Substring Sum Set

Question

Introduction

Let's observe this array: [3, 2, 4, 1, 1, 5, 1, 2].

Each element displays the length of the substring which must be summed up. Let's take a look at the first element of the above array:

[3, 2, 4, 1, 1, 5, 1, 2]
 ^

The element at the first index is 3, so we now take a substring of length three with the same index as the starting position:

[3, 2, 4]

When summed up, this results into 9, so the first element of the substring sum set is 9.

We do this for all the elements in the array:

3 -> [3, 2, 4]
2 -> [2, 4]
4 -> [4, 1, 1, 5]
1 -> [1]
1 -> [1]
5 -> [5, 1, 2]
1 -> [1]
2 -> [2]

You can see that the number 5 is a bit of a weird case. That number exceeds the length of the array:

[3, 2, 4, 1, 1, 5, 1, 2]
                ^  ^  ^  ^  ^

We'll ignore everything that exceeds the array, so we just use [5, 1, 2].

The last step is to sum everything up:

[3, 2, 4]     -> 9
[2, 4]        -> 6
[4, 1, 1, 5]  -> 11
[1]           -> 1
[1]           -> 1
[5, 1, 2]     -> 8
[1]           -> 1
[2]           -> 2

And that is the array that needs to be outputted:

[9, 6, 11, 1, 1, 8, 1, 2]

The Task

Given an non-empty array with positive (non-zero) integers, output the substring sum set. This is code-golf, so the submission with the smallest number of bytes wins!

Test cases

[1, 2, 3, 4, 5] -> [1, 5, 12, 9, 5]
[3, 3, 3, 3, 3, 3, 3, 3] -> [9, 9, 9, 9, 9, 9, 6, 3]
[5, 1, 2, 4, 1] -> [13, 1, 6, 5, 1]
[1] -> [1]

Answer 1

Jelly, 6 bytes

ṫJḣ"ḅ1

Try it online! or verify all test cases.

How it works

ṫJḣ"ḅ1  Main link. Argument: A (array)

 J      Index; yield the 1-based indices of A.
ṫ       Tail; map k to the postfix of A that begins with the k-th element.
  ḣ"    Vectorized head; for each k in A, truncate the corr. postfix to length k.
    ḅ1  Convert the resulting slices from base 1 to integer.

Answer 2

Python, 40 bytes

f=lambda x:x and[sum(x[:x[0]])]+f(x[1:])

Test it on Ideone.

Answer 3

Excel, 21 bytes

=SUM(OFFSET(A1,,,A1))

Open a new spreadsheet, put the test values in column A. Enter the formula in B1 and double click the cell handle to ride the range.

Answer 4

Python 3, 47 bytes

lambda X:[sum(X[i:i+k])for i,k in enumerate(X)]

Pretty straightforward implementation. Python's default behavior for slices that go past the end of the list was very convenient here.

Answer 5

Haskell, 34, 33 bytes

f l@(x:y)=sum(take x l):f y
f x=x

One byte saved by nimi.

Answer 6

JavaScript ES6, 50 bytes

a=>a.map((e,i)=>a.slice(i,i+e).reduce((a,b)=>a+b))

Pretty self-explanatory. It maps over each element in the array, getting the slice from that index through the index plus that element's value, and reduceing by adding.

f=
  a=>a.map((e,i)=>a.slice(i,i+e).reduce((a,b)=>a+b))

;[
  [3, 2, 4, 1, 1, 5, 1, 2],
  [1, 2, 3, 4, 5],
  [3, 3, 3, 3, 3, 3, 3, 3,],
  [5, 1, 2, 4, 1],
  [1]
].forEach(function(test){
  document.getElementById('p').textContent += test + ' => ' + f(test) + '\n';
});

<pre id="p"></pre>

Answer 7

J, 11 bytes

+/@{."_1]\.

Usage

   f =: +/@{."_1]\.
   f 3 2 4 1 1 5 1 2
9 6 11 1 1 8 1 2
   f 1 2 3 4 5
1 5 12 9 5

Explanation

+/@{."_1]\.  Input: A
        ]\.  Get each suffix of A from longest to shortest
   {."_1     For each value in A, take that many values from its corresponding suffix
+/@          Sum that group of values taken from that suffix
             Return the sums

Answer 8

JavaScript (ES6), 45

reduce beaten again!

a=>a.map((v,i)=>eval(a.slice(i,v+i).join`+`))

F=
a=>a.map((v,i)=>eval(a.slice(i,v+i).join`+`))

;[[3, 2, 4, 1, 1, 5, 1, 2],
  [1, 2, 3, 4, 5],
  [3, 3, 3, 3, 3, 3, 3, 3,],
  [5, 1, 2, 4, 1],
  [1]].forEach(t=>console.log(t+' -> '+F(t)))

Answer 9

Mathematica 60 55 bytes

Tr@Take[#,UpTo@#&@@#]&/@Drop[#,t-1]~Table~{t,Length@#}&

eg

f = %; f /@ {{1, 2, 3, 4, 5}, {3, 3, 3, 3, 3, 3, 3, 3}, {5, 1, 2, 4, 1}, {1}}

(*    {{1, 5, 12, 9, 5}, {9, 9, 9, 9, 9, 9, 6, 3}, {13, 1, 6, 5, 1}, {1}}    *)

Thanks @MartinEnder for shaving off 5 bytes :)

Answer 10

Retina, 38 bytes

Byte count assumes ISO 8859-1 encoding.

\d+
$*
M!&`\b1(1)*(?<-1>,1+)*
M%`1
¶
,

Input and output are comma-separated lists.

Try it online! (The first line enables a linefeed-separated test suite.)

Answer 11

05AB1E, 11 8 bytes

[D¬£Oˆ¦Ž

Explanation

[         # infinite loop
 D        # duplicate current list
  ¬       # get head of list
   £      # get that many elements from list
    O     # sum
     ˆ    # add to global array
      ¦   # remove first element of list
       Ž  # break if stack is empty
          # implicitly push and print global array

Try it online

Answer 12

Pyth, 8 bytes

.es:Qk+b

Test suite.

Translation of El's answer in Python.

Answer 13

Erlang, 69 bytes

f(A)->put(1,1),L=lists,[L:sum(L:sublist(A,put(1,get(1)+1),X))||X<-A].

Erlang's higher-order functions for lists do not receive the index of the current element. This uses the process dictionary to set the index of the current element.

Answer 14

Pyke, 12 7 bytes

FKo>i<s

Try it here!

        - o = 0
F       - for i in input:
  o     -    o+=1
   >    -    input[o:]
    i<  -   ^[:i]
      s -  sum(^)

Answer 15

VBA, 160 bytes

Function e(g())
Dim h()
k=LBound(g)
l=UBound(g)
ReDim h(k To l)
On Error Resume Next
For i=k To l
For j=i To i+g(i)-1
h(i)=h(i)+g(j)
Next
Next
e=h
End Function

Answer 16

Pyth, 6 bytes

ms<~tQ

Test suite

This is a different solution from any others so far. It loops over the input, slicing an summing the initial values, then removing the first element of the stored input, and repeat.

Explanation:

ms<~tQ
ms<~tQdQ    Implicit variable introduction
            Implicit: Q = eval(input())
m      Q    Map d over the input, Q
  <  Qd     Take the first d elements of Q
 s          Sum them
   ~tQ      Afterwards, set Q to the tail of Q, removing the first element.

Answer 17

Clojure, 63 bytes

(defn f[[b & r]](concat[(apply + b(take(dec b)r))](if r(f r))))

Uses pattern matching to decompose input argument in to the first and the rest of the arguments.

Answer 18

MATL, 17 14 13 bytes

fGy+!-R0<G*!s

Explanation

Try it online! Or verify all test cases (code modified to handle several inputs).

f     % Take input implicitly. Indices of nonzero elements: this gives [1 2 ... n]
      % where n is input size
G     % Push input again
y     % Push a copy of [1 2 ... n]
+     % Add. Gives [a+1 b+2...] where [a b...] is the input
!     % Transpose into a column vector
-     % Subtraction with broadcast. Gives 2D array
R     % Keep upper triangular part, making the rest of entries 0
0<    % True for negative entries. Each row corresponds to a substring sum.
      % For each row, this gives true for the entries of the input that make up
      % that substring sum. Each row is thus a mask to select entries of the input
G     % Push input again
*     % Multiply with broadcast. This multiplies the input times each row
!s    % Sum of each row. Implicitly display

Answer 19

Javascript (using External Library) (66 bytes)

n=>_.From(n).Select((v,i)=>_.From(n).Slice(i,i+v).Sum()).ToArray()

Link to lib: https://github.com/mvegh1/Enumerable

Code explanation: _.From is loading the input array into the library, which is basically LINQ for js. Then each item in the array is mapped according to the following predicate: Take the input, and slice it from current item index and take that index plus the current item's value. Then Sum up that subsequence. Convert the result to a native JS array and return it

Answer 20

F#, 84 82 bytes

let f(A:int[])=[for i in 0..A.Length-1->Seq.skip i A|>Seq.truncate A.[i]|>Seq.sum]

Answer 21

Julia, 39 bytes

!x=x!=[]?[take(x,x[])|>sum;!x[2:end]]:x

Try it online!

Answer 22

JavaScript (ES6) - 79 Bytes

A recursive solution that does not use any of the Array methods:

f=([a,...t],n)=>a&&n?a+f(t,n-1):0;g=([a,...t],r=[])=>a?g(t,[...r,a+f(t,a-1)]):r

Testing:

f=([a,...t],n)=>a&&n?a+f(t,n-1):0;
g=([a,...t],r=[])=>a?g(t,[...r,a+f(t,a-1)]):r;

[
  [3, 2, 4, 1, 1, 5, 1, 2],
  [1, 2, 3, 4, 5],
  [3, 3, 3, 3, 3, 3, 3, 3,],
  [5, 1, 2, 4, 1],
  [1]
].forEach(a=>console.log(''+g(a)));

Answer 23

C#, 89 bytes

int[]s(List<int>a)=>a.Select((n,i)=>a.GetRange(i,Math.Min(n,a.Count-i)).Sum()).ToArray();

pretty straight forward

improvement ideas appreciated

Answer 24

Brachylog, 27 bytes

.v|h~l(A:Tc?;A?)b:0&~b.h~+A

Try it online! or verify all test cases.

Explanation

  .v           Input = Output = []
|            Or
  h~l          A is a list, its length is the value of the first element of the Input
  (
    A:Tc?        The concatenation of A with another list T results in the Input
  ;            Or
    A?           A = Input
  )
  b:0&         Call recursively on Input minus the first element
  ~b.          Output is the output of that call with an extra element at the beginning
  h~+A         That extra element is the sum of the elements of A

Answer 25

Dyalog APL, 15 bytes

{+/¨⍵↑∘⌽¨⌽,\⌽⍵}

or

{⌽+/¨(-↑¨,\)⌽⍵}

Answer 26

PHP program, 72 Bytes

<?foreach($a=$_GET[a]as$i=>$v)echo array_sum(array_slice($a,$i,$v)),"
";

call with php-cgi -f <filename> 'a[]=3&a[]=2&a[]=4...

+11 as a function:

function f($a){foreach($a as$i=>$v)$r[]=array_sum(array_slice($a,$i,$v));return$r;}

+9 without builtins:

function p($a){foreach($c=$r=$a as$i=>$v)for($k=$i;$k--;)if(--$a[$k]>0)$r[$k]+=$v;return$r;}

($c keeps the original values, $a counts down for each index, $r gets the sums)

-3 as program:

<?foreach($a=$r=$c=$_GET[a]as$i=>$v)for($k=$i;$k--;)if(--$c[$k]>0)$r[$k]+=$v;print_r($r);

Answer 27

q (37 bytes)

{sum each(til[count x],'x)sublist\:x}

Example:

q){sum each(til[count x],'x)sublist\:x}3 2 4 1 1 5 1 2
9 6 11 1 1 8 1 2

Answer 28

Matricks, 25 bytes

Yay, finally a challenge I don't need new features for!

md{z:l-g:c;+c;q:c;};:1:l;

Run with: python matricks.py substring.txt [[<input>]] 0

Explanation:

m                  :1:l;   #loop over entire input
                           #set each value to...
 d{               }        #the sum of...
   z:l-g:c:+c;q:c;         #the input cropped to
                           #the length of the value in the cell

Answer 29

C#, 94 bytes

Console.Write(String.Join(",",a.Select((v,i)=>a.Skip(i).Take(v).Sum().ToString()).ToArray()));

Where a is an int[] that represents the input to be solved.