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:Â
Input: mat[][] = {{2, 3, 0}, {0, 2, 0}, {0, 1, 1}}Â
Output: 2Input: mat[][] = {{2, 3, 4, {0, 2, 0}, {6, 1, 1}}Â
Output: 1
Approach:Â
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:Â
Â
C++
// C++ program to find the farthest distance// of a 0 from the center of the matrix#include <bits/stdc++.h>#define n 3using namespace std;Â
// function to return farthest distance// of zero from center of the matrixint farthestDistance(int matrix[][n]){Â
    int result = 0;Â
    // 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));        }    }Â
    // return result    return result;}Â
// driver programint main(){Â Â Â Â int matrix[n][n] = { { 1, 2, 3 }Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â , { 0, 1, 1 }Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â , { 0, 0, 0 } };Â
    cout << farthestDistance(matrix);    return 0;} |
Java
//Â Java program to find the farthest distance// of a 0 from the center of the matrixÂ
import java.io.*;Â
class GFG {Â Â Â Â Â
static int n = 3;Â
Â
// function to return farthest distance// of zero from center of the matrixstatic int farthestDistance(int matrix[][]){Â
    int result = 0;Â
    // 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));        }    }Â
    // return result    return result;}Â
// driver programÂ
    public static void main (String[] args) {            int matrix[][] = { { 1, 2, 3 }                    , { 0, 1, 1 }                    , { 0, 0, 0 } };Â
    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 matrixÂ
n = 3Â
# function to return farthest distance# of zero from center of the matrixdef farthestDistance(matrix):Â Â Â Â result = 0Â
    # 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 resultÂ
# Driver Codematrix = [[1, 2, 3],           [0, 1, 1],          [0, 0, 0]]Â
print(farthestDistance(matrix))Â
# 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;Â
class GFG{Â Â Â Â Â static int n = 3; Â
// function to return farthest distance // of zero from center of the matrix static int farthestDistance(int [,]matrix) { Â
    int result = 0; Â
    // 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));         }     } Â
    // return result     return result; } Â
// Driver Code static public void Main (){Â Â Â Â int [,]matrix = {{ 1, 2, 3 }, Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â { 0, 1, 1 }, Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â { 0, 0, 0 }}; Â
    Console.WriteLine(farthestDistance(matrix)); } } Â
// This code is contributed by Sachin |
PHP
<?php// PHP program to find the farthest distance // of a 0 from the center of the matrix $n = 3; Â
// function to return farthest distance // of zero from center of the matrix function farthestDistance($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));         }     } Â
    // return result     return $result; } Â
// Driver Code$matrix = array(array( 1, 2, 3 ),                 array( 0, 1, 1 ),                array( 0, 0, 0 )); Â
echo farthestDistance($matrix); Â Â Â Â Â // This code is contributed by Sach_code?> |
Javascript
<script>Â
// Javascript program to find the farthest distance// of a 0 from the center of the matrixvar n = 3;Â
// function to return farthest distance// of zero from center of the matrixfunction farthestDistance(matrix){Â
    var result = 0;Â
    // 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));        }    }Â
    // return result    return result;}Â
// driver programvar matrix = [ [ 1, 2, 3 ]Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â , [ 0, 1, 1 ]Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â , [ 0, 0, 0 ] ];document.write( farthestDistance(matrix));Â
</script> |
Output
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.
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