Find pair with maximum difference in any column of a Matrix

Given a N*N matrix of positive integers. The task is to find the maximum difference between any pair of elements in any column of the matrix.

Examples:

Input : mat[N][N] = {
        { 1, 2, 3, 4, 5 },
        { 5, 3, 5, 4, 0 },
        { 5, 6, 7, 8, 9 },
        { 0, 6, 3, 4, 12 },
        { 9, 7, 12, 4, 3 },
    };
Output : Max difference : 12
5th column has the pair with max difference
(0, 12)

Input : mat[N][N] = {
        { 1, 2, 3 },
        { 5, 3, 5 },
        { 9, 6, 7 }
    };
Output : Max difference : 8

The idea is to observe that the pair with maximum difference in any column is the difference between the maximum and minimum element of that column. Now traverse the matrix column wise. Find the difference between the max and min element of every column and return the maximum difference.

Below is the implementation of the above approach:

C++

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// C++ program to find column with
// max difference of any pair of elements
#include <bits/stdc++.h>
using namespace std;
  
#define N 5 // No of rows and column
  
// Function to find the column with max difference
int colMaxDiff(int mat[N][N])
{
    int max_diff = INT_MIN;
  
    // Traverse matrix column wise
    for (int i = 0; i < N; i++) {
  
        // Insert elements of column to vector
        int max_val = mat[0][i], min_val = mat[0][i];
        for (int j = 1; j < N; j++) {
            max_val = max(max_val, mat[j][i]);
            min_val = min(min_val, mat[j][i]);
        }
  
        // calculating difference between maximum and
        // minimum
        max_diff = max(max_diff, max_val - min_val);
    }
  
    return max_diff;
}
  
// driver code
int main()
{
    int mat[N][N] = {
        { 1, 2, 3, 4, 5 },
        { 5, 3, 5, 4, 0 },
        { 5, 6, 7, 8, 9 },
        { 0, 6, 3, 4, 12 },
        { 9, 7, 12, 4, 3 },
    };
  
    cout << "Max difference : " << colMaxDiff(mat) << endl;
  
    return 0;
}

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Java

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// Java program to find column with 
// max difference of any pair of elements 
  
public class GOC1 {
  
    static int N = 5; // No of rows and column 
  
    // Function to find the column with max difference
    static int colMaxDiff(int mat[][]) {
        int max_diff = Integer.MIN_VALUE;
  
        // Traverse matrix column wise
        for (int i = 0; i < N; i++) {
  
            // Insert elements of column to vector
            int max_val = mat[0][i], min_val = mat[0][i];
            for (int j = 1; j < N; j++) {
                max_val = Math.max(max_val, mat[j][i]);
                min_val = Math.min(min_val, mat[j][i]);
            }
  
            // calculating difference between maximum and
            // minimum
            max_diff = Math.max(max_diff, max_val - min_val);
        }
  
        return max_diff;
    }
  
    // Driver Code
    public static void main(String args[]) {
        int mat[][] = { 
                { 1, 2, 3, 4, 5 }, 
                { 5, 3, 5, 4, 0 }, 
                { 5, 6, 7, 8, 9 }, 
                { 0, 6, 3, 4, 12 }, 
                { 9, 7, 12, 4, 3 }, 
            }; 
            
        System.out.println("Max difference : "+colMaxDiff(mat));
    }
}

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Python3

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# Python3 program to find column with
# max difference of any pair of elements
  
N = 5 # No of rows and column
  
# Function to find the column 
# with max difference
def colMaxDiff(mat):
  
    max_diff = 0
  
    # Traverse matrix column wise
    for i in range (N):
  
        # Insert elements of column 
        # to vector
        max_val = mat[0][i]
        min_val = mat[0][i]
        for j in range (1, N) :
            max_val = max(max_val, mat[j][i])
            min_val = min(min_val, mat[j][i])
  
        # calculating difference between 
        # maximum and minimum
        max_diff = max(max_diff, max_val - 
                                 min_val)
  
    return max_diff
  
# Driver Code
if __name__ == "__main__":
    mat = [[ 1, 2, 3, 4, 5 ],
           [5, 3, 5, 4, 0 ],
           [ 5, 6, 7, 8, 9 ],
           [ 0, 6, 3, 4, 12 ],
           [ 9, 7, 12, 4, 3 ]]
  
    print ("Max difference :", colMaxDiff(mat))
  
# This code is contributed by ita_c

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C#

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// C# program to find column  
// with max difference of 
// any pair of elements 
using System;
  
class GFG 
{
  
static int N = 5; // No of rows and column 
  
// Function to find the column
// with max difference
static int colMaxDiff(int [,]mat) 
{
    int max_diff = int.MinValue;
  
    // Traverse matrix column wise
    for (int i = 0; i < N; i++)
    {
  
        // Insert elements of column
        // to vector
        int max_val = mat[0, i], 
            min_val = mat[0, i];
        for (int j = 1; j < N; j++) 
        {
            max_val = Math.Max(max_val, 
                               mat[j, i]);
            min_val = Math.Min(min_val, 
                               mat[j, i]);
        }
  
        // calculating difference between
        // maximum and minimum
        max_diff = Math.Max(max_diff, 
                            max_val - min_val);
    }
  
    return max_diff;
}
  
// Driver Code
public static void Main() 
{
    int [,]mat = { { 1, 2, 3, 4, 5 }, 
                   { 5, 3, 5, 4, 0 }, 
                   { 5, 6, 7, 8, 9 }, 
                   { 0, 6, 3, 4, 12 }, 
                   { 9, 7, 12, 4, 3 }}; 
          
    Console.WriteLine("Max difference : "
                          colMaxDiff(mat));
}
}
  
// This code is contributed
// by Subhadeep

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PHP

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<?php
// PHP program to find column with
// max difference of any pair of elements
  
// Function to find the column with max difference
function colMaxDiff($mat)
{
    $N = 5;
    $max_diff = PHP_INT_MIN;
  
    // Traverse matrix column wise
    for ($i = 0; $i < $N; $i++) 
    {
  
        // Insert elements of column to vector
        $max_val = $mat[0][$i]; $min_val = $mat[0][$i];
        for ($j = 1; $j < $N; $j++)
        {
            $max_val = max($max_val, $mat[$j][$i]);
            $min_val = min($min_val, $mat[$j][$i]);
        }
  
        // calculating difference between maximum and
        // minimum
        $max_diff = max($max_diff, $max_val - $min_val);
    }
  
    return $max_diff;
}
  
// driver code
$mat = array(array( 1, 2, 3, 4, 5 ),
             array(5, 3, 5, 4, 0 ),
             array(5, 6, 7, 8, 9 ),
             array(0, 6, 3, 4, 12 ),
             array(9, 7, 12, 4, 3 ));
  
echo "Max difference : "
      colMaxDiff($mat) . "\n";
  
// This code is contributed
// by Akanksha Rai

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Output:

Max difference : 12

Time Complexity: O(n^2)



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