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Farthest distance of a 0 from the center of a 2-D matrix
  • Last Updated : 04 Feb, 2019

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 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++

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// 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;
}

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Java

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//  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..

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Python3

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# 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

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C#

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// 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 

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PHP

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<?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
?>

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Output:

2

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