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Avoid if statements for checking neighboring indexes in a 2D array
```My goal is to find connected components in a 2D array for example finding connected '*'
chars below.

x x x x x x
x x x x x x
x x * * x x
x x * * x x
x x x * * x
* x x x x x

There are two connected '*' group in this example. First group is composes of six '*' located closer to middle and the second group composes only one '*' char located in the left bottom corner.

Do to this I generally implement a recursive algorithm which repeat calling the same function by checking all neighbors around the current index. I generally end up with something like :

void foo( int row, int col)
{
//Do something here like caching the index

if ( twoDimensionData[row - 1][col] == '*')
foo(row- 1, col);
else if ( twoDimensionData[row + 1][col] == '*')
foo(row+ 1, col);
else if ( twoDimensionData[row - 1 ][col - 1] == '*')
foo(row - 1, col - 1);

//..... I need 5 more of this bad boys I mean if checks
}

Is there any better way to achieve this with cool std functions like enumerate or iota without needing to write eight if checks?
```
```On Sunday, 16 July 2017 at 10:37:39 UTC, kerdemdemir wrote:
> My goal is to find connected components in a 2D array for example finding connected '*'
> chars below.
>
>       x x x x x x
>       x x x x x x
>       x x * * x x
>       x x * * x x
>       x x x * * x
>       * x x x x x
>
>
> There are two connected '*' group in this example. First group is composes of six '*' located closer to middle and the second group composes only one '*' char located in the left bottom corner.
>
> Do to this I generally implement a recursive algorithm which repeat calling the same function by checking all neighbors around the current index. I generally end up with something like :
>
> void foo( int row, int col)
> {
>     //Do something here like caching the index
>
>     if ( twoDimensionData[row - 1][col] == '*')
>        foo(row- 1, col);
>     else if ( twoDimensionData[row + 1][col] == '*')
>        foo(row+ 1, col);
>     else if ( twoDimensionData[row - 1 ][col - 1] == '*')
>        foo(row - 1, col - 1);
>
> //..... I need 5 more of this bad boys I mean if checks
> }
>
> Is there any better way to achieve this with cool std functions like enumerate or iota without needing to write eight if checks?

What you probably want is a convolution, used a lot in image processing.

insted of using recursion you walk left to right in blocks of 3x3 and compute a "sum"
and then do the same vertically, then each cell contains the number of neighbours that are *.
In this case you want the kernel
111
101
111

o o o x x x
o o o x x x
o o # * x x
x x * * x x
x x x * * x
* x x x x x

x o o o x x
x o o o x x
x o # # x x
x x * * x x
x x x * * x
* x x x x x

x x o o o x
x x o o o x
x x # # o x
x x * * x x
x x x * * x
* x x x x x

x x x o o o
x x x o o o
x x * # o o
x x * * x x
x x x * * x
* x x x x x

Have a look at the video on http://halide-lang.org describing the different methods used.

```
```On Sunday, 16 July 2017 at 10:37:39 UTC, kerdemdemir wrote:
> My goal is to find connected components in a 2D array for example finding connected '*'
> chars below.
>
>       x x x x x x
>       x x x x x x
>       x x * * x x
>       x x * * x x
>       x x x * * x
>       * x x x x x

> ...

> Is there any better way to achieve this with cool std functions like enumerate or iota without needing to write eight if checks?

I don't know of a library facility to do this.

Still, there is a language-agnostic way to make it more concise.  Instead of repeating eight similar blocks, define an array of delta-rows and delta-columns to neighboring cells, and use that array in a loop.  A complete example follows:

-----
import std.algorithm, std.array, std.range, std.stdio;

immutable int dirs = 8;
immutable int [dirs] dRow = [-1, -1, -1,  0, +1, +1, +1,  0];
immutable int [dirs] dCol = [-1,  0, +1, +1, +1,  0, -1, -1];

char [] [] arr;

int componentSizeRecur (int row, int col)
{
int res = 1;
arr[row][col] = 'x';
foreach (dir; 0..dirs)
{
auto nRow = row + dRow[dir];
auto nCol = col + dCol[dir];
if (arr[nRow][nCol] == '*')
res += componentSizeRecur (nRow, nCol);
}
return res;
}

void main ()
{
arr = ["xxxxxxx",
"xxxx*xx",
"xx**xxx",
"xx**x*x",
"xxxxxxx",
].map !(line => line.dup).array;

foreach (row; 0..arr.length)
foreach (col; 0..arr.front.length)
if (arr[row][col] == '*')
writeln (componentSizeRecur (row, col));
}
-----

If the neighbors array is regular and known in advance (like, 4 edge-connected cells, or 8 corner-connected cells as here), you may also like to loop over possible deltas and pick the good ones, like below:

-----
int componentSizeRecur (int row, int col)
{
int res = 1;
arr[row][col] = 'x';
foreach (dRow; -1..+2)
foreach (dCol; -1..+2)
if (dRow || dCol)
{
auto nRow = row + dRow;
auto nCol = col + dCol;
if (arr[nRow][nCol] == '*')
res += componentSizeRecur (nRow, nCol);
}
return res;
}
-----

I have to make two additional notes.

1. This works only if the border does not contain '*' characters.
To make it work without that restriction, either add two sentinel rows and columns at the four borders of the array, or put an if on nRow and nCol before using them.

2. The recursive solution can eat up lots of stack.  If you intend using it on large arrays, make sure you don't hit the stack size limit of the environment.  On Windows, it can be achieved by a compiler switch like "-L/STACK:268435456".  On Linux, the "ulimit" command may help.

Ivan Kazmenko.

```
```On 16.07.2017 12:37, kerdemdemir wrote:
> My goal is to find connected components in a 2D array for example finding connected '*'
> chars below.
>
>        x x x x x x
>        x x x x x x
>        x x * * x x
>        x x * * x x
>        x x x * * x
>        * x x x x x
>
>
> There are two connected '*' group in this example. First group is composes of six '*' located closer to middle and the second group composes only one '*' char located in the left bottom corner.
>
> Do to this I generally implement a recursive algorithm which repeat calling the same function by checking all neighbors around the current index. I generally end up with something like :
>
> void foo( int row, int col)
> {
>      //Do something here like caching the index
>
>      if ( twoDimensionData[row - 1][col] == '*')
>         foo(row- 1, col);
>      else if ( twoDimensionData[row + 1][col] == '*')
>         foo(row+ 1, col);
>      else if ( twoDimensionData[row - 1 ][col - 1] == '*')
>         foo(row - 1, col - 1);
>
> //..... I need 5 more of this bad boys I mean if checks
> }
> ...

It is wrong to explore in only one direction, so I assume you do not mean "else".

> Is there any better way to achieve this
foreach(i;row-1..row+2){
foreach(j;col-1..col+2){
if(i==row && j==col) continue;
if(twoDimensionData[i][j] == '*')
foo(row,col);
}
}

> with cool std functions like enumerate or iota without needing to write eight if checks?

cartesianProduct(iota(row-1,row+2),iota(col-1,col+2))
.filter!(a=>(a[0]!=row||a[1]!=col))
.filter!(a=>twoDimensionData[a[0]][a[1]]=='*')
.each!(a=>foo(a.expand));

(You can usually drop the first filter because "doing something" will usually involve checking if the node has been visited and returning or else marking the node as visited.)
```
```On 16.07.2017 18:55, Timon Gehr wrote:
> On 16.07.2017 12:37, kerdemdemir wrote:
>> My goal is to find connected components in a 2D array for example finding connected '*'
>> chars below.
>>
>>        x x x x x x
>>        x x x x x x
>>        x x * * x x
>>        x x * * x x
>>        x x x * * x
>>        * x x x x x
>>
>>
>> There are two connected '*' group in this example. First group is composes of six '*' located closer to middle and the second group composes only one '*' char located in the left bottom corner.
>>
>> Do to this I generally implement a recursive algorithm which repeat calling the same function by checking all neighbors around the current index. I generally end up with something like :
>>
>> void foo( int row, int col)
>> {
>>      //Do something here like caching the index
>>
>>      if ( twoDimensionData[row - 1][col] == '*')
>>         foo(row- 1, col);
>>      else if ( twoDimensionData[row + 1][col] == '*')
>>         foo(row+ 1, col);
>>      else if ( twoDimensionData[row - 1 ][col - 1] == '*')
>>         foo(row - 1, col - 1);
>>
>> //..... I need 5 more of this bad boys I mean if checks
>> }
>> ...
>
> It is wrong to explore in only one direction, so I assume you do not mean "else".
>
>> Is there any better way to achieve this
> foreach(i;row-1..row+2){
>      foreach(j;col-1..col+2){
>          if(i==row && j==col) continue;
>          if(twoDimensionData[i][j] == '*')
>              foo(row,col);
>      }
> }
>
>> with cool std functions like enumerate or iota without needing to write eight if checks?
>
> cartesianProduct(iota(row-1,row+2),iota(col-1,col+2))
>      .filter!(a=>(a[0]!=row||a[1]!=col))
>      .filter!(a=>twoDimensionData[a[0]][a[1]]=='*')
>      .each!(a=>foo(a.expand));
>
> (You can usually drop the first filter because "doing something" will usually involve checking if the node has been visited and returning or else marking the node as visited.)

Ivan's example in this style:

import std.stdio, std.range, std.algorithm, std.array;
char[][] arr;
int componentSize(size_t row, size_t col){
if(row>=arr.length||col>=arr[row].length||arr[row][col]!='*')
return 0;
arr[row][col]='x';
return 1+cartesianProduct(iota(row-1,row+2),iota(col-1,col+2))
.map!(a=>componentSize(a.expand)).sum;
}
void main (){
arr=["xxxxxx*",
"xxxx*xx",
"xx**xxx",
"xx**x**",
"xxxxxxx"].map!dup.array;
cartesianProduct(iota(arr.length),iota(arr[0].length))
.filter!(a=>arr[a[0]][a[1]]=='*')
.each!(a=>writeln(componentSize(a.expand)));
}

(This works even if there are * at the border.)
```
```On 16.07.2017 19:10, Timon Gehr wrote:
> ...
>
> (This works even if there are * at the border.)

Well, not really. :)

Version that actually works if there are * at the border:

import std.stdio, std.range, std.algorithm, std.array;
char[][] arr;
int componentSize(int row,int col){
if(row>=arr.length||col>=arr[row].length||arr[row][col]!='*')
return 0;
arr[row][col]='x';
return 1+cartesianProduct(iota(row-1,row+2),iota(col-1,col+2))
.map!(a=>componentSize(a.expand)).sum;
}
void main (){
arr=["**xxxx*",
"xxxx*xx",
"xx**xxx",
"xxx*x**",
"**xxxxx"].map!dup.array;

cartesianProduct(iota(cast(int)arr.length),iota(cast(int)arr[0].length))
.filter!(a=>arr[a[0]][a[1]]=='*')
.each!(a=>writeln(componentSize(a.expand)));
}
```
```Hi Guys,

@Nicholas , thanks a lot for cool solution but actually I weren't working on image processing. I was trying to solve "http://codeforces.com/contest/828/problem/B". I really needed finding connected components this time.

@Ivan, your solution is much more elegant than what I did. But I find @Timon's solution with cartesian product a bit nicer in this case since I love to see std function more and more.

Thanks guys for all your advises. D community is really the best.

Here is my solution to question. It seems I didn't get it working completely yet. In my debugger(Msvc MonoD) even there are many rows it seems Recurse function only loops the columns in the first row. And debugger is jumping so strangely I couldn't tag the problem.
But I don't expect a big change there should be a small bug that is it.

Sorry if code contains some foreign words I just replaced many variable names from my native language I might be missing some.

import std.stdio;
import std.string;
import std.algorithm;
import std.conv;
import std.array;
import std.range;
import std.math;

int totalrow;
int totalcolumn;
dchar[][] twoDimensionArray;

struct ConnectedElementsSolver
{
this(  dchar[][] twoDimArray )
{
m_twoDimStruct = twoDimArray;
Recurse(0, 0);
}

void Recurse ( int row, int column )
{
if( row < 0 || column < 0  )
return;

for ( ; row <  m_twoDimStruct.length ; row++  )
{
for ( ; column <  m_twoDimStruct[row].length; column++  )
{
Process( row, column, m_twoDimStruct.length, m_twoDimStruct[row].length );
}
}
}

void Process( int row, int column, ulong maxrow, ulong maxcolumn )
{
if( row < 0 || column < 0 || row >= maxrow || column >= maxcolumn  )
return;

if (  m_twoDimStruct[row][column] == 'B' )
{
m_twoDimStruct[row][column] = 'W';
m_tempResult.Process(row, column );
Process(row-1,column-1, maxrow, maxcolumn);
Process(row,column-1, maxrow, maxcolumn);
Process(row+1,column-1, maxrow, maxcolumn);
Process(row-1,column, maxrow, maxcolumn);
Process(row+1,column, maxrow, maxcolumn);
Process(row-1,column+1, maxrow, maxcolumn);
Process(row,column+1, maxrow, maxcolumn);
Process(row-1,column+1, maxrow, maxcolumn);
}
else
{
if ( m_tempResult.HowManyFilled )
m_results ~= m_tempResult;
m_tempResult.Resetle();
}
}

SquareCandidate   m_tempResult;
SquareCandidate[] m_results;
dchar[][] m_twoDimStruct;
}

struct SquareCandidate
{
int MaxY;
int MinY;
int MaxX;
int MinX;
int HowManyFilled;

this( int howManyFilled )
{
HowManyFilled = howManyFilled;
}

void Resetle()
{
this = SquareCandidate();
}

void Process( int row, int column )
{
HowManyFilled++;
MaxY = max( column, MaxY);
MinY = min( column, MinY);
MaxX = max( row, MaxX);
MinX = min( row, MinX);
}

int FindEmptySlots()
{
int kareKenarUzunlugu = max(MaxX-MinX, MaxY-MinY);
int kareAlani = kareKenarUzunlugu*kareKenarUzunlugu;
return kareAlani - HowManyFilled;
}

bool CanCreateSquare( int xMax, int yMax )
{
int xUzunlugu = MaxX-MinX;
int yUzunlugu = MaxY-MinY;
if ( xUzunlugu > yUzunlugu )
{
return yMax >= xUzunlugu;
}
else
{
return xMax >= yUzunlugu;
}
}
}

void main()
{
auto dimensions = stdin.readln.strip.split().map!(a => to!int(a)).array();
totalrow = dimensions[0];
totalcolumn = dimensions[1];
twoDimensionArray = stdin
.byLine()
.take(totalrow)
.map!(line => line
.map!(a => to!dchar(a))
.array())
.array;

ConnectedElementsSolver baglantiliElemCozucu = ConnectedElementsSolver(twoDimensionArray);
bool isAnyProblemMakingSquare = baglantiliElemCozucu.m_results.any!(a => a.CanCreateSquare(totalrow, totalcolumn) == false );
if ( isAnyProblemMakingSquare )
writeln(-1);

int sonuc;
baglantiliElemCozucu.m_results.each!( a => sonuc += a.FindEmptySlots() );
writeln( sonuc );
}
```
```Of course now I will try to have it work first. Than replace for loops with Cartesian product calls. Than I will make 2D array template and even maybe with random access range. And finally for being able to use this class later in the some other coding challenge I will make Searching( == 'W' part) and Process functions passed by parameter.

Thanks a lot for help.
Erdem
```
```On Sunday, 16 July 2017 at 10:37:39 UTC, kerdemdemir wrote:
> My goal is to find connected components in a 2D array for example finding connected '*'
> chars below.

You can also use a queue to avoid recursion that should improve performances and readibility.

Andrea
```
```On Sunday, 16 July 2017 at 21:50:19 UTC, kerdemdemir wrote:

> 			Process(row-1,column-1, maxrow, maxcolumn);
> 			Process(row,column-1, maxrow, maxcolumn);
> 			Process(row+1,column-1, maxrow, maxcolumn);
> 			Process(row-1,column, maxrow, maxcolumn);
> 			Process(row+1,column, maxrow, maxcolumn);
> 			Process(row-1,column+1, maxrow, maxcolumn);
> 			Process(row,column+1, maxrow, maxcolumn);
> 			Process(row-1,column+1, maxrow, maxcolumn);

One of "row-1,column+1" should actually be "row+1,column+1".  That's where the mentioned ways help.

As for the problem itself, it can be solved without finding connected components.  I won't post the solution right away because it is potentially a spoiler.  See http://codeforces.com/blog/entry/53268 for problem analysis (828B) and http://codeforces.com/contest/828/submission/28637184 for an example implementation in D.

Ivan Kazmenko.

```
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