# Farthest distance of a 0 from the center of a 2-D matrix

Given a matrix of odd order mat, the task is to find the farthest distance of a 0 from the center of the matrix. Distance between two elements at locations (i1, j1) and (i2, j2) of the matrix is calculated as |i1- i2| + |j1-j2|. If no 0 occurs in the matrix then print 0 as the result.

Examples:

Input: mat[][] = {{2, 3, 0}, {0, 2, 0}, {0, 1, 1}}
Output: 2

Input: mat[][] = {{2, 3, 4, {0, 2, 0}, {6, 1, 1}}
Output: 1

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The center of any matrix with odd order is at index i = j = floor(n/2). Now for finding farthest distance of any 0 from the center, calculate the distance of each 0 from center of the matrix as |i-n/2| + |j-n/2| and update the maximum distance as result. Print the result in the end or if the matrix doesn’t contain any 0 then print 0.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the farthest distance ` `// of a 0 from the center of the matrix ` `#include ` `#define n 3 ` `using` `namespace` `std; ` ` `  `// function to return farthest distance ` `// of zero from center of the matrix ` `int` `farthestDistance(``int` `matrix[][n]) ` `{ ` ` `  `    ``int` `result = 0; ` ` `  `    ``// traverse the matrix ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``for` `(``int` `j = 0; j < n; j++) { ` `            ``if` `(matrix[i][j] == 0) ` `                ``result = max(result ` `                           ``, ``abs``(i - n/2) + ``abs``(j - n/2)); ` `        ``} ` `    ``} ` ` `  `    ``// return result ` `    ``return` `result; ` `} ` ` `  `// driver program ` `int` `main() ` `{ ` `    ``int` `matrix[n][n] = { { 1, 2, 3 } ` `                       ``, { 0, 1, 1 } ` `                       ``, { 0, 0, 0 } }; ` ` `  `    ``cout << farthestDistance(matrix); ` `    ``return` `0; ` `} `

## Java

 `//  Java program to find the farthest distance ` `// of a 0 from the center of the matrix ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `    `  ` `  `static` `int` `n = ``3``; ` ` `  ` `  `// function to return farthest distance ` `// of zero from center of the matrix ` `static` `int` `farthestDistance(``int` `matrix[][]) ` `{ ` ` `  `    ``int` `result = ``0``; ` ` `  `    ``// traverse the matrix ` `    ``for` `(``int` `i = ``0``; i < n; i++) { ` `        ``for` `(``int` `j = ``0``; j < n; j++) { ` `            ``if` `(matrix[i][j] == ``0``) ` `                ``result = Math.max(result ` `                        ``, Math.abs(i - n/``2``) + Math.abs(j - n/``2``)); ` `        ``} ` `    ``} ` ` `  `    ``// return result ` `    ``return` `result; ` `} ` ` `  `// driver program ` ` `  `    ``public` `static` `void` `main (String[] args) { ` `            ``int` `matrix[][] = { { ``1``, ``2``, ``3` `} ` `                    ``, { ``0``, ``1``, ``1` `} ` `                    ``, { ``0``, ``0``, ``0` `} }; ` ` `  `    ``System.out.print(farthestDistance(matrix)); ` `    ``} ` `} ` `// This code is contributed by anuj_67.. `

## Python3

 `# Python3 program to find the farthest distance ` `# of a 0 from the center of the matrix ` ` `  `n ``=` `3` ` `  `# function to return farthest distance ` `# of zero from center of the matrix ` `def` `farthestDistance(matrix): ` `    ``result ``=` `0` ` `  `    ``# traverse the matrix ` `    ``for` `i ``in` `range` `(``0``, n):  ` `        ``for` `j ``in` `range` `(``0``, n): ` `            ``if` `(matrix[i][j] ``=``=` `0``): ` `                ``result ``=` `max``(result, ``abs``(i ``-` `n ``/``/` `2``) ``+`  `                                     ``abs``(j ``-` `n``/``/``2``)) ` `         `  `    ``# return result ` `    ``return` `result ` ` `  `# Driver Code ` `matrix ``=` `[[``1``, ``2``, ``3``],  ` `          ``[``0``, ``1``, ``1``], ` `          ``[``0``, ``0``, ``0``]] ` ` `  `print``(farthestDistance(matrix)) ` ` `  `# This code is contributed by ` `# Archana_kumari `

## C#

 `// C# program to find the farthest distance  ` `// of a 0 from the center of the matrix  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `static` `int` `n = 3;  ` ` `  `// function to return farthest distance  ` `// of zero from center of the matrix  ` `static` `int` `farthestDistance(``int` `[,]matrix)  ` `{  ` ` `  `    ``int` `result = 0;  ` ` `  `    ``// traverse the matrix  ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `    ``{  ` `        ``for` `(``int` `j = 0; j < n; j++)  ` `        ``{  ` `            ``if` `(matrix[i,j] == 0)  ` `                ``result = Math.Max(result , ` `                         ``Math.Abs(i - n / 2) + ` `                         ``Math.Abs(j - n / 2));  ` `        ``}  ` `    ``}  ` ` `  `    ``// return result  ` `    ``return` `result;  ` `}  ` ` `  `// Driver Code  ` `static` `public` `void` `Main () ` `{ ` `    ``int` `[,]matrix = {{ 1, 2, 3 },  ` `                     ``{ 0, 1, 1 },  ` `                     ``{ 0, 0, 0 }};  ` ` `  `    ``Console.WriteLine(farthestDistance(matrix));  ` `}  ` `}  ` ` `  `// This code is contributed by Sachin  `

## PHP

 ` 0)  ` `                ``\$result` `= max(``\$result``,  ` `                          ``abs``(``\$i` `- ``\$n` `/ 2) +  ` `                          ``abs``(``\$j` `- ``\$n` `/ 2));  ` `        ``}  ` `    ``}  ` ` `  `    ``// return result  ` `    ``return` `\$result``;  ` `}  ` ` `  `// Driver Code ` `\$matrix` `= ``array``(``array``( 1, 2, 3 ),  ` `                ``array``( 0, 1, 1 ), ` `                ``array``( 0, 0, 0 ));  ` ` `  `echo` `farthestDistance(``\$matrix``);  ` `     `  `// This code is contributed by Sach_code ` `?> `

Output:

```2
```

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