Build a steady brick wall

Question

A brick wall is a rectangle made of horizontal 1-by-n bricks stacked into rows. Here's a wall of height 4 and width 8, with brick sizes shown on the right.

[______][______]    4 4
[__][____][__][]    2 3 2 1
[][______][____]    1 4 3
[____][______][]    3 4 1

This wall is unsteady because it has a fault, a place where two vertical cracks between bricks line up, shown below with parens in the surrounding bricks.

[______][______]    
[__][____)(__][]
[][______)(____]
[____][______][]

But, the cracks bordering the size-1 bricks on the right don't form a fault because they are separated by a row.

Write code that finds and displays a steady wall constructed out of bricks of specified sizes. Fewest bytes wins.

Input

A non-empty list of brick sizes (positive numbers) and a height that's at least 2. This list may be sorted if you wish. You may alternatively take in a count of bricks of each size.

Output

A picture of a steady rectangular wall of the required height that uses all the bricks given. Print it or return it as a string with newlines.

Draw a brick of size n as 2n characters, underscores surrounded by brackets.

1: []
2: [__]
3: [____]
4: [______]
...

The input is guaranteed to have at least one solution. If there's multiple, you should still only draw one wall.

There's no time restriction; use as much brute force as you want. Your algorithm should in theory work on inputs of any size.

Test cases:

There are multiple solutions, so your outputs might be different.

>> [1, 1, 2, 2], 2
[][__]
[__][]

>> [1, 1, 1, 2, 2, 2, 2, 3], 2
[__][____][__]
[][__][][__][]

>> [1, 1, 2, 2, 3, 3, 3, 3], 3
[][__][____]
[__][____][]
[____][____]

>> [1, 2, 3, 4, 5, 6, 7, 8, 9], 5
[][______________]
[__][____________]
[________________]
[____][__________]
[______][________]

>> [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 5
[][__][__]
[__][__][]
[][__][__]
[__][__][]
[][__][__]

Answer 1

Perl, 166 170 194

A perfect task for a language created by Larry Wall.

#!perl -pa
$_=(1x($x=2/($y=pop@F)*map{1..$_}@F)."
")x$y;sub
f{my$l=$_;$-|=!@_;for$=(@_){$Z=__
x~-$=;$f=0;s/(11){$=}/[$Z]/&!/\]..{$x}\[/s&&f(grep$=ne$_||$f++,@_);$-or$_=$l}}f@F

Brute force, but quite fast on the test cases (<1s). Usage:

$ perl ~/wall.pl <<<"1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 5"
[][__][__]
[__][__][]
[][__][__]
[__][__][]
[][__][__]

Test me.

Answer 2

CJam, 94 92 82 bytes

This is the 92 bytes version. 82 byte version follows.

l~1$,:L,:)m*{1bL=},\e!\m*{~W<{/(\e_}%}%{::+)-!},{{_,,\f<1fb}%2ew{:&,(},!}={{(2*'_*'[\']}/N}/

This partitions the bricks into every possible way and take only the one which is valid. Pretty brute force for now but still runs the last test case in about 10 seconds on the Java Interpreter on my machine.

Explanation:

The code is split into 5 parts:

1) Given an array of length L, how all can we partition it into H parts.

l~1$,:L,:)m*{1bL=},
l~                     e# Read the input as string and evaluate it.
  `$,:L                e# Copy the array and take its length. Store that in L
       ,:)             e# Get an array of 1 to L
          m*           e# Cartesian power of array 1 to L of size H (height of wall)
            {1bL=},    e# Take only those parts whose sum is L

After this, we have all possible ways of splitting up our input array into H brick layers.

2) Get all permutations of the input array and then further get all partitions for all permutations

\e!\m*{~W<{/(\e_}%}%
\e!                    e# Put the input array on top of stack and get all its permutations
   \m*                 e# Put the all possible partition array on top and to cartesian
                       e# product of the two permutations. At this point, every
                       e# permutation of the input array is linked up with every
                       e# permutation of splitting L sized array into H parts
      {           }%   e# Run each permutation pair through this
       ~W<             e# Unwrap and remove the last part from the partition permutation
          {     }%     e# For each part of parts permutation array
           /           e# Split the input array permutation into size of that part
            (\         e# Take out the first part and put the rest of the parts on top
              e_       e# Flatten the rest of the parts so that in next loop, they can be
                       e# split into next part length

After this, we have all possible layouts of the input bricks into an H layers brick wall.

3) Filter out only those layouts whose brick lengths are same

{::+)-!},
{      },              e# Filter all brick layouts on this condition
 ::+                   e# Add up brick sizes in each layer
    )-!                e# This checks if the array contains all same lengths.

After the end of this filter, all remaining layouts would be perfect rectangles.

4) Take out the first brick layout which matches the stability criteria

{{_,,\f<1fb}%2ew{:&,(},!}=
{                       }=   e# Choose the first array element that leaves truthy on stack
 {         }%                e# For each brick layer
  _,,                        e# Create an array of 0 to layer length - 1
     \f<                     e# Get all sublists starting at 0 and ending at 0
                             e# through length - 1
        1fb                  e# Get sum of each sub list. This gives us the cumulative
                             e# length of each brick crack except for the last one
           2ew               e# Pair up crack lengths for every adjacent layer
              {    },        e# Filter layer pairs
               :&            e# See if any cumulative crack length is same in any two
                             e# adjacent layers. This means that the layout is unstable
                 ,(          e# make sure that length of union'd crack lengths is greater
                             e# than 1. 1 because 0 will always be there.
                     !       e# If any layer is filtered through this filter,
                             e# it means that the layer is unstable. Thus negation

After this step, we simply have to print the layout

5) Print the layout

{{(2*'_*'[\']}/N}/
{               }/           e# For each brick layer
 {           }/              e# For each brick
  (2*'_*                     e# Get the (brick size - 1) * 2 underscores
        '[\']                e# Surround with []
               N             e# Newline after each layer

Try it online here

---

82 bytes

l~:H;{e_mrH({H-X$,+(mr)/(\e_}%_::+)-X${_,,\f<1fb}%2ew{:&,(},+,}g{{(2*'_*'[\']}/N}/

This is almost similar to the 92 byte version, except that it has a touch of randomness. If you have read the explanation for the 92 byte version, then in the 82 byte version, parts 3, 4 and 5 are exactly same, while instead of iterating over all permutations from part 1 and 2, this version simply randomly generates one of the permutation at a time, tests it using part 3 and 4, and then restarts the process if the tests of part 3 and 4 fail.

This prints the results very quickly for the first 3 test cases. The height = 5 test case is yet to give an output on my computer.

Explanation of the difference

l~:H;{e_mrH({H-X$,+(mr)/(\e_}%_::+)-X${_,,\f<1fb}%2ew{:&,(},+,}g
l~:H;                           e# Eval the input and store the height in H
     {   ...   }g               e# A do-while loop to iterate until a solution is found
      e_mr                      e# Flatten the array and shuffle it.
          H({               }%  e# This is the random partition generation loop
                                e# Run the loop height - 1 times to get height parts
             H-X$,+(            e# While generating a random size of this partition, we
                                e# have to make sure that the remaining parts get at least
                                e# 1 brick. Thus, this calculation
                    mr)         e# Get a random size. Make sure its at least 1
                       /(\e_    e# Similar to 92's part 2. Split, pop, swap and flatten

_::+)-                          e# 92's part 3. Copy and see if all elements are same
      X${_,,\f<1fb}%2ew{:&,(},  e# 92's part 4. Copy and see if layers are stable
+,                              e# Both part 3 and 4 return empty array if
                                e# the layout is desirable. join the two arrays and
                                e# take length. If length is 0, stop the do-while

The idea for this version was given by randomra (Get it ?)

Try this one online

Answer 3

Python 2, 680 670 660 bytes

I don't know why I insist on having these super long "golfs"... but anyway, here you go.

M,L,R,N=map,len,range,None
exec"J=@:M(''.join,x);B=@:'['+'_'*2*~-x+']';K=@:M(B,x);W=@:J(M(K,x));C=@:set(M(sum,[x[:i]for i in R(L(x))]))-{0};T=@,w:w[x:]+w[:x]\ndef F(i):f=filter(@:i[x-1]&i[x],R(1,L(i)));return f and f[0]".replace('@','lambda x')
def P(e,x,i,w,h):
 for j in[-~_%h for _ in R(i-1,h+i-2)]:
    for s in R(w):
     if not e&C(T(s,x[j])):return j,s
 return N,N
def b(l,h):
 w,d=[[]for _ in R(h)],2*sum(l)/h
 for _ in l[::-1]:q=M(L,W(w));w[[q.index(i)for i in sorted(q)if i+L(B(_))<=d][-1]]+=_,
 g=M(C,w);i=F(g)
 while i:
    e=g[i-1];j,s=P(e,w,i,d,h)
    if j!=N:w[j]=T(s,w[j]);w[i],w[j]=w[j],w[i];g=M(C,w);i=F(g)
    else:b(T(-1,l),h);return
 print'\n'.join(W(w))

This requires the output in sorted ascending order, and is called via b(brick_sizes, height).

Test cases:

>>> tests = [([1, 1, 2, 2], 2),([1, 1, 1, 2, 2, 2, 2, 3], 2), ([1, 1, 2, 2, 3, 3, 3, 3], 3), ([1, 2, 3, 4, 5, 6, 7, 8, 9], 5), ([1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 5)]
>>> for t in tests:
...     b(*t); print
... 
[__][]
[][__]

[____][__][__]
[][][__][__][]

[____][____]
[__][__][][]
[____][____]

[________________]
[______________][]
[____________][__]
[__________][____]
[________][______]

[__][__][]
[][__][__]
[__][__][]
[][__][__]
[__][__][]

The way this works is:

1. Assign the bricks (longest->shortest) to layers, trying to fill each layer before moving to the next.
2. Whenever adjacent layers are unstable, try swapping layers and shifting bricks until you find something that works.
3. If nothing works, move the longest brick to the front of the sizes list and recurse.

Answer 4

Haskell, 262 bytes

import Data.List
c=concat
n=init.scanl1(+)
1%l=[[[l]]]
n%l=[map(h:)(c$(n-1)%t)|(h,t)<-map(`splitAt`l)[1..length l]]
v[x]=1<2
v(x:y:z)=sum x==sum y&&n x==n x\\n y&&v(y:z)
l#n=unlines$map(>>=(\b->'[':replicate(2*b-2)'_'++"]"))$head$filter v$c.(n%)=<<permutations l

Example usage:

*Main> putStr $  [1, 2, 3, 4, 5, 6, 7, 8, 9] # 5
[______][________]
[__________][____]
[____________][__]
[][______________]
[________________]

*Main> putStr $ [1, 1, 2, 2, 3, 3, 3, 3] # 3
[____][____]
[__][__][][]
[____][____]

How it works: the main function # takes a list l (list of bricks) and a number h (height) and splits all permutations of l into h sublists at all possible positions (via function %, e.g. 2%[1,2,3,4] -> [ [[1],[2,3]] , [[1,2],[3]] , [[1,2,3],[]] ]) . It keeps those where two consecutive elements have the same sum (i.e. same length in bricks) and the lists of subtotals don't have common elements (i.e. cracks don't line up, function v). Take the first list that fits and build a string of bricks.

Answer 5

Python 2, 528, 417, 393, 381

Very long, bruteforce solution. It works but that's about it, the universe may end before getting the result for the last test case.

exec u"from itertools import*;m=map;g=@w,n:([[w]],[[w[:i]]+s#i?range(1,len(w))#s?g(w[i:],n-1)])[n>1];r=@x:set(m(sum,[x[:i]#i?range(1,len(x))]));f=@w:1-all(m(@(x,y):not x&y,zip(m(r,w[:-1]),m(r,w[1:]))));a=@s,h:['\\n'.join([''.join(['[%s]'%(' '*(s-1)*2)#s?r])#r?o])#p?permutations(s)#o?g(p,h)if len(set([sum(r)#r?o]))<2 and~-f(o)][0]".translate({64:u"lambda ",35:u" for ",63:u" in "})

a is the main function:

>> a([1, 1, 2, 2], 2)
'[][  ]\n[  ][]'

Answer 6

JavaScript (ES6) 222 232 265 279 319

Still to be golfed. This one find all the solutions, output just the last found, and it's quite fast.

Run snippet in Firefox to test

f=(n,h,b=[],s=0)=>
  (R=(z,l,p,k,t)=>
    z?b.map((v,a)=>
      v&&k.indexOf(v=t+a)<0&v<=s&&(
        --b[a],h=l+`[${'__'.repeat(a-1)}]`,
        v-s?R(z,h,[...p,v],k,v):R(z-1,h+'\n',[],p,0),
        ++b[a]
      ))
    :n=l
  )(h,'',[],[],0,n.map(n=>(b[n]=-~b[n],s+=n)),s/=h)&&n

// Test suite


out=x=>OUT.innerHTML=OUT.innerHTML+x+'\n'

;[ 
 [[1, 1, 2, 2], 2], [[1, 1, 1, 2, 2, 2, 2, 3], 2], [[1, 1, 2, 2, 3, 3, 3, 3], 3]
,[[1, 2, 3, 4, 5, 6, 7, 8, 9], 5], [[1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 5]]
.forEach(([a,b])=>out(a+' '+b+'\n'+f(a,b)))

<pre id=OUT></pre>

Ungolfed And explained

function f(n, h) {
  var b=[], s=0, result // in golfed version will re-use n for result variable
  n.forEach(function (n) {
    b[n] = -~b[n] // group equal input numbers in buckets
    s+=n          // calc sum of input numbers
  });
  // example of buckets: input 1,1,4,1,5,4 -> b[1]=3,b[4]=2,b[5]=1
  s /= h // total sum / height => sum expected for each brick layer

  // recursive scan function 
  function R(z, // layer count, from h downto 1
             l, // output so far
             p, // current layer partial sums array, mark intervals between bricks
             k, // prev layer parial sums, checked to avoid faulds
             t  // current partial sum 
             ) 
  {
    if (z > 0) 
    { // still building
      b.forEach( function (v,a) { // a:number from input list, v: repeat count 
        var w, m   // locals (in golfed version, reuse other variables avoid defining locals)
        w = t + a; // increased running total for current layer
        if (v != 0  // repeat count still > 0 
           && k.indexOf(w) < 0 // running total not found on list in prev layer (no fault)
           && w <= s) // current layer length not exceeded
        {
           --b[a]; // decrease repeat count, number used one more time
           m = l+"["+ '__'.repeat(a-1) + "]"; // new output with a brick added
           // l is not changed, it will be used again in this loop
           if (w == s) 
           {   // layer complete, go to next (if any)
               // recurse, new layer, add newline to output, p goes in k, and t start at 0 again
               R(z-1, m+'\n', [], p, 0); 
           }
           else
           {   // layer still to complete
               // recurse, same layer, m goes in l, add current sum to array p
               R(z, m, [...p,w], k, w);
           }
           ++b[a]; // restore value of repeat count for current loop
        }
      })
    }   
    else
    { // z == 0, all layers Ok, solution found, save in result and go on to next
      result = l;
    }
  }

  R(h,'',[],[],0);
  return result; // this is the last solution found
}

Answer 7

Python 2, grid method (290 chars)

x,h=input()
from itertools import *
w = sum(x)*2/h
for p in permutations(x):
 bricks = ''.join('[' + '_'*(2*n-2) + ']' for n in p)
 cols = map(''.join,zip(*zip(*[iter(bricks)]*w)))
 if all(c=='[' for c in cols[0]) and all(c==']' for c in cols[-1]) and not any(']]' in col or '[[' in col for col in cols[1:-1]):
  print('\n'.join(map(''.join,zip(*cols))))
  print()

The method here is you transpose the grid and look for a [[ or ]] anywhere in the columns. You also test that all the bricks on the left and right sides of the wall line up: the cute thing here is to test that all elements of a string are the same: '[[[[[['.strip('[')==''

---

mini version of above:

x,h=input()
from itertools import*
w=sum(x)*2/h
z=zip
j=''.join
for p in permutations(x):
 C=map(j,z(*z(*[iter(j('['+'_'*(2*n-2)+']'for n in p))]*w)))
 if C[0].strip('[')==''and C[-1].strip(']')==''and not any(']]'in c or '[['in c for c in C[1:-1]):
  print('\n'.join(map(j,z(*C))))
  break

---

This could probably be done more easily in a matrix-manipulation language.

...or abuse of regexes, which lets us combine the "blocks align on ends" condition with the "no cracks" condition:

Say the width of the wall was w=6. The locations of the substring "[.....[", and "].....]" must be exactly the set {0,w-1,w,2w-1,2w,3w-1,...}. Not-existence at those points means the bricks 'linewrap' like so:

       v
[][__][_
___][__]
       ^

Existence NOT at those points means there is an unsteady 'crack' in the wall:

     vv
[][__][]
[    ][]
     ^^

Therefore we reduce the problem to set equivalence, where the sets in questions are the indices of a regular expression match.

# assume input is x and height is h

from itertools import *
import re
w=sum(x)*2/h

STACKED_BRACKET_RE = r'(?=\[.{%i}\[|\].{%i}\])'%(w-1,w-1)  # ]....] or [....[
STRING_CHUNK_RE = '.{%i}'%w  # chunk a string with a regex!
bracketGoal = set().union(*[(x*w,x*w+w-1) for x in range(h-1)])  # expected match locations

for p in permutations(x):
 string = ''.join('['+'_'*(2*n-2)+']'for n in p)
 bracketPositions = {m.start() for m in re.finditer(STACKED_BRACKET_RE,string)}
 print(string, bracketPositions, bracketGoal, STACKED_BRACKET_RE) #debug
 if bracketPositions==bracketGoal:
  break

print('\n'.join(re.findall(STRING_CHUNK_RE,string)))

---

Python, regexp method (304 chars):

from itertools import*
import re
x,h=input()
w=sum(x)*2/h
for p in permutations(x):
 s=''.join('['+'_'*(2*n-2)+']'for n in p)
 if {m.start()for m in re.finditer(r'(?=\[.{%i}\[|\].{%i}\])'%(w-1,w-1),s)}==set().union(*[(x*w,x*w+w-1) for x in range(h-1)]):
  break

print('\n'.join(re.findall('.{%i}'%w,s)))

Answer 8

PowerShell, 266 bytes

param($b,$h)$w=($b|%{'['+'__'*--$_+']'})+,"
"*--$h|sort;filter p{if($k=--$_){$k|p;0..($k-1)|%{$j=($_,0)[$_%2];$w[$j],$w[$k]=$w[$k,$j]
$k|p}}else{,(-join$w-split"
")}}$w.Length|p|?{!(($x=($a=$_)|% Le*|gu).Rank-or-join(1..($x-2)|%{$a|% Ch* $_})-match']]')}|select -f 1

Try it online!

This script is brute force algorithm:

1. converts numbers to related strings [], [__], [____], ...
2. adds as many LFs as the height is
3. generates all permutations by Heap's algorithm
4. checks and PassThru a valid wall only
5. returns first only wall

What can be improved: generate permutations for numbers, not strings. build a string representation in final.

Unrolled:

param($briks,$height)

$wall =                               
    ($briks|%{'['+'__'*--$_+']'})   +   # string [], [__], ... related to numbers
    ,"`n"*--$height                 |   # as many LF as the height
    sort                                # sort briks and LFs

# Heap's algorithm generates all possible permutations of $_ objects
# https://en.wikipedia.org/wiki/Heap%27s_algorithm
filter get-permutation{                 
    if($k=--$_){
        $k|get-permutation
        0..($k-1)|%{
            $j=($_,0)[$_%2]
            $wall[$j],$wall[$k]=$wall[$k,$j]
            $k|get-permutation
        }
    }
    else{
        ,(-join$wall -split "`n")       # return an array of strings represent a wall
    }
}

$wall.Length|get-permutation|where{     # generates all permutations, then check and PassThru a valid wall only
    !(                                                  # not
        ($x=($a=$_)|% Length|Get-Unique).Rank -or       #   length of all wall rows are different or
        -join(1..($x-2)|%{$a|% Chars $_})-match']]'     #   the wall is not steady
    )        
}|select -First 1

Answer 9

05AB1E, 36 bytes

œIδ.Œ€`ʒOË}.ΔεηO¨}üåà≠}<·'_×€€…[ÿ]J»

Slow brute-force approach (already times out for the last test case on TIO), but it works.

First input is the list of brick sizes and second input is the height integer.

Try it online or verify a few test cases at once.

Explanation:

First get all possible ways to divide the list of bricks into the height amount of rows (resulting in a list of list of list of integers, which we'll reference to as list of walls for now):

œ       # Take the powerset of the (implicit) input-list
        # (this holds a list of all possible ways to order the input-list)
 I      # Using the second height integer,
  δ     # map each inner permutation of the input-list to:
   .Π  #  Get all possible ways to divide the permutation into the height amount of pieces
     €` # Then flatten once

Then we'll filter this list to only keep walls whose rows have an equal width (so we're left with all rectangular walls):

ʒ       # Filter this list of walls by:
 O      #  Take the sum of each inner row
  Ë     #  Check if the sums of all the rows are equal
}       # Close the filter

Then we'll search for the first wall which doesn't have any vertical gaps between two adjacent rows:

.Δ      # Find the first wall which is truthy for:
  ε     #  Map each row to:
   η    #   Get the prefixes of bricks in this row
    O   #   Sum each prefix
     ¨  #   Remove the last (right side of the wall), since those are supposed to line up
  }     #  Close the inner map (we now have a list of list of integers, a.k.a. list of gaps)
   ü    #  Map over each pair of gaps:
    å   #   Check for each gap in the second gaps-list if it's in the first gaps-list
     à  #  Take the flattened maximum to check if any is truthy
      ≠ #  And invert that boolean, since we want to find a wall without gaps lining up
}       # Close the find_first

Now we've found our wall. All that's left is to transform it into the desired output-format and print it:

<       # Decrease each brick-value by 1
 ·      # Then double each
  '_×  '# And convert those integers to that amount of "_" as string
€       # Then map over each row:
 €      #  And each inner brick consisting of "_"
  …[ÿ]  # And surround it by "[" and "]"
J       # Then join each list of bricks together to form the rows
 »      # And join those rows by newlines to form the wall
        # (after which this is output implicitly as result)

Answer 10

PHP, 918 870 650 bytes

[$z,$h]=json_decode($argn);$j=$h-1;$p=array_fill(0,$c=100,[0,array_chunk($z,ceil(count($z)/$h))]);$r=fn($x)=>rand(0,$x);g:foreach($p as&$s){$b=[];for($s[0]=$l=0;$l<$h;$l++){for($m=$k=0;$k<~-count($v=$s[1][$l]);)$b[$l][]=$m+=$v[$k++];$s[0]+=abs(array_sum($z)/$h-$m-$v[$k]);}for($l=0;$l<$j;){if(array_intersect($b[$l]??[],$b[1+$l++]??[]))$s[0]+=9;}}usort($p,fn($a,$b)=>$a[0]<=>$b[0]);if(!$p[0][0]){foreach($p[0][1]as$l){foreach($l as$b)echo'[',str_repeat('_',~-$b*2),']';echo"\n";}die;}for($o=0;$o<99;$o++){$w=&$p[(int)sqrt($r($c*$c-1))][1];$a=&$w[$r($j)];$t=&$a[$i=$r($u=count($a)-1)];if($u){unset($a[$i]);$a=array_values($a);$w[$r($j)][]=$t;}}goto g;

Try it online!

Ungolfed

The idea is to use a hill climbing approach.

A population of walls is set up and each wall is scored. There are penalties for a wall's row of bricks not matching the expected width and for bricks lining up on consecutive rows. The scores are then ordered and a mutation operation applied favouring higher (worse) scoring walls.

Scoring and mutation are applied in succesive rounds until a solution is found. Solutions are usually found in under a second - except for the last test case, so it's quick (although bloaty).

[$brick_sizes,$height]=json_decode($argn);

$width = array_sum($brick_sizes)/$height;

$walls=[];

$walls[0]=array_chunk($brick_sizes,ceil(count($brick_sizes)/$height));

$population_count = 100;

// Clone default wall and set up initial population
for ($wall_index=1;$wall_index<$population_count;$wall_index++) {
    $walls[$wall_index] = $walls[0];
}

$iteration = 0;
do {
    // score population
    $scores = array_fill(0,$population_count, [0,0]);
    foreach ($walls as $wall_index => $wall) {
        foreach ($wall as $level) {
            $scores[$wall_index][0] += abs($width - array_sum($level));
            $scores[$wall_index][1] = $walls[$wall_index];
        }

        // Score alignment of bricks with penalty
        $brick_positions=[];
        for ($level=0;$level<$height;$level++) {
            $running_sum=0;

            for ($brick_index=0;$brick_index<(count($wall[$level])-1);$brick_index++) {
                $running_sum += $wall[$level][$brick_index];
                $brick_positions[$level][] = $running_sum;
            }

        }

        for ($level=0;$level<($height-1);$level++) {
            if (array_intersect($brick_positions[$level]??[],$brick_positions[$level+1]??[])) {
                $scores[$wall_index][0] += 10;
            }
        }
        
    }

    // sort score by best fit first
    usort($scores, function ($a, $b) {
        return $a[0] <=> $b[0];
    });

    //echo $iteration,':',$scores[0][0],"\n";
	
    // draw wall and exit
    if ($scores[0][0] == 0) {
        foreach ($scores[0][1] as $level){
            foreach ($level as $brick){
                echo '['.str_repeat('_',2*($brick-1)).']';
            }
            echo "\n";
        }
        die;
    }

    // sort population by score
    $walls = array_map(function($m){return $m[1];},$scores);

    // randomise bricks in population
    for ($rando = 0; $rando < 100; $rando++) {
        $wall_index = (int)sqrt(rand(0, $population_count*$population_count - 1));
        $level = [];
        $index = [];
        for ($do = 0; $do <= 1; $do++) {
            $level[$do] = rand(0, $height - 1);
            $index[$do] = rand(0, count($walls[$wall_index][$level[$do]]) - 1);
        }

        $temp = $walls[$wall_index][$level[0]][$index[0]];
        
        if (count($walls[$wall_index][$level[0]])>1) {
           unset($walls[$wall_index][$level[0]][$index[0]]);
           $walls[$wall_index][$level[0]]=array_values($walls[$wall_index][$level[0]]);
           $walls[$wall_index][$level[1]][] = $temp;
        }
    }

    $iteration++;
    
} while (true);

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Answer 11

Matlab (359)

function p(V),L=perms(V);x=sum(V);D=find(rem(x./(1:x),1)==0);for z= 2:numel(D-1)for y=1:numel(L),x=L(y,:);i=D(z);b=x;l=numel(x);for j=1:l,for k=j-1:-1:2,m=sum(x(1:k));if mod(m,i),if mod(m,i)<mod(sum(x(1:k-1)),i)||sum(x(1:j))-m==i,b=0;,end,end,end,end,if b,for j=1:l,fprintf('[%.*s]%c',(b(j)-2)+b(j),ones(9)*'_',(mod(sum(x(1:j)),i)<1)*10);end,return,end;end,end

Input

a vector of integers , example: p([1 1 2 2 3])

Output

the scheme of the wall example:

[____]

[__][]

[][__]