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

Last Updated : 09 Sep, 2022

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

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 <bits/stdc++.h> #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# 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

<?php // PHP program to find the farthest distance  // of a 0 from the center of the matrix  $n = 3;   // function to return farthest distance  // of zero from center of the matrix  function farthestDistance($matrix)  {      global $n;      $result = 0;           // traverse the matrix      for ($i = 0; $i < $n; $i++)      {          for ($j = 0; $j < $n; $j++)         {              if (($matrix[$i][$j] == 0) > 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

<script>  // Javascript program to find the farthest distance // of a 0 from the center of the matrix var n = 3;  // function to return farthest distance // of zero from center of the matrix function farthestDistance(matrix) {      var result = 0;      // traverse the matrix     for (var i = 0; i < n; i++) {         for (var 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 var matrix = [ [ 1, 2, 3 ]                    , [ 0, 1, 1 ]                    , [ 0, 0, 0 ] ]; document.write( farthestDistance(matrix));  </script>

Output

Complexity Analysis:

Time Complexity: O(N*M), as we are using nested loops to traverse N*M times.
Auxiliary Space: O(1), as we are not using any extra space for matrix.

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

Shivam.Pradhan

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

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