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 a 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 elements of every column and return the maximum difference.

Below is the implementation of the above approach:  

C++

// 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;
}

Java

// 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));
    }
}

Python3

# 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

C#

// 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

PHP

<?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

Javascript

<script>
// Javascript program to find column with
// max difference of any pair of elements

    let N = 5; // No of rows and column

    // Function to find the column with max difference
    function colMaxDiff(mat)
    {
        let max_diff = Number.MIN_VALUE;

        // Traverse matrix column wise
        for (let i = 0; i < N; i++) {

            // Insert elements of column to vector
            let max_val = mat[0][i], min_val = mat[0][i];
            for (let 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
    let 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 ]];

    document.write("Max difference :"+ colMaxDiff(mat))


// This code is contributed by rag2127
</script>

Output

Max difference : 12

Time Complexity: O(n^2)