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# Problem of 8 Neighbours of an element in a 2-D Matrix

Given a 2-D Matrix and an integer ‘K’, the task is to predict the matrix after ‘K’ iterations given as follows:

• An element 1 in the current matrix remains 1 in the next iteration only if it is surrounded by A number of 1s, where 0 <= range1a <= A <= range1b.
• An element 0 in the current matrix becomes 1 in the next iteration only if it is surrounded by B numbers of 1s, where 0 <= range0a <= B <= range0b.

Let’s understand this with an example:

Constraints:
1 <= K <= 100000
0 <= range1a, range1b, range0a, range0b <= 8

• In the above image for cell(0, 0), the cell was ‘0’ in the first iteration but, since it was surrounded by only one adjacent cell containing ‘1’, which does not fall within the range [range0a, range0b]. So it will continue to remain ‘0’.
• For the second iteration, cell (0, 0) was 0, but this time it is surrounded by two cells containing ‘1’, and two falls within the range [range0a, range0b]. Therefore, it becomes ‘1’ in the next (2nd) iteration.

Examples:

Input: range1a = 2
range1b = 2
range0a = 2
range0b = 3
K = 1
Output:
0 1 1 0
0 1 1 1
1 0 0 1
0 0 1 0

Input: range1a = 2
range1b = 2
range0a = 2
range0b = 3
K = 2
Output:
1 0 0 1
1 0 0 0
0 0 0 0
0 1 0 1

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Dimension of Array``#define N 4` `void` `predictMatrix(``int` `arr[N][N],``                   ``int` `range1a,``                   ``int` `range1b,``                   ``int` `range0a,``                   ``int` `range0b,``                   ``int` `K,``                   ``int` `b[N][N])``{` `    ``// Count of 1s``    ``int` `c = 0;` `    ``while` `(K--) {``        ``for` `(``int` `i = 0; i < N; i++) {``            ``for` `(``int` `j = 0; j < N; j++) {``                ``c = 0;` `                ``// Counting all neighbouring 1s` `                ``if` `(i > 0 && arr[i - 1][j] == 1)``                    ``c++;``                ``if` `(j > 0 && arr[i][j - 1] == 1)``                    ``c++;``                ``if` `(i > 0 && j > 0``                    ``&& arr[i - 1][j - 1] == 1)``                    ``c++;``                ``if` `(i < N - 1 && arr[i + 1][j] == 1)``                    ``c++;``                ``if` `(j < N - 1 && arr[i][j + 1] == 1)``                    ``c++;``                ``if` `(i < N - 1 && j < N - 1``                    ``&& arr[i + 1][j + 1] == 1)``                    ``c++;``                ``if` `(i < N - 1 && j > 0``                    ``&& arr[i + 1][j - 1] == 1)``                    ``c++;``                ``if` `(i > 0 && j < N - 1``                    ``&& arr[i - 1][j + 1] == 1)``                    ``c++;` `                ``// Comparing the number of``                ``// neighbouring 1s with``                ``// given ranges``                ``if` `(arr[i][j] == 1) {``                    ``if` `(c >= range1a && c <= range1b)``                        ``b[i][j] = 1;``                    ``else``                        ``b[i][j] = 0;``                ``}``                ``if` `(arr[i][j] == 0) {``                    ``if` `(c >= range0a && c <= range0b)``                        ``b[i][j] = 1;``                    ``else``                        ``b[i][j] = 0;``                ``}``            ``}``        ``}` `        ``// Copying changes to``        ``// the main matrix``        ``for` `(``int` `k = 0; k < N; k++)``            ``for` `(``int` `m = 0; m < N; m++)``                ``arr[k][m] = b[k][m];``    ``}``}` `// Driver code``int` `main()``{``    ``int` `arr[N][N] = { 0, 0, 0, 0,``                      ``0, 1, 1, 0,``                      ``0, 0, 1, 0,``                      ``0, 1, 0, 1 };``    ``int` `range1a = 2, range1b = 2;``    ``int` `range0a = 2, range0b = 3;``    ``int` `K = 3, b[N][N] = { 0 };` `    ``// Function call to calculate``    ``// the resultant matrix``    ``// after 'K' iterations.``    ``predictMatrix(arr, range1a, range1b,``                  ``range0a, range0b, K, b);` `    ``// Printing Result``    ``for` `(``int` `i = 0; i < N; i++) {``        ``cout << endl;``        ``for` `(``int` `j = 0; j < N; j++)``            ``cout << b[i][j] << ``" "``;``    ``}``    ``return` `0;``}`

## Java

 `// Java implementation of the approach``public` `class` `GFG{``    ` `// Dimension of Array``final` `static` `int` `N  = ``4` `;` `static` `void` `predictMatrix(``int` `arr[][],``                   ``int` `range1a,``                   ``int` `range1b,``                   ``int` `range0a,``                   ``int` `range0b,``                   ``int` `K,``                   ``int` `b[][])``{` `    ``// Count of 1s``    ``int` `c = ``0``;` `    ``while` `(K != ``0``) {``        ``K--;``        ``for` `(``int` `i = ``0``; i < N; i++) {``            ``for` `(``int` `j = ``0``; j < N; j++) {``                ``c = ``0``;` `                ``// Counting all neighbouring 1s` `                ``if` `(i > ``0` `&& arr[i - ``1``][j] == ``1``)``                    ``c++;``                ``if` `(j > ``0` `&& arr[i][j - ``1``] == ``1``)``                    ``c++;``                ``if` `(i > ``0` `&& j > ``0``                    ``&& arr[i - ``1``][j - ``1``] == ``1``)``                    ``c++;``                ``if` `(i < N - ``1` `&& arr[i + ``1``][j] == ``1``)``                    ``c++;``                ``if` `(j < N - ``1` `&& arr[i][j + ``1``] == ``1``)``                    ``c++;``                ``if` `(i < N - ``1` `&& j < N - ``1``                    ``&& arr[i + ``1``][j + ``1``] == ``1``)``                    ``c++;``                ``if` `(i < N - ``1` `&& j > ``0``                    ``&& arr[i + ``1``][j - ``1``] == ``1``)``                    ``c++;``                ``if` `(i > ``0` `&& j < N - ``1``                    ``&& arr[i - ``1``][j + ``1``] == ``1``)``                    ``c++;` `                ``// Comparing the number of``                ``// neighbouring 1s with``                ``// given ranges``                ``if` `(arr[i][j] == ``1``) {``                    ``if` `(c >= range1a && c <= range1b)``                        ``b[i][j] = ``1``;``                    ``else``                        ``b[i][j] = ``0``;``                ``}``                ``if` `(arr[i][j] == ``0``) {``                    ``if` `(c >= range0a && c <= range0b)``                        ``b[i][j] = ``1``;``                    ``else``                        ``b[i][j] = ``0``;``                ``}``            ``}``        ``}` `        ``// Copying changes to``        ``// the main matrix``        ``for` `(``int` `k = ``0``; k < N; k++)``            ``for` `(``int` `m = ``0``; m < N; m++)``                ``arr[k][m] = b[k][m];``    ``}``    ` `}` `// Driver code``public` `static` `void` `main(String []args)``{``    ``int` `arr[][] = { {``0``, ``0``, ``0``, ``0``},``                      ``{``0``, ``1``, ``1``, ``0``},``                      ``{``0``, ``0``, ``1``, ``0``},``                      ``{``0``, ``1``, ``0``, ``1` `} };``    ``int` `range1a = ``2``, range1b = ``2``;``    ``int` `range0a = ``2``, range0b = ``3``;``    ``int` `K = ``3``;``    ``int` `b[][] = ``new` `int``[N][N] ;` `    ``// Function call to calculate``    ``// the resultant matrix``    ``// after 'K' iterations.``    ``predictMatrix(arr, range1a, range1b,``                  ``range0a, range0b, K, b);` `    ``// Printing Result``    ``for` `(``int` `i = ``0``; i < N; i++) {``        ``System.out.println();``        ``for` `(``int` `j = ``0``; j < N; j++)``            ``System.out.print(b[i][j]+ ``" "``);``    ``}``    ` `}``// This Code is contributed by Ryuga``}`

## Python 3

 `# Python3 implementation of the approach` `# Dimension of Array``N ``=` `4` `def` `predictMatrix(arr, range1a, range1b,``                  ``range0a, range0b, K, b):` `    ``# Count of 1s``    ``c ``=` `0` `    ``while` `(K):``        ``for` `i ``in` `range``(N) :``            ``for` `j ``in` `range``(N):``                ``c ``=` `0` `                ``# Counting all neighbouring 1s``                ``if` `(i > ``0` `and` `arr[i ``-` `1``][j] ``=``=` `1``):``                    ``c ``+``=` `1``                ``if` `(j > ``0` `and` `arr[i][j ``-` `1``] ``=``=` `1``):``                    ``c ``+``=` `1``                ``if` `(i > ``0` `and` `j > ``0` `and``                    ``arr[i ``-` `1``][j ``-` `1``] ``=``=` `1``):``                    ``c ``+``=` `1``                ``if` `(i < N ``-` `1` `and` `arr[i ``+` `1``][j] ``=``=` `1``):``                    ``c ``+``=` `1``                ``if` `(j < N ``-` `1` `and` `arr[i][j ``+` `1``] ``=``=` `1``):``                    ``c ``+``=` `1``                ``if` `(i < N ``-` `1` `and` `j < N ``-` `1``                    ``and` `arr[i ``+` `1``][j ``+` `1``] ``=``=` `1``):``                    ``c ``+``=` `1``                ``if` `(i < N ``-` `1` `and` `j > ``0``                    ``and` `arr[i ``+` `1``][j ``-` `1``] ``=``=` `1``):``                    ``c ``+``=` `1``                ``if` `(i > ``0` `and` `j < N ``-` `1``                    ``and` `arr[i ``-` `1``][j ``+` `1``] ``=``=` `1``):``                    ``c ``+``=` `1` `                ``# Comparing the number of neighbouring``                ``# 1s with given ranges``                ``if` `(arr[i][j] ``=``=` `1``) :``                    ``if` `(c >``=` `range1a ``and` `c <``=` `range1b):``                        ``b[i][j] ``=` `1``                    ``else``:``                        ``b[i][j] ``=` `0``                ` `                ``if` `(arr[i][j] ``=``=` `0``):``                    ``if` `(c >``=` `range0a ``and` `c <``=` `range0b):``                        ``b[i][j] ``=` `1``                    ``else``:``                        ``b[i][j] ``=` `0``        ``K ``-``=` `1` `        ``# Copying changes to the main matrix``        ``for` `k ``in` `range``(N):``            ``for` `m ``in` `range``( N):``                ``arr[k][m] ``=` `b[k][m]` `# Driver code``if` `__name__ ``=``=` `"__main__"``:``    ` `    ``arr ``=` `[[``0``, ``0``, ``0``, ``0``],``           ``[``0``, ``1``, ``1``, ``0``],``           ``[``0``, ``0``, ``1``, ``0``],``           ``[``0``, ``1``, ``0``, ``1``]]``    ``range1a ``=` `2``    ``range1b ``=` `2``    ``range0a ``=` `2``    ``range0b ``=` `3``    ``K ``=` `3``    ``b ``=` `[[``0` `for` `x ``in` `range``(N)]``            ``for` `y ``in` `range``(N)]` `    ``# Function call to calculate``    ``# the resultant matrix``    ``# after 'K' iterations.``    ``predictMatrix(arr, range1a, range1b,``                  ``range0a, range0b, K, b)` `    ``# Printing Result``    ``for` `i ``in` `range``( N):``        ``print``()``        ``for` `j ``in` `range``(N):``            ``print``(b[i][j], end ``=` `" "``)` `# This code is contributed``# by ChitraNayal`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{` `// Dimension of Array``readonly` `static` `int` `N = 4 ;` `static` `void` `predictMatrix(``int` `[,]arr, ``int` `range1a,``                          ``int` `range1b, ``int` `range0a,``                          ``int` `range0b, ``int` `K, ``int` `[,]b)``{` `    ``// Count of 1s``    ``int` `c = 0;` `    ``while` `(K != 0)``    ``{``        ``K--;``        ``for` `(``int` `i = 0; i < N; i++)``        ``{``            ``for` `(``int` `j = 0; j < N; j++)``            ``{``                ``c = 0;` `                ``// Counting all neighbouring 1s` `                ``if` `(i > 0 && arr[i - 1, j] == 1)``                    ``c++;``                ``if` `(j > 0 && arr[i, j - 1] == 1)``                    ``c++;``                ``if` `(i > 0 && j > 0``                    ``&& arr[i - 1, j - 1] == 1)``                    ``c++;``                ``if` `(i < N - 1 && arr[i + 1, j] == 1)``                    ``c++;``                ``if` `(j < N - 1 && arr[i, j + 1] == 1)``                    ``c++;``                ``if` `(i < N - 1 && j < N - 1 &&``                    ``arr[i + 1, j + 1] == 1)``                    ``c++;``                ``if` `(i < N - 1 && j > 0 &&``                    ``arr[i + 1, j - 1] == 1)``                    ``c++;``                ``if` `(i > 0 && j < N - 1 &&``                    ``arr[i - 1, j + 1] == 1)``                    ``c++;` `                ``// Comparing the number of``                ``// neighbouring 1s with``                ``// given ranges``                ``if` `(arr[i,j] == 1)``                ``{``                    ``if` `(c >= range1a && c <= range1b)``                        ``b[i, j] = 1;``                    ``else``                        ``b[i, j] = 0;``                ``}``                ``if` `(arr[i,j] == 0)``                ``{``                    ``if` `(c >= range0a && c <= range0b)``                        ``b[i, j] = 1;``                    ``else``                        ``b[i, j] = 0;``                ``}``            ``}``        ``}` `        ``// Copying changes to the main matrix``        ``for` `(``int` `k = 0; k < N; k++)``            ``for` `(``int` `m = 0; m < N; m++)``                ``arr[k, m] = b[k, m];``    ``}``}` `// Driver code``public` `static` `void` `Main()``{``    ``int` `[,]arr = { {0, 0, 0, 0},``                   ``{0, 1, 1, 0},``                   ``{0, 0, 1, 0},``                   ``{0, 1, 0, 1 } };``    ``int` `range1a = 2, range1b = 2;``    ``int` `range0a = 2, range0b = 3;``    ``int` `K = 3;``    ``int` `[,]b = ``new` `int``[N, N];` `    ``// Function call to calculate``    ``// the resultant matrix``    ``// after 'K' iterations.``    ``predictMatrix(arr, range1a, range1b,``                ``range0a, range0b, K, b);` `    ``// Printing Result``    ``for` `(``int` `i = 0; i < N; i++)``    ``{``        ``Console.WriteLine();``        ``for` `(``int` `j = 0; j < N; j++)``            ``Console.Write(b[i, j] + ``" "``);``    ``}``}``}` `// This code is contributed by 29AjayKumar`

## PHP

 ` 0 && ``\$arr``[``\$i` `- 1][``\$j``] == 1)``                    ``\$c``++;``                ``if` `(``\$j` `> 0 && ``\$arr``[``\$i``][``\$j` `- 1] == 1)``                    ``\$c``++;``                ``if` `(``\$i` `> 0 && ``\$j` `> 0 && ``\$arr``[``\$i` `- 1][``\$j` `- 1] == 1)``                    ``\$c``++;``                ``if` `(``\$i` `< ``\$N` `- 1 && ``\$arr``[``\$i` `+ 1][``\$j``] == 1)``                    ``\$c``++;``                ``if` `(``\$j` `< ``\$N` `- 1 && ``\$arr``[``\$i``][``\$j` `+ 1] == 1)``                    ``\$c``++;``                ``if` `(``\$i` `< ``\$N` `- 1 && ``\$j` `< ``\$N` `- 1 &&``                    ``\$arr``[``\$i` `+ 1][``\$j` `+ 1] == 1)``                    ``\$c``++;``                ``if` `(``\$i` `< ``\$N` `- 1 && ``\$j` `> 0 && ``\$arr``[``\$i` `+ 1][``\$j` `- 1] == 1)``                    ``\$c``++;``                ``if` `(``\$i` `> 0 && ``\$j` `< ``\$N` `- 1 && ``\$arr``[``\$i` `- 1][``\$j` `+ 1] == 1)``                    ``\$c``++;` `                ``// Comparing the number of``                ``// neighbouring 1s with``                ``// given ranges``                ``if` `(``\$arr``[``\$i``][``\$j``] == 1)``                ``{``                    ``if` `(``\$c` `>= ``\$range1a` `&& ``\$c` `<= ``\$range1b``)``                        ``\$b``[``\$i``][``\$j``] = 1;``                    ``else``                        ``\$b``[``\$i``][``\$j``] = 0;``                ``}``                ``if` `(``\$arr``[``\$i``][``\$j``] == 0) {``                    ``if` `(``\$c` `>= ``\$range0a` `&& ``\$c` `<= ``\$range0b``)``                        ``\$b``[``\$i``][``\$j``] = 1;``                    ``else``                        ``\$b``[``\$i``][``\$j``] = 0;``                ``}``            ``}``        ``}` `        ``// Copying changes to``        ``// the main matrix``        ``for` `(``\$k` `= 0; ``\$k` `< ``\$N``; ``\$k``++)``            ``for` `(``\$m` `= 0; ``\$m` `< ``\$N``; ``\$m``++)``                ``\$arr``[``\$k``][``\$m``] = ``\$b``[``\$k``][``\$m``];``    ``}``    ``return` `\$b``;``}` `// Driver code``\$N` `= 4;``\$arr``= ``array``(``array``(0, 0, 0, 0),``        ``array``(0, 1, 1, 0),``        ``array``(0, 0, 1, 0),``        ``array``(0, 1, 0, 1));``\$range1a` `= 2; ``\$range1b` `= 2;``\$range0a` `= 2; ``\$range0b` `= 3;``\$K` `= 3; ``\$b` `= ``array``(``array``(0));` `// Function call to calculate``// the resultant matrix``// after 'K' iterations.``\$b1` `= predictMatrix(``\$arr``, ``\$range1a``, ``\$range1b``,``            ``\$range0a``, ``\$range0b``, ``\$K``, ``\$b``);` `// Printing Result``for` `(``\$i` `= 0; ``\$i` `< ``\$N``; ``\$i``++)``{``    ``echo` `"\n"``;``    ``for` `(``\$j` `= 0; ``\$j` `< ``\$N``; ``\$j``++)``        ``echo` `\$b1``[``\$i``][``\$j``] . ``" "``;``}` `// This code is contributed by Akanksha Rai`

## Javascript

 ``

Output

```0 1 0 0
0 1 0 0
1 1 1 0
0 0 1 0 ```

Complexity Analysis:

• Time Complexity: O(K*N2)
• Auxiliary Space: O(N2)

My Personal Notes arrow_drop_up