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Farthest distance of a 0 from the center of a 2-D matrix
• Last Updated : 30 Apr, 2021

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:

Approach: The center of any matrix with odd order is at index i = j = floor(n/2). Now for finding the farthest distance of any 0 from the center, calculate the distance of each 0 from the 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``?>`

## Javascript

 ``
Output:
`2`

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