplicate (2-take)
         1+         / add 1
      1_            / 1 drop (_), remove first element
   x#'              / x take each-both
+/'                 / sum (+/) each

Answer 9

R, 62 58 bytes

function(a,l)diag(diffinv(matrix(a,max(a)*l+1,l))[a+2,])-a

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An alternative to the other R solution. In the comments JayCe made a mention of cumsum which triggered something in my brain to use diffinv and matrix recycling instead of rep.

Explanation:

Given input array a, let M=max(a) and l=length(a).

Observe that M+l is the maximum possible index we'd need to access, and that M+l<=M*l+1, since if M,l>1,M+l<=M*l (with equality only when M=l=2) and if l==1 or M==1, then M+l==M*l+1.

By way of example, let a=c(4,3,2,1). Then M=l=4.

We construct the M*l+1 x l matrix in R by matrix(a,max(a)*l+1,l). Because R recycles a in column-major order, we end up with a matrix repeating the elements of a as such:

      [,1] [,2] [,3] [,4]
 [1,]    4    3    2    1
 [2,]    3    2    1    4
 [3,]    2    1    4    3
 [4,]    1    4    3    2
 [5,]    4    3    2    1
 [6,]    3    2    1    4
 [7,]    2    1    4    3
 [8,]    1    4    3    2
 [9,]    4    3    2    1
[10,]    3    2    1    4
[11,]    2    1    4    3
[12,]    1    4    3    2
[13,]    4    3    2    1
[14,]    3    2    1    4
[15,]    2    1    4    3
[16,]    1    4    3    2
[17,]    4    3    2    1

Each column is the cyclic successors of each element of a, with a across the first row; this is due to the way that R recycles its arguments in a matrix.

Next, we take the inverse "derivative" with diffinv, essentially the cumulative sum of each column with an additional 0 as the first row, generating the matrix

      [,1] [,2] [,3] [,4]
 [1,]    0    0    0    0
 [2,]    4    3    2    1
 [3,]    7    5    3    5
 [4,]    9    6    7    8
 [5,]   10   10   10   10
 [6,]   14   13   12   11
 [7,]   17   15   13   15
 [8,]   19   16   17   18
 [9,]   20   20   20   20
[10,]   24   23   22   21
[11,]   27   25   23   25
[12,]   29   26   27   28
[13,]   30   30   30   30
[14,]   34   33   32   31
[15,]   37   35   33   35
[16,]   39   36   37   38
[17,]   40   40   40   40
[18,]   44   43   42   41

In the first column, entry 6=4+2 is equal to 14=4 + (3+2+1+4), which is the cyclic successor sum (CSS) plus a leading 4. Similarly, in the second column, entry 5=3+2 is equal to 10=3 + (4+1+2), and so forth.

So in column i, the a[i]+2nd entry is equal to CSS(i)+a[i]. Hence, we take rows indexed by a+2, yielding a square matrix:

     [,1] [,2] [,3] [,4]
[1,]   14   13   12   11
[2,]   10   10   10   10
[3,]    9    6    7    8
[4,]    7    5    3    5

The entries along the diagonal are equal to the cyclic successor sums plus a, so we extract the diagonal and subtract a, returning the result as the cyclic successor sums.

Answer 10

Jelly, 7 bytes

R+"Jị⁸§

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Answer 11

Attache, 26 bytes

{Sum=>_[(_2+1:_)%#_]}#Iota

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Explanation

This is a fork of two functions:

• {Sum=>_[(_2+1:_)%#_]}
• Iota

What this means is, the right tine Iota is applied to the argument x and is passed as the second argument to the center tine (the first function). So this becomes, for input x:

{Sum=>_[(_2+1:_)%#_]}[x, Iota[x]]

Replacing those in for _ and _2:

Sum => x[(Iota[x] + 1:x) % #x]

Iota[x] returns an array of the indices of x. It's equivalent to 0...#x. #x is a short way of saying the size of x, or Size[x]. In essence, this function is mapping the Sum function over the second expression:

x[(Iota[x] + 1:x) % #x]

The outer x[...] bit means that ... will generate a series of indices to be selected from x. The most important part of generating the indices is this:

Iota[x] + 1:x

This expression uses a bit of vectorization. To visualize this, let's suppose the input is x := [1, 3, 4, 5]. Then, this expression is equivalent to:

Iota[[1, 3, 4, 5]] + 1:[1, 3, 4, 5]
[0, 1, 2, 3] + [1:1, 1:3, 1:4, 1:5]
[0, 1, 2, 3] + [[1], [1, 2, 3], [1, 2, 3, 4], [1, 2, 3, 4, 5]]
[0 + [1], 1 + [1, 2, 3], 2 + [1, 2, 3, 4], 3 + [1, 2, 3, 4, 5]]
[[0 + 1], [1 + 1, 1 + 2, 1 + 3], [2 + 1, 2 + 2, 2 + 3, 2 + 4], [3 + 1, 3 + 2, 3 + 3, 3 + 4, 3 + 5]]
[[1], [2, 3, 4], [3, 4, 5, 6], [4, 5, 6, 7, 8]]

This is a list of indices which represent the indices next N elements in x mod #x. To make them safe for retrieval, we take this array mod #x:

(Iota[x] + 1:x) % #x

This gives us the proper indices, which are then obtained from x and each array is summed, giving the proper results.

Other attempts

36 bytes: {Sum@_&Get=>((_2+1.._2+_)%#_)}#Iota - I forgot x[...] fully vectorizes, so that becomes:

30 bytes: {Sum=>_[(_2+1.._2+_)%#_]}#Iota - but then I realized the _2+ in the inner range could be factored out, which means we could save parentheses by using : instead of .., giving us the current version.

Answer 12

R, 89 64 bytes

j=rep(x<-scan(),max(x));Map(function(u,v)sum(j[v+1:u]),x,seq(x))

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Main idea to to generate a way-long-enough cycling index vector you can use to get the needed elements from the input vector.

Original version:

function(x,i=seq(x),j=rep(i,max(x))){for(k in i){T=c(T,sum(x[j[(k+1):(k+x[k])]]))};T[-1]}

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Answer 13

Pyth, 13 11 bytes

.esm@Q+dkSb

Saved 2 bytes thanks to Mr. Xcoder.
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Explanation

.esm@Q+dkSb
.e         Q   For each index k and value b in (implicit) input...
         Sb    ... get the list [1, ..., b]...
   m  +dk      ... add k to each...
    @Q         ... and index into the input...
  s            ... then take the sum.

Answer 14

Charcoal, 12 bytes

ＩＥθΣＥι§θ⊕⁺κλ

Try it online! Link is to verbose version of code. Explanation:

  θ             Input array
 Ｅ              Map over elements
     ι          Current element
    Ｅ           Map over implicit range
           λ    Inner index
          κ     Outer index
         ⁺      Sum
        ⊕       Increment
       θ        Input array
      §         Cyclically index
   Σ            Sum
Ｉ               Cast to string
                Implicitly print on separate lines

Answer 15

JavaScript ES6, 65 bytes

a=>a.map((x,y)=>{for(s=0,i=y;i<y+x;)s+=a[++i%a.length];return s})

Straightforward solution. Ungolfed:

a => a.map((x,y) => {
    var s = 0;
    for (i = y; i < y + x; i++) {
        s += a[i % a.length];
    }
    return s;
});

JavaScript's map() function is perfect for the job, it runs the given callback against each element and replaced it by the result of the callback. The callback receives two parameters, the first x is the value and the second y is the index. By taking the modulus i % a.length we can easily loop over the array, multiple times if needed.

Test snippet

(Put the input as JSON notation)

let f = a=>a.map((x,y)=>{for(s=0,i=y;i<y+x;)s+=a[++i%a.length];return s})

<input id=I type="text" size=70 value="[4,3,2,1]"><button onclick="console.log(f(JSON.parse(I.value)))">Run</button>

Answer 16

Java 8, 87 bytes

A curried void lambda taking an int[] list and int length.

l->s->{for(int i=-1,j,t;++i<s;System.out.println(t))for(j=t=0;j++<l[i];)t+=l[(i+j)%s];}

Try It Online. Note that I've shadowed System.out in this program in order to grab results for prettier printing.

Answer 17

Julia 0.6, 63 55 53 bytes

A->[sum(repmat(A,v+1)[i+1:i+v])for(i,v)=enumerate(A)]

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Older solution:

Julia 0.6, 65 bytes

A->(l=length(A);[sum(A[mod1(j,l)]for j∈i+1:i+A[i])for i∈1:l])

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---

Another solution. Not great by bytecount, but I like it, and it's probably more efficient than the other two, especially if the input has big numbers.

Julia 0.6, 69 bytes

A->(l=length(A);[sum([A;A][i+1:i+A[i]%l])+A[i]÷l*sum(A)for i∈1:l])

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Answer 18

Canvas, 10 bytes

²Ｘ｛ｘ＋⁸＠］∑］

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Explanation:

{         ] map over the items in the input
 ²X           save this loops counter on X (because of a bad design choice..)
   {    ]     map over 1..current item
    x+          add to it X
      ⁸@        and index in the input using that
         ∑    sum the map

Answer 19

QBasic 1.1, 115 bytes

INPUT L
DIM A(L)
FOR I=0TO L-1
INPUT C
A(I)=C
NEXT
FOR I=0TO L-1
S=0
FOR C=I+1TO I+A(I)
S=S+A(C MOD L)
NEXT
?S
NEXT

First input is the length L, then L subsequent inputs are the elements in order. L outputs represent the resulting array, with the elements in the order they're presented.

Answer 20

Japt, 7 bytes

ËÆg°EÃx

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Answer 21

JavaScript, 46 bytes

a=>a.map(g=(x,y)=>x--&&a[++y%a.length]+g(x,y))

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Answer 22

APL+WIN, 37 bytes

Prompts for input:

+/¨v↑¨⊂[2](⍳⍴v)⌽((⍴v),⍴n)⍴n←(+/v)⍴v←⎕

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Explanation:

n←(+/v)⍴v←⎕ prompts for input and creates a repeating vector of length max v

((⍴v),⍴n)⍴n converts n to a matrix of length v x length n

(⍳⍴v)⌽ rotates each row of n by the size of each element of v

⊂[2] converts each row of m to an element in a nested vector

+/¨v↑¨ selects the number of elements from each element of the nested vector according to v and sums

Answer 23

Ruby, 38 bytes

->a{w=0;a.map{|x|(a*-~x)[w+=1,x].sum}}

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Answer 24

JavaScript, 65 bytes 3̶0̶0̶ ̶b̶y̶t̶e̶s̶

golfed

n=>n.map((z,x)=>{for(s=0,i=x;i<z+x;)s+=n[++i%n.length];return s})

ungolfed

     f = n=>n.map((z,x)=>{
            for(s=0,i=x;i<z+x;)s+=n[++i%n.length];
            return s
            }
        );
console.log(f(process.argv[2].slice(1, -1).split(", ").map(x=>+x)))

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(ungolfed version above) I'm new to this codegolf thing!

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*updated! thanks to the useful links provided in comments, I managed to reduce the size to 65 bytes!

Answer 25

Perl 5 with -M5.010, 42 bytes

say sum+((@F,@F)x$_)[++$-..($-+$_-1)]for@F

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Answer 26

Pip -rn, 14 bytes

$+g@(_+\,B)MEg

Takes input numbers on successive lines of stdin; gives output numbers on successive lines of stdout. Try it online!

Explanation

             g  List of lines of stdin (from -r flag)
           ME   Enumerate and map this function to the (index, value) pairs:
       \,B       One-based range(value)
     _+          To each element, add the index of that value
  g@(     )      Use the resulting range to slice into the original list g
                 (cyclical indexing is built in)
$+               Sum the numbers in the slice
                Output the list of results one per line (from -n flag)

Or, using a worked example:

             g  [1 3 4 5]
           ME   
       \,B      [(1,2) (1,4) (1,5) (1,6)]
     _+         [(1,2) (2,5) (3,7) (4,9)]
  g@(     )     [[3] [4 5 1] [5 1 3 4] [1 3 4 5 1]]
$+              [3 10 13 14]

Answer 27

APL (Dyalog Classic), 12 bytes

+/¨⊢⍴¨⍳∘≢⌽¨⊂

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uses ⎕io←1

Answer 28

Perl 6, 50 32 bytes

{$_>>.&{.[++$+ ^$^a X%+$_].sum}}

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I'm new to golfing in Perl 6, so I'm sure this can be shorter. Not new anymore, and back to golf this!

Answer 29

Thunno 2, 6 bytes

ıRṅ+iS

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Explanation

ıRṅ+iS  # Implicit input
ı       # Map over the input:
 R      #  [1..item]
  ṅ+    #  Plus 0-based index
    i   #  Index into input
     S  #  Sum the list
        # Implicit output

Answer 30

Vyxal, 10 bytes

ėƛ÷$?$›ǓẎ∑

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Explanation

ėƛ÷$?$›ǓẎ∑  # Implicit input
ėƛ          # Enumerate (index, item) and map over:
  ÷$        #  Dump onto stack and swap
    ?$›Ǔ    #  Rotate input left by (index + 1)
        Ẏ∑  #  Take the first (item) elements and sum
            # Implicit output