Nsryjdtyk

Question

Sixteen piles of cheese are put on a 4x4 square. They're labeled from $1$ to $16$. The smallest pile is $1$ and the biggest one is $16$.

The Hungry Mouse is so hungry that it always goes straight to the biggest pile (i.e. $16$) and eats it right away.

After that, it goes to the biggest neighboring pile and quickly eats that one as well. (Yeah ... It's really hungry.) And so on until there's no neighboring pile anymore.

A pile may have up to 8 neighbors (horizontally, vertically and diagonally). There's no wrap-around.

Example

We start with the following piles of cheese:

$$begin{matrix}
3&7&10&5\
6&8&12&13\
15&9&11&4\
14&1&16&2
end{matrix}$$

The Hungry Mouse first eats $16$, and then its biggest neighbor pile, which is $11$.

$$begin{matrix}
3&7&10&5\
6&8&12&13\
15&9&🐭&4\
14&1&color{grey}uparrow&2
end{matrix}$$

Its next moves are $13$, $12$, $10$, $8$, $15$, $14$, $9$, $6$, $7$ and $3$ in this exact order.

$$begin{matrix}
🐭&color{grey}leftarrow&smallcolor{grey}swarrow&5\
smallcolor{grey}nearrow&smallcolor{grey}swarrow&color{grey}uparrow&color{grey}leftarrow\
color{grey}downarrow&smallcolor{grey}nwarrow&smallcolor{grey}nearrow&4\
smallcolor{grey}nearrow&1&color{grey}uparrow&2
end{matrix}$$

There's no cheese anymore around the Hungry Mouse, so it stops there.

The challenge

Given the initial cheese configuration, your code must print or return the sum of the remaining piles once the Hungry Mouse has stopped eating them.

For the above example, the expected answer is $12$.

Rules

Because the size of the input matrix is fixed, you may take it as either a 2D array or a one-dimensional array.

Each value from $1$ to $16$ is guaranteed to appear exactly once.

This is code-golf.

Test cases

[ [ 4,  3,  2,  1], [ 5,  6,  7,  8], [12, 11, 10,  9], [13, 14, 15, 16] ] --> 0

[ [ 8,  1,  9, 14], [11,  6,  5, 16], [13, 15,  2,  7], [10,  3, 12,  4] ] --> 0

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

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

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

[ [ 8,  9,  3,  6], [13, 11,  7, 15], [12, 10, 16,  2], [ 4, 14,  1,  5] ] --> 34

[ [ 8, 11, 12,  9], [14,  5, 10, 16], [ 7,  3,  1,  6], [13,  4,  2, 15] ] --> 51

[ [13, 14,  1,  2], [16, 15,  3,  4], [ 5,  6,  7,  8], [ 9, 10, 11, 12] ] --> 78

[ [ 9, 10, 11, 12], [ 1,  2,  4, 13], [ 7,  8,  5, 14], [ 3, 16,  6, 15] ] --> 102

[ [ 9, 10, 11, 12], [ 1,  2,  7, 13], [ 6, 16,  4, 14], [ 3,  8,  5, 15] ] --> 103

78? You can be meaner than that! I think 102 is as mean as one can get though (e.g. [[9, 10, 11, 12], [1, 2, 4, 13], [7, 8, 5, 14], [3, 16, 6, 15]]) - hmm [0, 0, 19, 102, ...] — yesterday
...make that 103: [[9, 10, 11, 12], [1, 2, 7, 13], [6, 16, 4, 14], [3, 8, 5, 15]] — yesterday
What a nicely written challenge! I'll keep it in mind for the best-of nominations. — yesterday
After misreading I was a little sad that this was not a hungry moose. — 14 hours ago

score 11 · Answer 1 · 2018-11-20 02:38:27Z

up vote
11
down vote

Python 2, ₁₃₃ 130 bytes

a=input();m=16

for i in range(m):a[i*5:i*5]=0,

while m:i=a.index(m);a[i]=0;m=max(a[i+x]for x in[-6,-5,-4,-1,1,4,5,6])

print sum(a)

Try it online!

Takes a flattened list of 16 elements.

How it works

a=input();m=16



# Add zero padding on each row, and enough zeroes at the end to avoid index error

for i in range(m):a[i*5:i*5]=0,



# m == maximum element found in last iteration

# i == index of last eaten element

# eaten elements of `a` are reset to 0

while m:i=a.index(m);a[i]=0;m=max(a[i+x]for x in[-6,-5,-4,-1,1,4,5,6])

print sum(a)

edited yesterday

answered yesterday

Bubbler

5,624755

The adjacent-cell expression a[i+x]for x in[-6,-5,-4,-1,1,4,5,6] can be shortened to a[i+j+j/3*2-6]for j in range(9) (the zero entry is harmless). Python 3 can surely do shorter by hardcoding a length-8 bytestring, but Python 2 might still be better overall.
– xnor
yesterday

1

Though your zero padding loop is clever, it looks like it's shorter to take a 2D list: a=[0]*5 for r in input():a=r+[0]+a. Perhaps there's a yet shorter string slicing solution that doesn't require iterating.
– xnor
yesterday

add a comment |

score 6 · Answer 2 · 2018-11-20 00:13:03Z

PHP, 177 174 171 bytes

for($v=16;$v;$u+=$v=max($p%4-1?max($a[$p-5],$a[$p-1],$a[$p+3]):0,$a[$p-4],$a[$p+4],$p%4?max($a[$p-3],$a[$p+1],$a[$p+5]):0))$a[$p=array_search($v,$a=&$argv)]=0;echo 120-$u;

Run with -nr, provide matrix elements as arguments or try it online.

xnor 88.9k18184437 · Answer 3 · 2018-11-20 02:47:16Z

Python 2, 111 bytes

i=x=a=input()

while x:x,i=max((y,j)for j,y in enumerate(a)if i>or 2>i/4-j/4>-2<i%4-j%4<2);a[i]=0

print sum(a)

Try it online!

Method and test cases adapted from Bubbler. Takes a flat list on STDIN.

The code checks whether two flat indices i and j represent touching cells by checking that both row different i/4-j/4 and column difference i%4-j%4 are strictly between -2 and 2. The first pass instead has this check automatically succeed so that the largest entry is found disregarding adjacency.

score 6 · Answer 4 · 2018-11-20 14:21:16Z

MATL, 50 49 47 bytes

16:HZ^!"2G@m1ZIm~]v16eXK68E16b"Ky0)Y)fyX-X>h]s-

Input is a matrix, using ; as row separator.

Try it online! Or verify all test cases.

Explanation

16:HZ^!  % Cartesian power of [1 2 ... 16] with exponent 2, transpose. Gives a 

         % 2-row matrix with 1st column [1; 1], 2nd [1; 2], ..., last [16; 16] 

"        % For each column, say [k; j]

  2      %   Push 2

  G@m    %   Push input matrix, then current column [k; j], then check membership.

         %   This gives a 4×4 matrix that contains 1 for entries of the input that

         %   contain k or j 

  1ZI    %   Connected components (based on 8-neighbourhood) of nonzero entries.

         %   This gives a 4×4 matrix with each connected component labeled with

         %   values 1, 2, ... respectively

  m~     %   True if 2 is not present in this matrix. That means there is only

         %   one connected component; that is, k and j are neighbours in the

         %   input matrix, or k=j

]        % End

v16e     % The stack now has 256 values. Concatenate them into a vector and

         % reshape as a 16×16 matrix. This matrix describes neighbourhood: entry 

         % (k,j) is 1 if values k and j are neighbours in the input or if k=j

XK       % Copy into clipboard K

68E      % Push 68 times 2, that is, 136, which is 1+2+...+16

16       % Push 16. This is the initial value eaten by the mouse. New values will

         % be appended to create a vector of eaten values

b        % Bubble up the 16×16 matrix to the top of the stack

"        % For each column. This just executes the loop 16 times

  K      %   Push neighbourhood matrix from clipboard K

  y      %   Copy from below: pushes a copy of the vector of eaten values

  0)     %   Get last value. This is the most recent eaten value

  Y)     %   Get that row of the neighbourhood matrix

  f      %   Indices of nonzeros. This gives a vector of neighbours of the last

         %   eaten value

  y      %   Copy from below: pushes a copy of the vector of eaten values

  X-     %   Set difference (may give an empty result)

  X>     %   Maximum value. This is the new eaten value (maximum neighbour not

         %   already eaten). May be empty, if all neighbours are already eaten

  h      %   Concatenate to vector of eaten values

]        % End

s        % Sum of vector of all eaten values

-        % Subtract from 136. Implicitly display

Idk MatLab, but can you save a little if you push -136 instead of +136? — 2 hours ago

Neil 78k744175 · Answer 5 · 2018-11-20 10:17:16Z

Charcoal, 47 bytes

ＥＡ⭆ι§αλ≔QθＷ›θA«≔⌕ＫＡθθＪ﹪θ⁴÷θ⁴≔⌈ＫＭθA»≔ΣＥＫＡ⌕αιθ⎚Ｉθ

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

ＥＡ⭆ι§αλ

Convert the input numbers into alphabetic characters (A=0 .. Q=16) and print them as a 4x4 grid.

≔Qθ

Start by eating the Q, i.e. 16.

Ｗ›θA«

Repeat while there is something to eat.

≔⌕ＫＡθθ

Find where the pile is. This is a linear view in row-major order.

Ｊ﹪θ⁴÷θ⁴

Convert to co-ordinates and jump to that location.

≔⌈ＫＭθ

Find the largest adjacent pile.

A»

Eat the current pile.

≔ΣＥＫＡ⌕αιθ

Convert the piles back to integers and take the sum.

⎚Ｉθ

Clear the canvas and output the result.

Shaggy 18.1k21663 · Answer 6 · 2018-11-20 17:25:02Z

up vote
2
down vote

JavaScript, 122 bytes

I took more than a couple of wrong turns on this one and now I've run out of time for further golfing but at least it's working. Will revisit tomorrow (or, knowing me, on the train home this evening!), if I can find a minute.

a=>(g=n=>n?g([-6,-5,-4,-1,1,4,5,6].map(x=>n=a[x+=i]>n?a[x]:n,a[i=a.indexOf(n)]=n=0)|n)-n:120)(16,a=a.flatMap(x=>[...x,0]))

Try it online

answered 10 hours ago

Shaggy

18.1k21663

1

+1 for flatMap() :p
– Arnauld
10 hours ago

:D I think this is the first time I've used it for golf! Out of interest (and to give me a target when I come back to this), what was your score when you tried it?
– Shaggy
10 hours ago

1

I didn't try to golf it. Unless I have a specific trick in mind, I usually just write clean code to test my challenges.
– Arnauld
10 hours ago

Ok, you've convinced me to try. :) I'm currently at <s>116</s> 114.
– Arnauld
8 hours ago

Finally reached 103 bytes.
– Arnauld
6 hours ago

add a comment |

score 2 · Answer 7 · 2018-11-20 18:51:59Z

SAS, 236 219 bytes

Input on punch cards, one line per grid (space-separated), output printed to the log.

This challenge is slightly complicated by the fact that SAS has no way to return the row and column indexes of a matching element from multidimensional data-step array - you have to treat the array as 1-d and then work them out for yourself.

data;input a1-a16;array a[4,4]a:;p=16;t=136;do while(p);m=whichn(p,of a:);t=t-p;j=mod(m-1,4)+1;i=ceil(m/4);a[i,j]=0;p=0;do k=max(1,i-1)to min(i+1,4);do l=max(1,j-1)to min(j+1,4);p=max(p,a[k,l]);end;end;end;put t;cards;

<insert punch cards here>

;

Updates:

Removed infile cards; statement (-13)

Used wildcard a: for array definition rather than a1-a16 (-4)

Ungolfed version:

data;                /*Produce a dataset using automatic naming*/

input a1-a16;        /*Read 16 variables*/

array a[4,4] a:;     /*Assign to a 4x4 array*/

p=16;                /*Initial pile to look for*/

t=136;               /*Total cheese to decrement*/

do while(p);         /*Stop if there are no piles available with size > 0*/

  m=whichn(p,of a:); /*Find array element containing current pile size*/

  t=t-p;             /*Decrement total cheese*/

  j=mod(m-1,4)+1;    /*Get column number*/

  i=ceil(m/4);       /*Get row number*/

  a[i,j]=0;          /*Eat the current pile*/

                     /*Find the size of the largest adjacent pile*/

  p=0;

  do k=max(1,i-1)to min(i+1,4);

    do l=max(1,j-1)to min(j+1,4);

      p=max(p,a[k,l]);

    end;

  end;

end;

put t;              /*Print total remaining cheese to log*/

                    /*Start of punch card input*/

cards; 

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

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

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

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

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

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

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

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

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

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

;                    /*End of punch card input*/

                     /*Implicit run;*/

+1 for use of punch cards in PPCG :)
– GNiklasch
9 hours ago — 9 hours ago

score 1 · Answer 8 · 2018-11-20 07:00:34Z

up vote
1
down vote

J, 82 bytes

g=.](]*{:@[~:])]_1}~[:>./]{~((,-)1 5 6 7)+]i.{:

[:+/[:(g^:_)16,~[:,0,~0,0,0,.~0,.]

Try it online!

I plan to golf this more tomorrow, and perhaps write a more J-ish solution similar to this one, but I figured I'd try the flattened approach since I hadn't done that before.

edited 20 hours ago

answered 21 hours ago

Jonah

1,951816

Do you really need the leftmost ] in g?
– Galen Ivanov
20 hours ago

Thanks Galen, you're right. It's the least of the issues with this code :) I have a much better solution which I'll implement when I have time.
– Jonah
2 hours ago

add a comment |

Galen Ivanov 5,90711032 · Answer 9 · 2018-11-20 09:02:04Z

Red, 277 bytes

func[a][k: 16 until[t:(index? find load form a k)- 1

p: do rejoin[t / 4 + 1"x"t % 4 + 1]a/(p/1)/(p/2): 0

m: 0 foreach d[-1 0x-1 1x-1 -1x0 1x0 -1x1 0x1 1][j: p + d

if all[j/1 > 0 j/1 < 5 j/2 > 0 j/2 < 5 m < t: a/(j/1)/(j/2)][m: t]]0 = k: m]s: 0

foreach n load form a[s: s + n]s]

Try it online!

It's really long solution and I'm not happy with it, but I spent so much time fixing it to work in TIO (apparently there are many differences between the Win and Linux stable versions of Red), so I post it anyway...

Java 10, 272 bytes

m->{int r=0,c=0,R=4,C,M=1,x,y,X=0,Y=0;for(;R-->0;)for(C=4;C-->0;)if(m[R][C]>15)m[r=R][c=C]=0;for(;M!=0;m[r=X][c=Y]=0)for(M=-1,C=9;C-->0;)try{if((R=m[x=C<3?r-1:C>5?r+1:r][y=C%3<1?c-1:C%3>1?c+1:c])>M){M=R;X=x;Y=y;}}catch(Exception e){}for(var Z:m)for(int z:Z)M+=z;return M;}

The cells are checked the same as in my answer for the All the single eights challenge.

Try it online.

Explanation:

m->{                       // Method with integer-matrix parameter and integer return-type

  int r=0,                 //  Row-coordinate for the largest number, starting at 0

      c=0,                 //  Column-coordinate for the largest number, starting at 0

      R=4,C,               //  Row and column indices (later reused as temp integers)

      M=1,                 //  Largest number the mouse just ate, starting at 1

      x,y,X=0,Y=0;         //  Temp integers

  for(;R-->0;)             //  Loop `R` in the range (4, 0]:

    for(C=4;C-->0;)        //   Inner loop `C` in the range (4, 0]:

      if(m[R][C]>15)       //    If the current cell is 16:

        m[r=R][c=C]        //     Set `r,c` to this coordinate

          =0;              //     And empty this cell

  for(;M!=0;               //  Loop as long as the largest number isn't 0:

      ;                    //    After every iteration:

       m[r=X][c=Y]         //     Change the `r,c` coordinates,

         =0)               //     And empty this cell

    for(M=-1,              //   Reset `M` to -1

        C=9;C-->0;)        //   Inner loop `C` in the range (9, 0]:

          try{if((R=       //    Set `R` to:

            m[x=C<3?       //     If `C` is 0, 1, or 2:

                 r-1       //      Look at the previous row

                :C>5?      //     Else-if `C` is 6, 7, or 8:

                 r+1       //      Look at the next row

                :          //     Else (`C` is 3, 4, or 5):

                 r]        //      Look at the current row

             [y=C%3<1?     //     If `C` is 0, 3, or 6:

                 c-1       //      Look at the previous column

                :C%3>1?    //     Else-if `C` is 2, 5, or 8:

                 c+1       //      Look at the next column

                :          //     Else (`C` is 1, 4, or 7):

                 c])       //      Look at the current column

               >M){        //    And if the number in this cell is larger than `M`

                 M=R;      //     Change `M` to this number

                 X=x;Y=y;} //     And change the `X,Y` coordinate to this cell

          }catch(Exception e){}

                           //    Catch and ignore ArrayIndexOutOfBoundsExceptions

                           //    (try-catch saves bytes in comparison to if-checks)

  for(var Z:m)             //  Then loop over all rows of the matrix:

    for(int z:Z)           //   Inner loop over all columns of the matrix:

      M+=z;                //    And sum them all together in `M` (which was 0)

  return M;}               //  Then return this sum as result

score 1 · Answer 11 · 2018-11-20 18:15:13Z

Jelly, 31 30 29 bytes

³œiⱮZIỊȦ

⁴ṖŒPŒ!€Ẏ⁴;ⱮṢÇƇṪ

FḟÇS

Since the method is far too slow to run within 60s with the mouse starting on 16 this starts her off at 9 and limits her ability such that she is only able to eat 9s or less Try it online! (thus here she eats 9, 2, 7, 4, 8, 6, 3 leaving 97).

How?

³œiⱮZIỊȦ - Link 1, isSatisfactory?: list of integers, possiblePileChoice

³        - (using a left argument of) program's 3rd command line argument (M)

   Ɱ     - map across (possiblePileChoice) with:

 œi      -   first multi-dimensional index of (the item) in (M)

    Z    - transpose the resulting list of [row, column] values

     I   - get the incremental differences

      Ị  - insignificant? (vectorises an abs(v) <= 1 test)

       Ȧ - any and all? (0 if any 0s are present in the flattened result [or if it's empty])



⁴ṖŒPŒ!€Ẏ⁴;ⱮṢÇƇṪ - Link 2, getChosenPileList: list of lists of integers, M

⁴               - literal 16

 Ṗ              - pop -> [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]

  ŒP            - power-set -> [,[1],[2],...,[1,2],[1,3],...,[2,3,7],...,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]]

      €         - for each:

    Œ!          -   all permutations

       Ẏ        - tighten (to a single list of all these individual permutations)

        ⁴       - (using a left argument of) literal 16

          Ɱ     - map across it with:

         ;      -   concatenate (put a 16 at the beginning of each one)

           Ṣ    - sort the resulting list of lists

             Ƈ  - filter keep those for which this is truthy:

            Ç   -   call last Link as a monad (i.e. isSatisfactory(possiblePileChoice)

              Ṫ - tail (get the right-most, i.e. the maximal satisfactory one)



FḟÇS - Main Link: list of lists of integers, M

F    - flatten M

  Ç  - call last Link (2) as a monad (i.e. get getChosenPileList(M))

 ḟ   - filter discard (the resulting values) from (the flattened M)

   S - sum

@Arnauld - finally got a little time to golf :D This should work, but will be (way) too slow for running at TIO with the test case you used before. — 10 hours ago

Jeff Freeman 20114 · Answer 12 · 2018-11-20 19:10:47Z

Not my best work. There's some definite improvements to be done, some probably fundamental to the algorithm used -- I'm sure it can be improved by using only an int, but I couldn't figure out how to efficiently enumerate neighbors that way. I'd love to see a PowerShell solution that uses only a single dimensional array!

PowerShell Core, 348 bytes

Function F($o){$t=120;$a=@{-1=,0*4;4=,0*4};0..3|%{$a[$_]=[int](-join$o[(3+18*$_)..(3+18*$_+13)]-split',')+,0};$m=16;while($m-gt0){0..3|%{$i=$_;0..3|%{if($a[$i][$_]-eq$m){$r=$i;$c=$_}}};$m=($a[$r-1][$c-1],$a[$r-1][$c],$a[$r-1][$c+1],$a[$r][$c+1],$a[$r][$c-1],$a[$r+1][$c-1],$a[$r+1][$c],$a[$r+1][$c+1]|Measure -Max).Maximum;$t-=$m;$a[$r][$c]=0}$t}

Try it online!

R, 128 124 bytes

r=rbind(0,cbind(0,matrix(scan(),4,4),0),0)

m=which(r==16)

while(r[m]){r[m]=0

m=which(r==max(r[m+c(-7:-5,-1,1,5:7)]))}

sum(r)

Try it online!

TIO link is slightly different, I am still trying to figure out how to make it work.

I do feel like I can golf a lot more out of this. But this works for now.

It creates a 4x4 matrix (which helped me to visualize things), pads it with 0's, then begins from 16 and searches it's surrounding "piles" for the next largest, and so forth.

Upon conclusion, it does output a warning, but it is of no consequence and does not change the result.

EDIT: -4 bytes by compressing the initialization of the matrix into 1 line

score 1 · Answer 14 · 2018-11-20 22:34:52Z

Powershell, 143 141 bytes

-2 bytes: Yeah, one zero as delimiter is enough.

$a=,0*6+($args|%{$_+0})+,0*4

for($n=16;$n){$a[($i=$a.IndexOf($n))]=0

[int]$n=-1,1+-6..-4+4..6|%{$a[$i+$_]}|measure -ma|% ma*}

$a|%{$s+=$_}

$s

Less golfed test script:

$f = {



$a=,0*6+($args|%{$_+0})+,0*4

for($n=16;$n){

    $i=$a.IndexOf($n)

    $a[$i]=0

    [int]$n=-1,1+-6..-4+4..6|%{

        $a[$i+$_]

    }|measure -maximum|% maximum

}

$a|%{$s+=$_}

$s



}



@(

    ,( 0  , ( 4,  3,  2,  1), ( 5,  6,  7,  8), (12, 11, 10,  9), (13, 14, 15, 16) )

    ,( 0  , ( 8,  1,  9, 14), (11,  6,  5, 16), (13, 15,  2,  7), (10,  3, 12,  4) )

    ,( 1  , ( 1,  2,  3,  4), ( 5,  6,  7,  8), ( 9, 10, 11, 12), (13, 14, 15, 16) )

    ,( 3  , (10, 15, 14, 11), ( 9,  3,  1,  7), (13,  5, 12,  6), ( 2,  8,  4, 16) )

    ,( 12 , ( 3,  7, 10,  5), ( 6,  8, 12, 13), (15,  9, 11,  4), (14,  1, 16,  2) )

    ,( 34 , ( 8,  9,  3,  6), (13, 11,  7, 15), (12, 10, 16,  2), ( 4, 14,  1,  5) )

    ,( 51 , ( 8, 11, 12,  9), (14,  5, 10, 16), ( 7,  3,  1,  6), (13,  4,  2, 15) )

    ,( 78 , (13, 14,  1,  2), (16, 15,  3,  4), ( 5,  6,  7,  8), ( 9, 10, 11, 12) )

    ,( 102, ( 9, 10, 11, 12), ( 1,  2,  4, 13), ( 7,  8,  5, 14), ( 3, 16,  6, 15) )

    ,( 103, ( 9, 10, 11, 12), ( 1,  2,  7, 13), ( 6, 16,  4, 14), ( 3,  8,  5, 15) )

) | % {

    $expected, $a = $_

    $result = &$f @a

    "$($result-eq$expected): $result"

}

Output:

True: 0

True: 0

True: 1

True: 3

True: 12

True: 34

True: 51

True: 78

True: 102

True: 103

Explanation:

First, add a border of 0 and make a single dimensional array:

0 0 0 0 0

0 # # # #

0 # # # #

0 # # # #

0 # # # #

0 0 0 0 0



     ↓



0 0 0 0 0 0 # # # # 0 # # # # 0 # # # # 0 # # # # 0 0 0 0 0 0

Second, loop biggest neighbor pile started from 16 to non-zero-maximum. And nullify it (The Hungry Mouse eats it).

for($n=16;$n){

    $i=$a.IndexOf($n)

    $a[$i]=0

    [int]$n=-1,1+-6..-4+4..6|%{

        $a[$i+$_]

    }|measure -maximum|% maximum

}

Third, sum of the remaining piles.

score 11 · Answer 15 · 2018-11-20 02:38:27Z

up vote
11
down vote

Python 2, ₁₃₃ 130 bytes

a=input();m=16

for i in range(m):a[i*5:i*5]=0,

while m:i=a.index(m);a[i]=0;m=max(a[i+x]for x in[-6,-5,-4,-1,1,4,5,6])

print sum(a)

Try it online!

Takes a flattened list of 16 elements.

How it works

a=input();m=16



# Add zero padding on each row, and enough zeroes at the end to avoid index error

for i in range(m):a[i*5:i*5]=0,



# m == maximum element found in last iteration

# i == index of last eaten element

# eaten elements of `a` are reset to 0

while m:i=a.index(m);a[i]=0;m=max(a[i+x]for x in[-6,-5,-4,-1,1,4,5,6])

print sum(a)

edited yesterday

answered yesterday

Bubbler

5,624755

The adjacent-cell expression a[i+x]for x in[-6,-5,-4,-1,1,4,5,6] can be shortened to a[i+j+j/3*2-6]for j in range(9) (the zero entry is harmless). Python 3 can surely do shorter by hardcoding a length-8 bytestring, but Python 2 might still be better overall.
– xnor
yesterday

1

Though your zero padding loop is clever, it looks like it's shorter to take a 2D list: a=[0]*5 for r in input():a=r+[0]+a. Perhaps there's a yet shorter string slicing solution that doesn't require iterating.
– xnor
yesterday

add a comment |

score 6 · Answer 16 · 2018-11-20 00:13:03Z

PHP, 177 174 171 bytes

for($v=16;$v;$u+=$v=max($p%4-1?max($a[$p-5],$a[$p-1],$a[$p+3]):0,$a[$p-4],$a[$p+4],$p%4?max($a[$p-3],$a[$p+1],$a[$p+5]):0))$a[$p=array_search($v,$a=&$argv)]=0;echo 120-$u;

Run with -nr, provide matrix elements as arguments or try it online.

xnor 88.9k18184437 · Answer 17 · 2018-11-20 02:47:16Z

Python 2, 111 bytes

i=x=a=input()

while x:x,i=max((y,j)for j,y in enumerate(a)if i>or 2>i/4-j/4>-2<i%4-j%4<2);a[i]=0

print sum(a)

Try it online!

Method and test cases adapted from Bubbler. Takes a flat list on STDIN.

The code checks whether two flat indices i and j represent touching cells by checking that both row different i/4-j/4 and column difference i%4-j%4 are strictly between -2 and 2. The first pass instead has this check automatically succeed so that the largest entry is found disregarding adjacency.

score 6 · Answer 18 · 2018-11-20 14:21:16Z

MATL, 50 49 47 bytes

16:HZ^!"2G@m1ZIm~]v16eXK68E16b"Ky0)Y)fyX-X>h]s-

Input is a matrix, using ; as row separator.

Try it online! Or verify all test cases.

Explanation

16:HZ^!  % Cartesian power of [1 2 ... 16] with exponent 2, transpose. Gives a 

         % 2-row matrix with 1st column [1; 1], 2nd [1; 2], ..., last [16; 16] 

"        % For each column, say [k; j]

  2      %   Push 2

  G@m    %   Push input matrix, then current column [k; j], then check membership.

         %   This gives a 4×4 matrix that contains 1 for entries of the input that

         %   contain k or j 

  1ZI    %   Connected components (based on 8-neighbourhood) of nonzero entries.

         %   This gives a 4×4 matrix with each connected component labeled with

         %   values 1, 2, ... respectively

  m~     %   True if 2 is not present in this matrix. That means there is only

         %   one connected component; that is, k and j are neighbours in the

         %   input matrix, or k=j

]        % End

v16e     % The stack now has 256 values. Concatenate them into a vector and

         % reshape as a 16×16 matrix. This matrix describes neighbourhood: entry 

         % (k,j) is 1 if values k and j are neighbours in the input or if k=j

XK       % Copy into clipboard K

68E      % Push 68 times 2, that is, 136, which is 1+2+...+16

16       % Push 16. This is the initial value eaten by the mouse. New values will

         % be appended to create a vector of eaten values

b        % Bubble up the 16×16 matrix to the top of the stack

"        % For each column. This just executes the loop 16 times

  K      %   Push neighbourhood matrix from clipboard K

  y      %   Copy from below: pushes a copy of the vector of eaten values

  0)     %   Get last value. This is the most recent eaten value

  Y)     %   Get that row of the neighbourhood matrix

  f      %   Indices of nonzeros. This gives a vector of neighbours of the last

         %   eaten value

  y      %   Copy from below: pushes a copy of the vector of eaten values

  X-     %   Set difference (may give an empty result)

  X>     %   Maximum value. This is the new eaten value (maximum neighbour not

         %   already eaten). May be empty, if all neighbours are already eaten

  h      %   Concatenate to vector of eaten values

]        % End

s        % Sum of vector of all eaten values

-        % Subtract from 136. Implicitly display

Idk MatLab, but can you save a little if you push -136 instead of +136? — 2 hours ago

Neil 78k744175 · Answer 19 · 2018-11-20 10:17:16Z

Charcoal, 47 bytes

ＥＡ⭆ι§αλ≔QθＷ›θA«≔⌕ＫＡθθＪ﹪θ⁴÷θ⁴≔⌈ＫＭθA»≔ΣＥＫＡ⌕αιθ⎚Ｉθ

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

ＥＡ⭆ι§αλ

Convert the input numbers into alphabetic characters (A=0 .. Q=16) and print them as a 4x4 grid.

≔Qθ

Start by eating the Q, i.e. 16.

Ｗ›θA«

Repeat while there is something to eat.

≔⌕ＫＡθθ

Find where the pile is. This is a linear view in row-major order.

Ｊ﹪θ⁴÷θ⁴

Convert to co-ordinates and jump to that location.

≔⌈ＫＭθ

Find the largest adjacent pile.

A»

Eat the current pile.

≔ΣＥＫＡ⌕αιθ

Convert the piles back to integers and take the sum.

⎚Ｉθ

Clear the canvas and output the result.

Shaggy 18.1k21663 · Answer 20 · 2018-11-20 17:25:02Z

up vote
2
down vote

JavaScript, 122 bytes

I took more than a couple of wrong turns on this one and now I've run out of time for further golfing but at least it's working. Will revisit tomorrow (or, knowing me, on the train home this evening!), if I can find a minute.

a=>(g=n=>n?g([-6,-5,-4,-1,1,4,5,6].map(x=>n=a[x+=i]>n?a[x]:n,a[i=a.indexOf(n)]=n=0)|n)-n:120)(16,a=a.flatMap(x=>[...x,0]))

Try it online

answered 10 hours ago

Shaggy

18.1k21663

1

+1 for flatMap() :p
– Arnauld
10 hours ago

:D I think this is the first time I've used it for golf! Out of interest (and to give me a target when I come back to this), what was your score when you tried it?
– Shaggy
10 hours ago

1

I didn't try to golf it. Unless I have a specific trick in mind, I usually just write clean code to test my challenges.
– Arnauld
10 hours ago

Ok, you've convinced me to try. :) I'm currently at <s>116</s> 114.
– Arnauld
8 hours ago

Finally reached 103 bytes.
– Arnauld
6 hours ago

add a comment |

score 2 · Answer 21 · 2018-11-20 18:51:59Z

SAS, 236 219 bytes

Input on punch cards, one line per grid (space-separated), output printed to the log.

This challenge is slightly complicated by the fact that SAS has no way to return the row and column indexes of a matching element from multidimensional data-step array - you have to treat the array as 1-d and then work them out for yourself.

data;input a1-a16;array a[4,4]a:;p=16;t=136;do while(p);m=whichn(p,of a:);t=t-p;j=mod(m-1,4)+1;i=ceil(m/4);a[i,j]=0;p=0;do k=max(1,i-1)to min(i+1,4);do l=max(1,j-1)to min(j+1,4);p=max(p,a[k,l]);end;end;end;put t;cards;

<insert punch cards here>

;

Updates:

Removed infile cards; statement (-13)

Used wildcard a: for array definition rather than a1-a16 (-4)

Ungolfed version:

data;                /*Produce a dataset using automatic naming*/

input a1-a16;        /*Read 16 variables*/

array a[4,4] a:;     /*Assign to a 4x4 array*/

p=16;                /*Initial pile to look for*/

t=136;               /*Total cheese to decrement*/

do while(p);         /*Stop if there are no piles available with size > 0*/

  m=whichn(p,of a:); /*Find array element containing current pile size*/

  t=t-p;             /*Decrement total cheese*/

  j=mod(m-1,4)+1;    /*Get column number*/

  i=ceil(m/4);       /*Get row number*/

  a[i,j]=0;          /*Eat the current pile*/

                     /*Find the size of the largest adjacent pile*/

  p=0;

  do k=max(1,i-1)to min(i+1,4);

    do l=max(1,j-1)to min(j+1,4);

      p=max(p,a[k,l]);

    end;

  end;

end;

put t;              /*Print total remaining cheese to log*/

                    /*Start of punch card input*/

cards; 

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

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

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

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

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

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

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

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

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

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

;                    /*End of punch card input*/

                     /*Implicit run;*/

+1 for use of punch cards in PPCG :)
– GNiklasch
9 hours ago — 9 hours ago

score 1 · Answer 22 · 2018-11-20 07:00:34Z

up vote
1
down vote

J, 82 bytes

g=.](]*{:@[~:])]_1}~[:>./]{~((,-)1 5 6 7)+]i.{:

[:+/[:(g^:_)16,~[:,0,~0,0,0,.~0,.]

Try it online!

I plan to golf this more tomorrow, and perhaps write a more J-ish solution similar to this one, but I figured I'd try the flattened approach since I hadn't done that before.

edited 20 hours ago

answered 21 hours ago

Jonah

1,951816

Do you really need the leftmost ] in g?
– Galen Ivanov
20 hours ago

Thanks Galen, you're right. It's the least of the issues with this code :) I have a much better solution which I'll implement when I have time.
– Jonah
2 hours ago

add a comment |

Galen Ivanov 5,90711032 · Answer 23 · 2018-11-20 09:02:04Z

Red, 277 bytes

func[a][k: 16 until[t:(index? find load form a k)- 1

p: do rejoin[t / 4 + 1"x"t % 4 + 1]a/(p/1)/(p/2): 0

m: 0 foreach d[-1 0x-1 1x-1 -1x0 1x0 -1x1 0x1 1][j: p + d

if all[j/1 > 0 j/1 < 5 j/2 > 0 j/2 < 5 m < t: a/(j/1)/(j/2)][m: t]]0 = k: m]s: 0

foreach n load form a[s: s + n]s]

Try it online!

It's really long solution and I'm not happy with it, but I spent so much time fixing it to work in TIO (apparently there are many differences between the Win and Linux stable versions of Red), so I post it anyway...

Java 10, 272 bytes

m->{int r=0,c=0,R=4,C,M=1,x,y,X=0,Y=0;for(;R-->0;)for(C=4;C-->0;)if(m[R][C]>15)m[r=R][c=C]=0;for(;M!=0;m[r=X][c=Y]=0)for(M=-1,C=9;C-->0;)try{if((R=m[x=C<3?r-1:C>5?r+1:r][y=C%3<1?c-1:C%3>1?c+1:c])>M){M=R;X=x;Y=y;}}catch(Exception e){}for(var Z:m)for(int z:Z)M+=z;return M;}

The cells are checked the same as in my answer for the All the single eights challenge.

Try it online.

Explanation:

m->{                       // Method with integer-matrix parameter and integer return-type

  int r=0,                 //  Row-coordinate for the largest number, starting at 0

      c=0,                 //  Column-coordinate for the largest number, starting at 0

      R=4,C,               //  Row and column indices (later reused as temp integers)

      M=1,                 //  Largest number the mouse just ate, starting at 1

      x,y,X=0,Y=0;         //  Temp integers

  for(;R-->0;)             //  Loop `R` in the range (4, 0]:

    for(C=4;C-->0;)        //   Inner loop `C` in the range (4, 0]:

      if(m[R][C]>15)       //    If the current cell is 16:

        m[r=R][c=C]        //     Set `r,c` to this coordinate

          =0;              //     And empty this cell

  for(;M!=0;               //  Loop as long as the largest number isn't 0:

      ;                    //    After every iteration:

       m[r=X][c=Y]         //     Change the `r,c` coordinates,

         =0)               //     And empty this cell

    for(M=-1,              //   Reset `M` to -1

        C=9;C-->0;)        //   Inner loop `C` in the range (9, 0]:

          try{if((R=       //    Set `R` to:

            m[x=C<3?       //     If `C` is 0, 1, or 2:

                 r-1       //      Look at the previous row

                :C>5?      //     Else-if `C` is 6, 7, or 8:

                 r+1       //      Look at the next row

                :          //     Else (`C` is 3, 4, or 5):

                 r]        //      Look at the current row

             [y=C%3<1?     //     If `C` is 0, 3, or 6:

                 c-1       //      Look at the previous column

                :C%3>1?    //     Else-if `C` is 2, 5, or 8:

                 c+1       //      Look at the next column

                :          //     Else (`C` is 1, 4, or 7):

                 c])       //      Look at the current column

               >M){        //    And if the number in this cell is larger than `M`

                 M=R;      //     Change `M` to this number

                 X=x;Y=y;} //     And change the `X,Y` coordinate to this cell

          }catch(Exception e){}

                           //    Catch and ignore ArrayIndexOutOfBoundsExceptions

                           //    (try-catch saves bytes in comparison to if-checks)

  for(var Z:m)             //  Then loop over all rows of the matrix:

    for(int z:Z)           //   Inner loop over all columns of the matrix:

      M+=z;                //    And sum them all together in `M` (which was 0)

  return M;}               //  Then return this sum as result

score 1 · Answer 25 · 2018-11-20 18:15:13Z

Jelly, 31 30 29 bytes

³œiⱮZIỊȦ

⁴ṖŒPŒ!€Ẏ⁴;ⱮṢÇƇṪ

FḟÇS

Since the method is far too slow to run within 60s with the mouse starting on 16 this starts her off at 9 and limits her ability such that she is only able to eat 9s or less Try it online! (thus here she eats 9, 2, 7, 4, 8, 6, 3 leaving 97).

How?

³œiⱮZIỊȦ - Link 1, isSatisfactory?: list of integers, possiblePileChoice

³        - (using a left argument of) program's 3rd command line argument (M)

   Ɱ     - map across (possiblePileChoice) with:

 œi      -   first multi-dimensional index of (the item) in (M)

    Z    - transpose the resulting list of [row, column] values

     I   - get the incremental differences

      Ị  - insignificant? (vectorises an abs(v) <= 1 test)

       Ȧ - any and all? (0 if any 0s are present in the flattened result [or if it's empty])



⁴ṖŒPŒ!€Ẏ⁴;ⱮṢÇƇṪ - Link 2, getChosenPileList: list of lists of integers, M

⁴               - literal 16

 Ṗ              - pop -> [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]

  ŒP            - power-set -> [,[1],[2],...,[1,2],[1,3],...,[2,3,7],...,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]]

      €         - for each:

    Œ!          -   all permutations

       Ẏ        - tighten (to a single list of all these individual permutations)

        ⁴       - (using a left argument of) literal 16

          Ɱ     - map across it with:

         ;      -   concatenate (put a 16 at the beginning of each one)

           Ṣ    - sort the resulting list of lists

             Ƈ  - filter keep those for which this is truthy:

            Ç   -   call last Link as a monad (i.e. isSatisfactory(possiblePileChoice)

              Ṫ - tail (get the right-most, i.e. the maximal satisfactory one)



FḟÇS - Main Link: list of lists of integers, M

F    - flatten M

  Ç  - call last Link (2) as a monad (i.e. get getChosenPileList(M))

 ḟ   - filter discard (the resulting values) from (the flattened M)

   S - sum

@Arnauld - finally got a little time to golf :D This should work, but will be (way) too slow for running at TIO with the test case you used before. — 10 hours ago

Jeff Freeman 20114 · Answer 26 · 2018-11-20 19:10:47Z

Not my best work. There's some definite improvements to be done, some probably fundamental to the algorithm used -- I'm sure it can be improved by using only an int, but I couldn't figure out how to efficiently enumerate neighbors that way. I'd love to see a PowerShell solution that uses only a single dimensional array!

PowerShell Core, 348 bytes

Function F($o){$t=120;$a=@{-1=,0*4;4=,0*4};0..3|%{$a[$_]=[int](-join$o[(3+18*$_)..(3+18*$_+13)]-split',')+,0};$m=16;while($m-gt0){0..3|%{$i=$_;0..3|%{if($a[$i][$_]-eq$m){$r=$i;$c=$_}}};$m=($a[$r-1][$c-1],$a[$r-1][$c],$a[$r-1][$c+1],$a[$r][$c+1],$a[$r][$c-1],$a[$r+1][$c-1],$a[$r+1][$c],$a[$r+1][$c+1]|Measure -Max).Maximum;$t-=$m;$a[$r][$c]=0}$t}

Try it online!

R, 128 124 bytes

r=rbind(0,cbind(0,matrix(scan(),4,4),0),0)

m=which(r==16)

while(r[m]){r[m]=0

m=which(r==max(r[m+c(-7:-5,-1,1,5:7)]))}

sum(r)

Try it online!

TIO link is slightly different, I am still trying to figure out how to make it work.

I do feel like I can golf a lot more out of this. But this works for now.

It creates a 4x4 matrix (which helped me to visualize things), pads it with 0's, then begins from 16 and searches it's surrounding "piles" for the next largest, and so forth.

Upon conclusion, it does output a warning, but it is of no consequence and does not change the result.

EDIT: -4 bytes by compressing the initialization of the matrix into 1 line

score 1 · Answer 28 · 2018-11-20 22:34:52Z

Powershell, 143 141 bytes

-2 bytes: Yeah, one zero as delimiter is enough.

$a=,0*6+($args|%{$_+0})+,0*4

for($n=16;$n){$a[($i=$a.IndexOf($n))]=0

[int]$n=-1,1+-6..-4+4..6|%{$a[$i+$_]}|measure -ma|% ma*}

$a|%{$s+=$_}

$s

Less golfed test script:

$f = {



$a=,0*6+($args|%{$_+0})+,0*4

for($n=16;$n){

    $i=$a.IndexOf($n)

    $a[$i]=0

    [int]$n=-1,1+-6..-4+4..6|%{

        $a[$i+$_]

    }|measure -maximum|% maximum

}

$a|%{$s+=$_}

$s



}



@(

    ,( 0  , ( 4,  3,  2,  1), ( 5,  6,  7,  8), (12, 11, 10,  9), (13, 14, 15, 16) )

    ,( 0  , ( 8,  1,  9, 14), (11,  6,  5, 16), (13, 15,  2,  7), (10,  3, 12,  4) )

    ,( 1  , ( 1,  2,  3,  4), ( 5,  6,  7,  8), ( 9, 10, 11, 12), (13, 14, 15, 16) )

    ,( 3  , (10, 15, 14, 11), ( 9,  3,  1,  7), (13,  5, 12,  6), ( 2,  8,  4, 16) )

    ,( 12 , ( 3,  7, 10,  5), ( 6,  8, 12, 13), (15,  9, 11,  4), (14,  1, 16,  2) )

    ,( 34 , ( 8,  9,  3,  6), (13, 11,  7, 15), (12, 10, 16,  2), ( 4, 14,  1,  5) )

    ,( 51 , ( 8, 11, 12,  9), (14,  5, 10, 16), ( 7,  3,  1,  6), (13,  4,  2, 15) )

    ,( 78 , (13, 14,  1,  2), (16, 15,  3,  4), ( 5,  6,  7,  8), ( 9, 10, 11, 12) )

    ,( 102, ( 9, 10, 11, 12), ( 1,  2,  4, 13), ( 7,  8,  5, 14), ( 3, 16,  6, 15) )

    ,( 103, ( 9, 10, 11, 12), ( 1,  2,  7, 13), ( 6, 16,  4, 14), ( 3,  8,  5, 15) )

) | % {

    $expected, $a = $_

    $result = &$f @a

    "$($result-eq$expected): $result"

}

Output:

True: 0

True: 0

True: 1

True: 3

True: 12

True: 34

True: 51

True: 78

True: 102

True: 103

Explanation:

First, add a border of 0 and make a single dimensional array:

0 0 0 0 0

0 # # # #

0 # # # #

0 # # # #

0 # # # #

0 0 0 0 0



     ↓



0 0 0 0 0 0 # # # # 0 # # # # 0 # # # # 0 # # # # 0 0 0 0 0 0

Second, loop biggest neighbor pile started from 16 to non-zero-maximum. And nullify it (The Hungry Mouse eats it).

for($n=16;$n){

    $i=$a.IndexOf($n)

    $a[$i]=0

    [int]$n=-1,1+-6..-4+4..6|%{

        $a[$i+$_]

    }|measure -maximum|% maximum

}

Third, sum of the remaining piles.

The Hungry Mouse

Example

The challenge

Rules

Test cases

Example

The challenge

Rules

Test cases

Example

The challenge

Rules

Test cases

Example

The challenge

Rules

Test cases

14 Answers 14

Python 2, 133 130 bytes

How it works

PHP, 177 174 171 bytes

Python 2, 111 bytes

MATL, 50 49 47 bytes

Explanation

Charcoal, 47 bytes

JavaScript, 122 bytes

SAS, 236 219 bytes

Updates:

J, 82 bytes

Red, 277 bytes

More readable:

Java 10, 272 bytes

Jelly, 31 30 29 bytes

How?

PowerShell Core, 348 bytes

R, 128 124 bytes

Powershell, 143 141 bytes

Your Answer

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14 Answers 14

14 Answers 14

Python 2, 133 130 bytes

How it works

Python 2, 133 130 bytes

How it works

Python 2, 133 130 bytes

How it works

Python 2, 133 130 bytes

How it works

PHP, 177 174 171 bytes

PHP, 177 174 171 bytes

PHP, 177 174 171 bytes

PHP, 177 174 171 bytes

Python 2, 111 bytes

Python 2, 111 bytes

Python 2, 111 bytes

Python 2, 111 bytes

MATL, 50 49 47 bytes

Explanation

MATL, 50 49 47 bytes

Explanation

MATL, 50 49 47 bytes

Explanation

MATL, 50 49 47 bytes

Explanation

Charcoal, 47 bytes

Charcoal, 47 bytes

Charcoal, 47 bytes

Charcoal, 47 bytes

JavaScript, 122 bytes

JavaScript, 122 bytes

JavaScript, 122 bytes

JavaScript, 122 bytes

SAS, 236 219 bytes

Updates:

SAS, 236 219 bytes

Updates:

SAS, 236 219 bytes

14 Answers
14

Python 2, ₁₃₃ 130 bytes

14 Answers
14

14 Answers
14

Python 2, ₁₃₃ 130 bytes

Python 2, ₁₃₃ 130 bytes

Python 2, ₁₃₃ 130 bytes

Python 2, ₁₃₃ 130 bytes