An element of a matrix is said to be \"Saddle Point\" if it is the strictly larg

Question

An element of a matrix is said to be "Saddle Point" if it is the strictly largest element (max) in its row and the strictly smallest element (min) in its column. For example, the matrix shown below has 2 saddle points: (A matrix may have 0 - 2 saddle points) [10 12 7 3 12 3 10 6 2 8 18 24 17 6 10 15 21 10 8 12 1 18 22 4 15] Please write a C program that ask the user to input any matrix (size of matrix, and all elements in matrix), and output any saddle point(s) in the matrix (output the value and position of the saddle points).

Explanation / Answer

Program for saddle point based on above description of saddle point

#include<stdio.h>

   int main()

   {
       int n,a[100][100];       //Assuming maximum size of matrix is 100, please change the value if size of more than 100 is required
       printf("Enter size of matrix: ");
       scanf("%d",&n);
       printf("Please enter the numbers: ");
       int i,j,k,min,max,p[2][2];
       for(i=0;i<n;i++)
       {
           for(int j=0;j<n;j++)
           {
               scanf("%d",&a[i][j]);
           }
       }
      
       for(i=0;i<n;i++)
       {
          
           max = a[i][0];

           //Calculating maximum element of the row
           for(j=0;j<n;j++)
           {
               if(a[i][j]>max)
               {
                   max = a[i][j];
                   p[0][0]=i;
                   p[0][1]=j;
               }
           }
          
           j=p[0][1];
           min = a[0][j];

           //Calculating the minimum element of the column
           for(k=0;k<n;k++)
           {
               if(a[k][j]<min)
               {
                   min = a[k][j];
                   p[1][0] = k;
                   p[1][1] = j;
               }
           }
          
           //Print Saddle point - strictly largest element (max) in its row and striclty smallest element (min) in its column
           if(min == max)
           {
               if(p[0][0]==p[1][0]&&p[0][1]==p[1][1])
               {
                   printf("Saddle point is %d and its position is (%d,%d) ",min,p[0][0],p[0][1]);
               }
           }

       }

       return 0;
   }

Sample Output

Enter size of matrix: 5

Please enter the numbers:

10 12 7 3 12 3 10 6 2 8 18 24 17 6 10 15 21 10 13 12 1 18 22 4 15

Saddle point is 10 and its position is (1,1)

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