Index sum and strip my matrix

Question 1

Index sum and strip my matrix

Given a matrix/2d array in your preferable language

Input:

The matrix will always have an odd length
The matrix will always be perfectly square
The matrix values can be any integer in your language (positive or negative)

Example:

1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 50 6 7 8 9
4 5 6 100 8 9 10
5 6 7 8 -9 10 11
6 7 8 9 10 11 12
7 8 900 10 11 12 0

Definitions:

The "central number" is defined as the number that has the same amount of numbers to the left,right,up and down

In this case its middlemost 100

The "outer shell" is the collection of numbers which their x and y index is or 0 or the matrix size

1 2 3 4 5 6 7
2 8
3 9
4 10
5 11
6 12
7 8 900 10 11 12 0

Your task:

Add to the central number the sum of each row and column after multiplying the values in each by their 1-based index

A single row for example

4 5 6 7 8

for each number

number * index + number * index.....
4*1 + 5*2 + 6*3 + 7*4 + 8*5 => 100

example:

 2 -3 -9 4 7 1 5 => 61
-2 0 -2 -7 -7 -7 -4 => -141
 6 -3 -2 -2 -3 2 1 => -10
 8 -8 4 1 -8 2 0 => -20
-5 6 7 -1 8 4 8 => 144
 1 5 7 8 7 -9 -5 => 10
 7 7 -2 2 -7 -8 0 => -60
 |
78 65 60 45 -15 -89 10 => 154
 |
 => -16

For all rows and columns you combine these values..
Now you sum these too => 154-16 = 138
You add that number to the "central number" and remove the "outer shell" of the matrix

 0 -2 -7 -7 -7 => -88
-3 -2 -2 -3 2 => -15
-8 4 1+138 -8 2 => 395
 6 7 -1 8 4 => 69
 5 7 8 7 -9 => 26
19 69 442 30 -26

do this untill you end up with a single number

-2 -2 -3 => -15
 4 1060 -8 => 2100
 7 -1 8 => 29
27 2115 5

Add 2114+2147 to 1060
Remove the "outer shell" and get 5321
Now we have a single number left

this is the output!

test cases:

-6
-6

-7 -1 8
-4 -6 7
-3 -6 6
2

 6 7 -2 5 1
-2 6 -4 -2 3
-1 -4 0 -2 -7
 0 1 4 -4 8
-8 -6 -5 0 2
-365

 8 3 5 6 6 -7 5
 6 2 4 -2 -1 8 3
 2 1 -5 3 8 2 -3
 3 -1 0 7 -6 7 -5
 0 -8 -4 -9 -4 2 -8
 8 -9 -3 5 7 8 5
 8 -1 4 5 1 -4 8
17611

-9 -7 2 1 1 -2 3 -7 -3 6 7 1 0
-7 -8 -9 -2 7 -2 5 4 7 -7 8 -9 8
-4 4 -1 0 1 5 -3 7 1 -2 -9 4 8
 4 8 1 -1 0 7 4 6 -9 3 -9 3 -9
-6 -8 -4 -8 -9 2 1 1 -8 8 2 6 -4
-8 -5 1 1 2 -9 3 7 2 5 -6 -1 2
-8 -5 -7 -4 -9 -2 5 0 2 -4 2 0 -2
-3 -6 -3 2 -9 8 1 -5 5 0 -4 -1 -9
-9 -9 -8 0 -5 -7 1 -2 1 -4 -1 5 7
-6 -9 4 -2 8 7 -9 -5 3 -1 1 8 4
-6 6 -3 -4 3 5 6 8 -2 5 -1 -7 -9
-1 7 -9 4 6 7 6 -8 5 1 0 -3 0
-3 -2 5 -4 0 0 0 -1 7 4 -9 -4 2
-28473770

This is a codegolf challenge so the program with the lowest bytecount wins

Question 2

you are correct, thats a typo

Question 3

why would negative numbers be an issue? I dont think the challenge should adjust for esolangs but maybe the other way around is more appropriate

Question 4

@LuisMendo I think it's not a problem, the rule "The matrix values can be any integer in your language" means to me that if your language doesn't have negative numbers, it shouldn't support them.

Question 5

actually thats correct. but then the test cases wont work properly

Question 6

"I dont think the challenge should adjust for esolangs but maybe the other way around is more appropriate" that should be engraved in stone

Question 7

MATL, (削除) 36 (削除ここまで) 34 bytes

tnq?`t&+stn:*sytn2/)+ 7M(6Lt3$)tnq

Input is a 2D array with ; as row separator

Try it online! Or verify all test cases.

Explanation

tnq % Take input. Duplicate, get number of elements, subtract 1
? % If greater than 0
 ` % Do...while
 t % Duplicate
 &+ % Sum matrix with its transpose
 s % Sum each column. Gives a row vector
 tn: % Vector [1 2 ...] with the same size
 * % Multiply element-wise
 s % Sum of vector. This will be added to center entry of the matrix
 y % Duplicate matrix
 tn2/ % Duplicate, get half its number of elements. Gives non-integer value
 ) % Get center entry of the matrix, using linear index with implicit rounding
 + % Add center entry to sum of previous vector
 7M % Push index of center entry again
 ( % Assgined new value to center of the matrix
 6Lt % Array [2 j1-1], twice. This will be used to remove shell
 3$) % Apply row and col indices to remove outer shell of the matrix
 tnq % Duplicate, number of elements, subtract 1. Falsy if matrix has 1 entry
 % End do...while implicitly. The loop is exited when matrix has 1 entry
 % End if implicitly
 % Display stack implicitly

Question 8

Python 2.7, 229 bytes

This is my first attempt at something like this, so hopefully I followed all the rules with this submission. This is just a function which takes in a list of lists as its parameter. I feel like the sums and list comprehension could probably be shortened a little bit, but it was too hard for me. :D

def r(M):
 t=len(M)
 if t==1:return M[0][0]
 M[t/2][t/2]+=sum(a*b for k in [[l[x] for l in M]for x in range(0,t)]for a,b in enumerate(k,1))+sum([i*j for l in M for i,j in enumerate(l,1)])
 return r([p[+1:-1]for p in M[1:-1]])

Thx to Easterly Irk for helping me shave off a few bytes.

Question 9

You can remove a couple spaces between operators (...) + sum([i*j... -> ...)+sum([i*j...), but overall, great first post!!!!

Question 10

oooh missed that. Thanks!

Question 11

Also, ...]for ... works. You can remove at least 2 space like that. (end of list hits the for loop)

Question 12

C#, 257 bytes

here is a non esolang answer

void f(int[][]p){while(p.Length>1){int a=p.Length;int r=0;for(int i=0;i<a;i++)for(int j=0;j<a;j++)r+=(i+j+2)*p[i][j];p[a/2][a/2]+=r;p=p.Where((i,n)=>n>0&&n<p.Length-1).Select(k=>k.Where((i,n)=>n>0&&n<p.Length-1).ToArray()).ToArray();}Console.Write(p[0][0]);

ungolfed:

void f(int[][]p)
 {
 while (p.Length>1)
 {
 int a=p.Length;
 int r=0; //integer for number to add to middle
 for (int i = 0; i < a; i++)
 for (int j = 0; j < a; j++)
 r +=(i+j+2)*p[i][j]; //add each element to counter according to their 1 based index
 p[a / 2][a / 2] += r; //add counter to middle
 p = p.Where((i, n) => n > 0 && n < p.Length - 1).Select(k => k.Where((i, n) => n > 0 && n < p.Length - 1).ToArray()).ToArray(); //strip outer shell from array
 }
 Console.Write(p[0][0]); //print last and only value in array
 }

Question 13

Hey now, J isn't an esolang.

Question 14

This doesn't compile if you don't include using System.Linq and using System. I'm not sure if it's required by the rules though.

Question 15

its not a full program, its only a function so its ok as far as i know. i mean, would i also need to include the App.config and all the bytes in the properties and makefile? no

Question 16

@downrep_nation It's just weird, since I've seen some people include them in the source when it has only been a function and they've included the bytes on the score.

Question 17

Now when I think about it, I'm on the line that you should import atleast System.Linq. Other languages that require importing in order to use certain features go through the same process, so I think it's unfair to assume that every module is loaded to memory in C#.

Question 18

J, 66 bytes

([:}:@}."1@}:@}.]+(i.@,~=](]+*)<.@-:)@#*[:+/^:2#\*]+|:)^:(<.@-:@#)

Straight-forward approach based on the process described in the challenge.

[:+/^:2#\*]+|: gets the sum. ]+(i.@,~=](]+*)<.@-:)@#* is a particularly ugly way to increment the center by the sum. [:}:@}."1@}:@}. removes the outer shell. There probably is a better way to do this.

Usage

 f =: ([:}:@}."1@}:@}.]+(i.@,~=](]+*)<.@-:)@#*[:+/^:2#\*]+|:)^:(<.@-:@#)
 f _6
_6
 f _7 _1 8 , _4 _6 7 ,: _3 _6 6
2
 f 6 7 _2 5 1 , _2 6 _4 _2 3 , _1 _4 0 _2 _7 , 0 1 4 _4 8 ,: _8 _6 _5 0 2 
_365
 f 8 3 5 6 6 _7 5 , 6 2 4 _2 _1 8 3 , 2 1 _5 3 8 2 _3 , 3 _1 0 7 _6 7 _5 , 0 _8 _4 _9 _4 2 _8 ,8 _9 _3 5 7 8 5 ,: 8 _1 4 5 1 _4 8
17611
 f (13 13 $ _9 _7 2 1 1 _2 3 _7 _3 6 7 1 0 _7 _8 _9 _2 7 _2 5 4 7 _7 8 _9 8 _4 4 _1 0 1 5 _3 7 1 _2 _9 4 8 4 8 1 _1 0 7 4 6 _9 3 _9 3 _9 _6 _8 _4 _8 _9 2 1 1 _8 8 2 6 _4 _8 _5 1 1 2 _9 3 7 2 5 _6 _1 2 _8 _5 _7 _4 _9 _2 5 0 2 _4 2 0 _2 _3 _6 _3 2 _9 8 1 _5 5 0 _4 _1 _9 _9 _9 _8 0 _5 _7 1 _2 1 _4 _1 5 7 _6 _9 4 _2 8 7 _9 _5 3 _1 1 8 4 _6 6 _3 _4 3 5 6 8 _2 5 _1 _7 _9 _1 7 _9 4 6 7 6 _8 5 1 0 _3 0 _3 _2 5 _4 0 0 0 _1 7 4 _9 _4 2)
_28473770

Question 19

Brachylog, 114 bytes

{l1,?hh.|:{:Im:I:?:{[L:I:M]h:JmN,Ll:2/D(IJ,M{$\:?c:{:{:ImN,I:1+:N*.}f+.}a+.}:N+.;'(DIJ),N.)}f.}f:7a$\:7a&.}.
brbr.

I'm suprised this even works to be honest. At least I realized that Brachylog really needs a "change value of that element" as a built-in though...

Usage example:

?- run_from_file('code.brachylog', '[[0:_2:_7:_7:_7]:[_3:_2:_2:_3:2]:[_8:4:139:_8:2]:[6:7:_1:8:4]:[5:7:8:7:_9]]', Z).
Z = 5321 .

Explanation

APL, 56 chars

{{1 1↓ ̄1 ̄1↓⍵+(-⍴⍵)↑(×ばつ⍴⍵)↑+/(⍵⍪⍉⍵)×ばつ⍳≢⍵}⍣(×ばつ≢⍵)⊣⍵}

In English:

⍣(×ばつ≢⍵) repeat "half the size of a dimension rounded"-times
(⍵⍪⍉⍵)×ばつ⍳≢⍵ inner product of the matrix and its transpose with the index vector
(-⍴⍵)↑(×ばつ⍴⍵)↑ transform result in matrix padded with 0s
1 1↓ ̄1 ̄1↓ removes outer shell

Luis Mendo Luis Mendo 107k10 gold badges139 silver badges381 bronze badges · Accepted Answer · 2016-06-23 21:54:34Z

MATL, (削除) 36 (削除ここまで) 34 bytes

tnq?`t&+stn:*sytn2/)+ 7M(6Lt3$)tnq

Input is a 2D array with ; as row separator

Try it online! Or verify all test cases.

Explanation

tnq % Take input. Duplicate, get number of elements, subtract 1
? % If greater than 0
 ` % Do...while
 t % Duplicate
 &+ % Sum matrix with its transpose
 s % Sum each column. Gives a row vector
 tn: % Vector [1 2 ...] with the same size
 * % Multiply element-wise
 s % Sum of vector. This will be added to center entry of the matrix
 y % Duplicate matrix
 tn2/ % Duplicate, get half its number of elements. Gives non-integer value
 ) % Get center entry of the matrix, using linear index with implicit rounding
 + % Add center entry to sum of previous vector
 7M % Push index of center entry again
 ( % Assgined new value to center of the matrix
 6Lt % Array [2 j1-1], twice. This will be used to remove shell
 3$) % Apply row and col indices to remove outer shell of the matrix
 tnq % Duplicate, number of elements, subtract 1. Falsy if matrix has 1 entry
 % End do...while implicitly. The loop is exited when matrix has 1 entry
 % End if implicitly
 % Display stack implicitly

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Index sum and strip my matrix