Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

Pair with maximum sum in a Matrix

  • Last Updated : 08 Jul, 2021

Given a NxM matrix with N rows and M columns of positive integers. The task is to find the sum of pair with maximum sum in the matrix. 
Examples
 

Input : mat[N][M] = {{1, 2, 3, 4},
                 {25, 6, 7, 8},
                 {9, 10, 11, 12},
                 {13, 14, 15, 16}}
Output : 41
Pair (25, 16) has the maximum sum

Input : mat[N][M] = {{1, 2, 3},
                 {4, 6, 7},
                 {9, 10, 5}}
Output : 19

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

Simple Approach: A simple approach is to traverse the matrix twice and find the first maximum and second maximum elements and return their sum.
Better Approach: A better approach is to find the first and second maximum in a single traversal of the matrix. 
 

1) Initialize two variables first and second to INT_MIN as,
   first = second = INT_MIN
2) Start traversing the matrix,
   a) If the current element in array say mat[i][j] is greater
      than first. Then update first and second as,
      second = first
      first = mat[i][j]
   b) If the current element is in between first and second,
      then update second to store the value of current variable as
      second = mat[i][j]
3) Return sum of both first and second maximum.

Below is the implementation of the above approach: 
 

C++




// C++ program to find maximum sum
// pair in a matrix
 
#include <bits/stdc++.h>
using namespace std;
 
#define N 4 // Rows
#define M 4 // Columns
 
// Function to find maximum sum
// pair from matrix
int maxSumPair(int mat[N][M])
{
    int max1 = INT_MIN; // First max
    int max2 = INT_MIN; // Second max
 
    // Traverse the matrix
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < M; j++) {
            if (mat[i][j] > max1) {
                max2 = max1; // second max = first max
                max1 = mat[i][j]; // first max = current
            }
            // If second max is between current element
            // and first max
            else if (mat[i][j] > max2 && mat[i][j] <= max1) {
                max2 = mat[i][j];
            }
        }
    }
 
    return max1 + max2;
}
 
// Driver Code
int main()
{
 
    // matrix
    int mat[N][M] = { { 1, 2, 3, 4 },
                      { 25, 6, 7, 8 },
                      { 9, 10, 11, 12 },
                      { 13, 14, 15, 16 } };
 
    cout << maxSumPair(mat) << endl;
 
    return 0;
}

Java




// Java program to find maximum sum
// pair in a matrix
import java.io.*;
 
class GFG {
    
static int  N = 4; // Rows
static int M = 4; // Columns
 
// Function to find maximum sum
// pair from matrix
static int maxSumPair(int [][]mat)
{
    int max1 = Integer.MIN_VALUE; // First max
    int max2 = Integer.MIN_VALUE; // Second max
 
    // Traverse the matrix
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < M; j++) {
            if (mat[i][j] > max1) {
                max2 = max1; // second max = first max
                max1 = mat[i][j]; // first max = current
            }
            // If second max is between current element
            // and first max
            else if (mat[i][j] > max2 && mat[i][j] <= max1) {
                max2 = mat[i][j];
            }
        }
    }
 
    return max1 + max2;
}
 
// Driver Code
 
    public static void main (String[] args) {
            // matrix
    int [][]mat = { { 1, 2, 3, 4 },
                    { 25, 6, 7, 8 },
                    { 9, 10, 11, 12 },
                    { 13, 14, 15, 16 } };
 
    System.out.println(maxSumPair(mat));
    }
}
// This code is contributed
// by shs

Python3




# Python 3 program to find maximum sum
# pair in a matrix
import sys
 
N = 4 # Rows
M = 4 # Columns
 
# Function to find maximum sum
# pair from matrix
def maxSumPair(mat):
 
    max1 = -sys.maxsize - 1 # First max
    max2 = -sys.maxsize - 1 # Second max
 
    # Traverse the matrix
    for i in range(0, N):
        for j in range (0, M):
            if (mat[i][j] > max1):
                max2 = max1 # second max = first max
                max1 = mat[i][j] # first max = current
             
            # If second max is between current
            # element and first max
            elif (mat[i][j] > max2 and
                  mat[i][j] <= max1):
                max2 = mat[i][j]
             
    return max1 + max2
 
# Driver Code
 
# matrix
mat = [ [1, 2, 3, 4 ],
        [25, 6, 7, 8 ],
        [9, 10, 11, 12 ],
        [13, 14, 15, 16 ]]
 
print(maxSumPair(mat))
 
# This code is contributed
# by ihritik

C#




// C# program to find maximum sum
// pair in a matrix
using System;
public class GFG {
     
static int  N = 4; // Rows
static int M = 4; // Columns
  
// Function to find maximum sum
// pair from matrix
static int maxSumPair(int [,]mat)
{
    int max1 = int.MinValue; // First max
    int max2 = int.MinValue; // Second max
  
    // Traverse the matrix
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < M; j++) {
            if (mat[i,j] > max1) {
                max2 = max1; // second max = first max
                max1 = mat[i,j]; // first max = current
            }
            // If second max is between current element
            // and first max
            else if (mat[i,j] > max2 && mat[i,j] <= max1) {
                max2 = mat[i,j];
            }
        }
    }
  
    return max1 + max2;
}
  
// Driver Code
  
    public static void Main () {
            // matrix
    int [,]mat = { { 1, 2, 3, 4 },
                    { 25, 6, 7, 8 },
                    { 9, 10, 11, 12 },
                    { 13, 14, 15, 16 } };
  
    Console.WriteLine(maxSumPair(mat));
    }
}
// This code is contributed by PrinciRaj1992

PHP




<?php
// PHP program to find maximum sum
// pair in a $matrix
 
$N = 4; // Rows
$M = 4; // Columns
 
// Function to find maximum sum
// pair from $matrix
function maxSumPair($mat)
{
    global $N;
    global $M;
    $max1 = PHP_INT_MIN; // First max
    $max2 = PHP_INT_MIN; // Second max
 
    // Traverse the $matrix
    for ($i = 0; $i < $N; $i++)
    {
        for ($j = 0; $j < $M; $j++)
        {
            if ($mat[$i][$j] > $max1)
            {
                $max2 = $max1; // second max = first max
                $max1 = $mat[$i][$j]; // first max = current
            }
             
            // If second max is between current
            // element and first max
            else if ($mat[$i][$j] > $max2 &&
                     $mat[$i][$j] <= $max1)
            {
                $max2 = $mat[$i][$j];
            }
        }
    }
 
    return $max1 + $max2;
}
 
// Driver Code
 
// matrix
$mat = array(array(1, 2, 3, 4 ),
             array(25, 6, 7, 8 ),
             array(9, 10, 11, 12 ),
             array(13, 14, 15, 16 ));
 
echo maxSumPair($mat);
 
// This code is contributed
// by ihritik
?>

Javascript




<script>
 
// JavaScript program to find maximum sum
// pair in a matrix
     
var N = 4; // Rows
var M = 4; // Columns
  
// Function to find maximum sum
// pair from matrix
function maxSumPair(mat)
{
    var max1 = -1000000000; // First max
    var max2 = -1000000000; // Second max
  
    // Traverse the matrix
    for (var i = 0; i < N; i++) {
        for (var j = 0; j < M; j++) {
            if (mat[i][j] > max1) {
                max2 = max1; // second max = first max
                max1 = mat[i][j]; // first max = current
            }
            // If second max is between current element
            // and first max
            else if (mat[i][j] > max2 && mat[i][j] <= max1) {
                max2 = mat[i][j];
            }
        }
    }
  
    return max1 + max2;
}
  
// Driver Code
 
// matrix
var mat = [ [ 1, 2, 3, 4 ],
                [ 25, 6, 7, 8 ],
                [ 9, 10, 11, 12 ],
                [ 13, 14, 15, 16 ] ];
 
document.write(maxSumPair(mat));
 
 
 
</script>
Output: 
41

 




My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!