Fold a List in Half

Question

We are going to fold a list of integers. The procedure to do so is as follows, If the list is of even length, make a list of half of its length where the nth item of the new list is the sum of the nth item of the old list and the nth-to-last item of the old list. For example if we had the list

[1 2 3 4 5 6 7 8]

We would fold it like so

 [8 7 6 5]
+[1 2 3 4]
__________
 [9 9 9 9]

If the list is of odd length, to fold it we first remove the middle item, fold it as if it were even and the append the middle item to the result.

For example if we had the list

[1 2 3 4 5 6 7]

We would fold it like so

 [7 6 5]
+[1 2 3]
__________
 [8 8 8]
++     [4]
__________
 [8 8 8 4]

Task

Write a program or function that takes a list of integers as input and outputs that list folded.

This is a code-golf question so answers will be scored in bytes, with fewer bytes being better.

Sample implementation

Here's an implementation in Haskell that defines a function f that performs a fold.

f(a:b@(_:_))=a+last b:f(init b)
f x=x

Try it online!

When you say integers, does this include zero or negative integers? — Neil, Jul 31, 2017 at 19:53
@GrzegorzPuławski You should not sort the list. Any ordered collection is allowed, e.g. vector or array. — Wheat Wizard, Jul 31, 2017 at 20:51
@DavidStarkey Most reasonable lists will not overflow with a reasonable amount of memory. Folding doesn't actually increase the sum so lists will converge to a singleton of the sum of the original list. — Wheat Wizard, Aug 1, 2017 at 14:05
@WheatWizard I don't know about that, I've heard it's impossible to fold any list in half more than 7 times. — Carmeister, Aug 2, 2017 at 4:23

xnor · Accepted Answer · 2017-07-31 20:24:27Z

11

Python, 46 bytes

f=lambda l:l[1:]and[l[0]+l[-1]]+f(l[1:-1])or l

Try it online!

Same length:

f=lambda l:l[1:]and[l.pop(0)+l.pop()]+f(l)or l

A much shorter solution works for even-length lists (30 bytes)

lambda l:[x+l.pop()for x in l]

Try it online!

I'm still trying to find a short way to correct it for odd length.

edited Jul 31, 2017 at 20:24

answered Jul 31, 2017 at 20:07

xnor

141k26 gold badges268 silver badges618 bronze badges

\$\begingroup\$ Oh, I got terribly outgolfed ÷_÷ \$\endgroup\$
– Mr. Xcoder
Jul 31, 2017 at 20:10
\$\begingroup\$ The "middle ground" solution f=lambda l:l[1:]and[l[0]+l.pop()]+f(l[1:])or l is also the same length... \$\endgroup\$
– ETHproductions
Jul 31, 2017 at 20:42

Add a comment |

betseg · Accepted Answer · 2017-07-31 21:42:50Z

10

Emojicode, 203 bytes

🐋🍨🍇🐖🔢🍇🔂i⏩0➗🐔🐕2🍇😀🔡➕🍺🔲🐽🐕i🚂🍺🔲🐽🐕➖🐔🐕➕1i🚂10🍉🍊😛1🚮🐔🐕2🍇😀🔡🍺🔲🐽🐕➗🐔🐕2🚂10🍉🍉🍉

This was the most painful Emojicode answer to code for me. The unnecessary length :/

Try it online!

answered Jul 31, 2017 at 21:42

betseg

8,7433 gold badges26 silver badges59 bronze badges

Add a comment |

Adnan · Accepted Answer · 2017-07-31 20:07:39Z

8

05AB1E, 5 bytes

Code

2ä`R+

Uses the 05AB1E encoding. Try it online!

Explanation

2ä        # Split the list into two pieces
  `       # Flatten the stack
   R      # Reverse the second element from the list
    +     # Vectorized addition

edited Jul 31, 2017 at 20:07

answered Jul 31, 2017 at 19:58

Adnan

43.9k6 gold badges80 silver badges241 bronze badges

Add a comment |

ETHproductions · Accepted Answer · 2017-08-01 17:19:40Z

4

Japt, 21 18 16 bytes


l
íUj°V/2V w)mx

Test it online!

~~Completely awful~~ Slightly less awful thanks to @Oliver. BRB after I implement more built-ins and fix some bugs...

edited Aug 1, 2017 at 17:19

answered Jul 31, 2017 at 19:58

ETHproductions

49.6k6 gold badges91 silver badges239 bronze badges

Add a comment |

Business Cat · Accepted Answer · 2017-07-31 20:07:35Z

3

Gaia, 7 bytes

e2÷ev+†

Explanation

e        Eval the input (push the list).
 2÷      Split it in half. The first half will be longer for an odd length.
   e     Dump the two halves on the stack.
    v    Reverse the second.
     +†  Element-wise addition. If the first half has an extra element, it is simply appended.

answered Jul 31, 2017 at 20:07

Business Cat

9,1371 gold badge15 silver badges37 bronze badges

Add a comment |

Erik the Outgolfer · Accepted Answer · 2017-08-01 08:12:06Z

3

Jelly, 7 bytes

œs2U2¦S

Try it online!

-2 thanks to ETHproductions...and me realizing before.

edited Aug 1, 2017 at 8:12

answered Jul 31, 2017 at 19:51

Erik the Outgolfer

40.3k5 gold badges39 silver badges120 bronze badges

\$\begingroup\$ ETH was right, 7 bytes \$\endgroup\$
– Mr. Xcoder
Jul 31, 2017 at 19:55
\$\begingroup\$ @ETHproductions Thanks, although I had already figured out after I shut my computer down. \$\endgroup\$
– Erik the Outgolfer
Aug 1, 2017 at 8:11

Add a comment |

emanresu A · Accepted Answer · 2023-01-17 20:27:05Z

3

Vyxal, 4 bytes

I÷Ṙ+

Try it Online!

I    # Halve the list
 ÷   # Push each half
  Ṙ  # Reverse the second half
   + # Add them together (vectorising)

edited Jan 17 at 20:27

answered Sep 29, 2021 at 8:37

emanresu A

32.5k5 gold badges77 silver badges186 bronze badges

\$\begingroup\$ 5 bytes by taking the input as a string of characters with corresponding ascii values \$\endgroup\$
– lyxal
Sep 30, 2021 at 2:28
\$\begingroup\$ 4 bytes because @lyxal's being a sussy baka and not using flags \$\endgroup\$
– Aaroneous Miller
Oct 6, 2021 at 20:20

Add a comment |

Community · Accepted Answer · 2020-06-17 09:04:33Z

2

Mathematica, 88 bytes

(d=Array[s[[#]]+s[[-#]]&,x=⌊t=Length[s=#]/2⌋];If[IntegerQ@t,d,d~AppendTo~s[[x+1]]])&

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered Jul 31, 2017 at 21:25

ZaMoC

24k2 gold badges28 silver badges77 bronze badges

Add a comment |

Kelly Lowder · Accepted Answer · 2017-07-31 21:30:50Z

2

Mathematica 57 Bytes

(#+Reverse@#)[[;;d-1]]&@Insert[#,0,d=⌈Length@#/2⌉+1]&

Inserts a zero at the midpoint, adds the list to its reverse and takes the appropriate length.

answered Jul 31, 2017 at 21:30

Kelly Lowder

3,4658 silver badges17 bronze badges

Add a comment |

Community · Accepted Answer · 2020-06-17 09:04:33Z

2

JavaScript (ES6), 41 bytes

f=a=>1/a[1]?[a.shift()+a.pop(),...f(a)]:a

f=a=>1/a[1]?[a.shift()+a.pop(),...f(a)]:a

console.log(JSON.stringify(f([1,2,3,4,5,6,7,8])));
console.log(JSON.stringify(f([1,2,3,4,5,6,7])));

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered Jul 31, 2017 at 22:05

Rick Hitchcock

2,5319 silver badges17 bronze badges

Add a comment |

Justin Mariner · Accepted Answer · 2017-07-31 23:03:48Z

2

Japt, 12 bytes

å@o +Y*(Z<Ul

Try it online! with the -Q flag to view the formatted array.

Alternate solution, 14 bytes

o(½*Ul)c)íU mx

Try it online!

answered Jul 31, 2017 at 23:03

Justin Mariner

4,9061 gold badge11 silver badges18 bronze badges

Add a comment |

Asaf · Accepted Answer · 2017-08-01 11:09:50Z

2

JavaScript (Node.js), 53 bytes

x=>x.splice(0,x.length/2).map(y=>y+x.pop()).concat(x)

Try it online!

Another suggestion:

JavaScript (Node.js), 43 bytes

f=x=>x+x?[x.pop()+(0|x.shift()),...f(x)]:[]

Try it online!

edited Aug 1, 2017 at 11:09

answered Jul 31, 2017 at 21:42

Asaf

1212 bronze badges

\$\begingroup\$ (0|x.shift()) => ~~x.shift() \$\endgroup\$
– l4m2
Jan 17 at 14:29

Add a comment |

Giuseppe · Accepted Answer · 2019-02-15 17:48:38Z

2

R, 81 70 68 57 bytes

function(l)c((l+rev(l))[1:(w=sum(l|1)/2)],l[w+1][!!w%%1])

Try it online!

anonymous function; returns the result.

edited Feb 15, 2019 at 17:48

answered Jul 31, 2017 at 20:19

Giuseppe

27.3k3 gold badges30 silver badges99 bronze badges

Add a comment |

GammaFunction · Accepted Answer · 2019-03-30 00:02:28Z

Zsh, 55 bytes

If the answer must be put to stdout, but output whitespace is flexible, 55 bytes:

for ((;++i<=#/2;))<<<$[$@[i]+$@[-i]]
<<<$@[#%2*(1+#/2)]

Try it online!

If the output must be stored in an array, 53 bytes: (We can't use this method in place of the above because of <<<...[--i].... The here-string forces a subshell, so the decremented value of i never makes it out.)

for n ($@[1,#/2])y+=($[$@[--i]+n])
y+=$@[#%2*(1+#/2)]

Try it online!

If the answer must be output in one line separated by spaces, then append <<<$y for a 6 byte penalty.

Zsh arrays are indexed from the start starting at 1, or from the end starting at -1. So what happens if you attempt to index at 0? Well, nothing! We take advantage of that here to only output the middle number based on a parity check:

$@[#%2*(1+#/2)]
   #      #       # parameter count
       (1+#/2)    # index of the middle element when count is odd
   #%2*(1+#/2)    # multiply by 0 if even, or 1 if odd
$@[           ]   # Index the parameter array

chunes · Accepted Answer · 2021-09-29 09:46:35Z

Factor, 35 bytes

[ halves reverse 0 pad-longest v+ ]

Try it online!

Explanation

It's a quotation (anonymous function) that takes a sequence from the data stack and leaves a sequence on the data stack. Assuming { 1 2 3 4 5 6 7 } is on the data stack when this quotation is called...

Snippet	Comment	Data stack (top on right)
`halves`	Split a sequence in half	`{ 1 2 3 } { 4 5 6 7 }`
`reverse`	Reverse a sequence	`{ 1 2 3 } { 7 6 5 4 }`
`0 pad-longest`	Pad the shorter of two sequences with 0s until it's the same length as the longer sequence	`{ 1 2 3 0 } { 7 6 5 4 }`
`v+`	Vector addition; element-wise addition between two sequences	`{ 8 8 8 4 }`

att · Accepted Answer · 2021-09-29 18:49:29Z

2

C (gcc), 55 41 bytes

f(_,l)int*_;{for(;l--;*_+++=l?_[l--]:0);}

Try it online!

Overwrites the first \$\left\lfloor\frac{l}{2}\right\rfloor\$ entries of the input array.

C (gcc), 46 bytes

f(_,l)int*_;{_=l>1?*_+=_[l-1],1+f(_+1,l-2):l;}

Try it online!

Additionally returns the length \$\left\lceil\frac{l}{2}\right\rceil\$ of the output.

edited Sep 29, 2021 at 18:49

answered Mar 30, 2019 at 12:36

att

18.2k2 gold badges13 silver badges53 bronze badges

Add a comment |

bigyihsuan · Accepted Answer · 2023-01-17 22:03:38Z

2

Go, 115 bytes

func(x[]int)(o[]int){s:=len(x)
for i:=range x[:s/2]{o=append(o,x[i]+x[s-i-1])}
if s%2>0{o=append(o,x[s/2])}
return}

Attempt This Online!

Generic with custom operator, 136 bytes

func f[T any](x[]T,O func(T,T)T)(o[]T){s:=len(x)
for i:=range x[:s/2]{o=append(o,O(x[i],x[s-i-1]))}
if s%2>0{o=append(o,x[s/2])}
return}

Attempt This Online!

edited Jan 17 at 22:03

answered Jan 17 at 21:51

bigyihsuan

6,1821 gold badge14 silver badges43 bronze badges

Add a comment |

alephalpha · Accepted Answer · 2023-01-18 07:28:05Z

2

Curry (PAKCS), 34 bytes

f(a:b++[c])=a+c:f b
f x@([]?[_])=x

Attempt This Online!

Based on the sample implementation in Haskell.

answered Jan 18 at 7:28

alephalpha

40.4k6 gold badges52 silver badges151 bronze badges

Add a comment |

Peter · Accepted Answer · 2023-01-18 18:39:33Z

C (gcc), 62 bytes 60 bytes

-2 bytes thanks to @ceilingcat

i;f(v,l)int*v;{for(i=0;i<l/2;++i)v[i]+=v[l+~i];return~l/-2;}

f is a function taking vector (v) and length (l) as arguments. It modifies the vector and returns the new length.

Try It Online!

How it works:

i;
f(v,l) int*v; // v is an integer pointer (or array), l is an integer
{
    for (i = 0; i < l / 2; ++i) // iterate through half the indices using i (if l is odd, the middle element won't be included)
        v[i] += v[l + ~i]; // add the value at the i'th index from the back to the i'th index from the front. ~i == -i - 1, so l + ~i == l + -i -1 = l - i - 1 (l - 1 is the first index from the back, and we subtract i for each index beyond the first)
    return ~l / -2; // return half the length rounded up (~l == -l - 1 => ~l / -2 == (-l - 1) / -2 => (l + 1) / 2
}

\$\begingroup\$ Welcome to Code Golf! Nice first answer. \$\endgroup\$
– alephalpha
Jan 18 at 7:27 — alephalpha, Jan 18 at 7:27

Jacobus Smit · Accepted Answer · 2023-01-20 20:58:31Z

2

BQN, 15 12 bytes

(⌊≠÷2˙)⊸↑⊢+⌽

Try it online!

-3 thanks to Marshall Lochbaum

Sum the list and its reverse, then take the first ⌊≠÷2˙ digits. ⌊≠÷2˙ the floor of the length divide 2. Floor is necessary because there is no integer division in BQN. ⊸ is used to bind the output of ⌊≠÷2˙ to the take operator ↑ on the left and also puts the output of (⊢+⌽) on the right. Better explanation here.

edited Jan 20 at 20:58

answered Jan 20 at 20:44

Jacobus Smit

1614 bronze badges

\$\begingroup\$ Welcome to Code Golf, and nice answer! \$\endgroup\$
– Rydwolf Programs
Jan 20 at 20:45
\$\begingroup\$ Thank you! I only wish my explanation was as concise... \$\endgroup\$
– Jacobus Smit
Jan 20 at 20:49

Add a comment |

Baby_Boy · Accepted Answer · 2023-01-21 07:44:27Z

2

Pip, 14 12 bytes

YCHa;@y+Ry@1

-2 Thanks to DLosc!

How?

YCHa;@y+Ry@1  : One arg; list
   a          : First input
 CH           : Chop iterable into 2 pieces of roughly equal length
Y             : Yank value
         y    : The two halves
          @1  : Get item/slice at index 1; The second half
        R     : Reverse
       +      : Add with
      y       : The two halves
     @        : Get item at index 0; The first half

Try It Online!

edited Jan 21 at 7:44

answered Jan 17 at 17:45

Baby_Boy

1,1134 silver badges14 bronze badges

\$\begingroup\$ @DLosc that was so obvious I don't know how I missed it lol, thanks for the spot! \$\endgroup\$
– Baby_Boy
Jan 20 at 14:07
\$\begingroup\$ @DLosc I see what you mean, it made sense when I wrote it, should be fixed now! :) \$\endgroup\$
– Baby_Boy
Jan 21 at 7:45

Add a comment |

Fmbalbuena · Accepted Answer · 2023-01-30 17:34:44Z

2

Fig, \$23\log_{256}(96)\approx\$ 18.932 bytes

J+t_HLxxt_HLx$xs_HLxtHL

Try it online!

\$-26\log_{256}(96)\approx21.401\$ thanks to Seggan

First time using Fig. Any golfing tips are welcome.

Explanation (outdated):

fw+[yfy$fy$fyx[yfy$fy$fy$x?h%1HLx[]yfy$fy$fyx]yW1
   [yfy$fy$fyx                                    First Mid
  +                                               Add
              [yfy$fy$fy$x                        Second Mid
fw                                                Concat
                          ?                       If
                           h%1HLx                 List length is odd,
                                 []yfy$fy$fyx     Mid
                                             ]yW1 Else Empty list

edited Jan 30 at 17:34

answered Jan 18 at 1:31

Fmbalbuena

2,8611 gold badge7 silver badges42 bronze badges

1

\$\begingroup\$ the entire if (?h%1HLx[]yfy$fy$fyx]yW1) can be replaced with s_HLxtHL (take half, drop half; will return empty list if even, middle item if odd). fw can be J \$\endgroup\$
– Seggan
Jan 19 at 15:28
1

\$\begingroup\$ J+t_HLxxt_HLx$xs_HLxtHL works \$\endgroup\$
– Seggan
Jan 19 at 15:37

Add a comment |

Mr. Xcoder · Accepted Answer · 2017-07-31 19:55:15Z

1

Python 3, 101 bytes

lambda l:[sum(x)for x in zip(l[:len(l)//2],l[int(len(l)/2+.5):][::-1])]+[[],[l[len(l)//2]]][len(l)%2]

Try it online!

answered Jul 31, 2017 at 19:55

Mr. Xcoder

42.1k9 gold badges77 silver badges214 bronze badges

Add a comment |

Business Cat · Accepted Answer · 2017-07-31 19:59:49Z

1

Python 3, 70 bytes

lambda l:[l[i]+l[~i]for i in range(len(l)//2)]+len(l)%2*[l[len(l)//2]]

Try it online!

answered Jul 31, 2017 at 19:59

Business Cat

9,1371 gold badge15 silver badges37 bronze badges

Add a comment |

score 1 · Accepted Answer · 2017-07-31 20:02:15Z

1

JavaScript, 75 71 bytes

a=>a.slice(0,n=a.length/2).map(b=>b+a[--z],z=n*2).concat(n%1?a[n|0]:[])

Try it online

Saved 2 bytes thanks to ETHproductions

edited Jul 31, 2017 at 20:02

answered Jul 31, 2017 at 19:57

user72349

Add a comment |

Community · Accepted Answer · 2020-06-17 09:04:33Z

MATL, 9 bytes

`6L&)swtn

Try it online!

How it works

Given an array [a b c ... x y z], let [a z] be called the "crust" subarray and [b c ... y z] the "core" subarray.

The code consists in a loop that removes the crust, computes its sum, and moves the core to the top of the stack, ready for the next iteration. The loop condition is the number of elements in the core subarray

`       % Do...while
  6L    %   Push [2 -1+1j]. As an index, this is interpreted as 2:end-1
  &)    %   2-output reference indexing: pushes a subarray with the indexed 
        %   elements (core) and another with the ramaining elements (crust)
  s     %   Sum of (crust) subarray
  w     %   Swap. Moves the core subarray to the top
  t     %   Duplicate
  n     %   Number of elements.
        % End (implicit). Procced with next iteration if top of the stack is
        % nonzero; else exit
        % Display stack (implicit)

Felix Guo · Accepted Answer · 2017-07-31 23:50:00Z

1

WendyScript, 72 bytes

<<f=>(l){<<r=[]<<b=l.size#i:0->b/2r+=l[i]+l[b-i-1]?b%2!=0r+=l[(b/2)]/>r}

f([1,2,3,4,5,6,7,8]) // => [9,9,9,9]
f([1,2,3,4,5,6,7]) // => [8,8,8,4]

Try it online!

answered Jul 31, 2017 at 23:50

Felix Guo

2111 silver badge4 bronze badges

Add a comment |

Phoenix · Accepted Answer · 2017-08-01 03:11:04Z

1

Scala, 91 bytes

(s:Seq[Int])=>(s.take(s.size/2),s.reverse).zipped.map(_+_)++s.drop(s.size/2).take(s.size%2)

answered Aug 1, 2017 at 3:11

Phoenix

1714 bronze badges

Add a comment |

Grzegorz Puławski · Accepted Answer · 2017-08-01 05:38:43Z

C# (.NET Core), 118 111 bytes

a=>a.Reverse().Zip(a,(c,d)=>c+d).Take(a.Length/2).Concat(a.Skip(a.Length/2).Take(a.Length%2))

Byte count also includes

using System.Linq;

Try it online!

As input please use numbers separated either with commas (,) or space. Explanation:

a =>                                  // Take one input parameter (array)
a.Reverse()                           // Reverse it
.Zip(a, (c, d) => c + d)              // Take every corresponding member of reversed
                                      //    and original, and add them together
.Take(a.Length / 2)                   // Get first half of the collection
.Concat(                              // Add another collection
    a.Skip(a.Length / 2)              // Take input and leave out first half of it
    .Take(a.Length % 2)               // If length is odd, take first element (so the middle)
                                      //    otherwise create an empty collection
);

Can you save bytes by setting the length to a variable and switching to an explicit return? — TheLethalCoder, Aug 1, 2017 at 8:07

Mr.Wizard · Accepted Answer · 2017-08-01 11:02:55Z

1

Mathematica, 52

(a=#;i=0;(i++;a[[i;;-i]]*=x)&/@a;(Tr@a+O@x^i)[[3]])&

answered Aug 1, 2017 at 11:02

Mr.Wizard

2,62117 silver badges17 bronze badges

Add a comment |

Fold a List in Half

Task

Sample implementation

52 Answers 52

Python, 46 bytes

Emojicode, 203 bytes

05AB1E, 5 bytes

Code

Explanation

Japt, 21 18 16 bytes

Gaia, 7 bytes

Explanation

Jelly, 7 bytes

Vyxal, 4 bytes

Mathematica, 88 bytes

Mathematica 57 Bytes

JavaScript (ES6), 41 bytes

Japt, 12 bytes

Alternate solution, 14 bytes

JavaScript (Node.js), 53 bytes

JavaScript (Node.js), 43 bytes

R, 81 70 68 57 bytes

Zsh, 55 bytes

Factor, 35 bytes

Explanation

C (gcc), 55 41 bytes

C (gcc), 46 bytes

Go, 115 bytes

Generic with custom operator, 136 bytes

Curry (PAKCS), 34 bytes

C (gcc), 62 bytes 60 bytes

BQN, 15 12 bytes

Pip, 14 12 bytes

Fig, \$23\log_{256}(96)\approx\$ 18.932 bytes

Explanation (outdated):

Python 3, 101 bytes

Python 3, 70 bytes

JavaScript, 75 71 bytes

MATL, 9 bytes

How it works

WendyScript, 72 bytes

Scala, 91 bytes

C# (.NET Core), 118 111 bytes

Mathematica, 52

Your Answer

Sign up or log in

Post as a guest

Not the answer you're looking for? Browse other questions tagged code-golfarray or ask your own question.

Linked

Related

Hot Network Questions

Not the answer you're looking for? Browse other questions tagged
code-golf
array
or ask your own question.