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

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++ 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 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 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 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
?>

<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>

2

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.