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

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 R_i-1. The difference will be calculated by subtracting the (sum of elements of R_y) - (sum of elements of R_x), where x<y.

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

Input 

M[4][4] = {
   { 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[4][4] = {
   { 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[1]-RSum[0]. Here RSum[0] is the sum of all elements of row 0 and RSums[1] is the sum of all elements of row 1.

• Also we are assuming that RSum[0] 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[1]-RSum[0];
   int MIN=RSum[0];
   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