# Maximum difference of sum of elements in two rows in a matrix in C

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We are given a matrix and the task is to find the greatest difference between the sum of elements in two rows of a matrix. Suppose we have a matrix M[i,j] with i rows and j columns. Let the rows be R0 to Ri-1. The difference will be calculated by subtracting the (sum of elements of Ry) - (sum of elements of Rx), where x<y.

Let’s now understand what we have to do using an example −

Input

M = {
{ 1,2,0,5 },
{0,1,1,0},
{7,2,3,2}
{1,2,4,1}};

Output

Maximum difference here is : 12

Explanation − Here sum of elements of Row 2 is maximum that is 14 and sum of elements of Row 1 is minimum, that is 2. So the maximum difference is 14-2=12.

Input

M = {
{ 0,2,0,5 },
{0,1,4,0},
{1,2,3,2}
{2,2,6,0}};

Output

Maximum difference here is : 5

Explanation − Here sum of elements of Row 4 is maximum that is 10 and sum of elements of Row 2 is minimum, that is 5. So the maximum difference is 10-5=10

## Approach used in the below program as follows

• Take inputs for the number of rows and columns in a matrix such that it has at-least two rows.

• In the rowmaxd() function we are passing the input matrix and it’s row count and column count and returning the maximum difference of sum of rows.

• Here we will first store the sum of elements of each row of matrix M[row][col] in an array named RSum[i]. Note that RSum[row] has length according to number of rows in M[row][col].

• Then we will assume MD as the maximum difference between RSum-RSum. Here RSum is the sum of all elements of row 0 and RSums is the sum of all elements of row 1.

• Also we are assuming that RSum is least in RSum[row] and storing it in MIN variable.

• In for loop from 0 to i we will traverse each RSum[row] and compare the difference between RSum[i]-MIN>MD. If it is so, update MD. Else check is RSum[row]<MIN and update MIN separately.

## Example

#include<stdio.h>
#define MAX 100
//create function to calculate maximum difference between sum of elements of two rows such
that second row appears before the first
int rowmaxd(int M[][MAX], int row, int col){
//for storing sum of elements of each row
int RSum[row];
for(int i=0;i<row;i++){
int sum=0;
for(int j=0;j<col;j++)
sum+=M[i][j];
RSum[i]=sum;
}
//calculate now max difference between two elements of RSum such that in RSum[j]-RSum[i], i<j
int MD=RSum-RSum;
int MIN=RSum;
for (i = 1; i < row; i++){
//if this difference is more than MD,the update MD
if(RSum[i]-MIN>MD)
MD=RSum[i]-MIN;
//if this value is even less than MIN,then update MIN
if(RSum[i]<MIN)
MIN=RSum[i];
}
return MD;
}
// Driver program
int main(){
int r = 5, c = 4;
int mat[][MAX] = {
{-1, 2, 3, 4},
{6, 3, 0, 1},
{-1, 7, 8, -3},
{3, 5, 1, 4},
{2, 1, 1, 0}};
cout<<”Maximum difference of sum of elements in two rows in a matrix is: ”<<rowmaxd(mat, r, c);
return 0;
}

## Output

If we run the above code we will get the following output −

Maximum difference of sum of elements in two rows in a matrix: 5