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: 2Input: 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 3using namespace std;// function to return farthest distance// of zero from center of the matrixint 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 programint 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 matriximport java.io.*;class GFG { static int n = 3;// function to return farthest distance// of zero from center of the matrixstatic 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 matrixn = 3# function to return farthest distance# of zero from center of the matrixdef 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 Codematrix = [[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
<?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 matrixvar n = 3;// function to return farthest distance// of zero from center of the matrixfunction 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 programvar matrix = [ [ 1, 2, 3 ] , [ 0, 1, 1 ] , [ 0, 0, 0 ] ];document.write( farthestDistance(matrix));</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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