Chapter 6: Multidimensional Arrays

A sparse matrix is a matrix in which most of the elements are zero A Multidimensional array is represented using the type name[capacity][capacity]...[capacity] format.
A 2d array is just an collection of arrays.
A 3d array is just an array of array[s] of array[s]. Collection of 2d arrays
Example: arr[4][4][4]
Is a array that consists of 4 - 2d arrays , where each 2d arrays consists of 4 - 1d array and each 1d array contains 4 elements .

Memory Representation of Multidimensional Arrays

Row-Major representation: is where the a complete row is stored fisrt in the memory
Column-Major representation: is where the complete column is stored in the memory

C, C++ , Java , python uses Row-major
Fortran, Matlab, R uses Column-Major

When a function calls another variable the second dimension must be specified in C in the called function's paramters

Addition and Subtraction of 2d Arrays

    

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#include<stdio.h>

int main(){
int a[10][10],b[10][10],i,j,n,m,x,y;

printf("Enter the rows and columns for matrix A: ");
scanf("%d %d",&n,&m);

printf("Enter the rows and columns for matrix B: ");
scanf("%d %d",&x,&y);

if(n!=x || m!=y){
printf("Addition / Subtraction is not possible");
return 0;
}

printf("\n\n\n\n Matrix 1 \n\n\n");
for(i=0;i<n;i++){
printf("\n\t\t\t At Row %d \n\n",i+1);
for(j=0;j<m;j++){
printf("Enter element %d ",j+1);
scanf("%d",&a[i][j]);
}
}
printf("\n\n\n\nMatrix 2: \n\n\n");
for(i=0;i<x;i++){
printf("\n\t\t\t At Row %d \n\n",i+1);
for(j=0;j<y;j++){
printf("Enter element %d ",j+1);
scanf("%d",&b[i][j]);
}
}

printf("\nA \t\tB \t\t Sum \t\tSub\n");
for(i =0;i<n;i++){
for(j=0;j<m;j++){
printf("%d ",a[i][j]);
}
printf("\t\t");
for(j=0;j<m;j++){
printf("%d ",b[i][j]);
}
printf("\t\t");

for(j=0;j<m;j++){
printf("%d ",a[i][j]+b[i][j]);
}
printf("\t\t");

for(j=0;j<m;j++){
printf("%d ",a[i][j]-b[i][j]);
}
printf("\n");
}

return 0;

}

Multiplication of 2D arrays

    

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#include<stdio.h>

int main(){
int a[10][10],b[10][10],i,j,n,m,x,y;

  printf("Enter the rows and columns for matrix A: ");
  scanf("%d %d",&n,&m);

  printf("Enter the rows and columns for matrix B: ");
  scanf("%d %d",&x,&y);

  if(n!=x  || m!=y){
    printf("Multiplication is not possible");
    return 0;
  }
  
 
  printf("\n\n\n\n Matrix 1 \n\n\n");
  for(i=0;i<n;i++){
    printf("\n\t\t\t At Row %d \n\n",i+1);
    for(j=0;j<m;j++){
    printf("Enter element %d ",j+1);
    scanf("%d",&a[i][j]);
    }
  }
  printf("\n\n\n\nMatrix 2: \n\n\n");
  for(i=0;i<x;i++){
  printf("\n\t\t\t At Row %d \n\n",i+1);
  for(j=0;j<y;j++){
    printf("Enter element %d ",j+1);
    scanf("%d",&b[i][j]);
  }
  }

  int sum=0;

  for(int k=0;k<n;k++){
    for(int i=0;i<n;i++){
    for(int j=0;j<m;j++){
      sum+=a[k][j]*b[j][i];
    }
    printf("%d ",sum);
      sum=0;
  }
  printf("\n");
  }
  return 0;


}
    ;

Sparse Matrix P.S: its Transpose

  

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#include<;stdio.h>

int main(){
  int i,s,j,count=0,n,m;
  printf("Enter the order of the matrix: \n");
  scanf("%d %d",&n,&m);

  int arr[n][m];
  int sm[n][m];
  int tm[n][m];
  for(i=0;i<;n;i++){
    printf("\n\n **** IN ROW %d **** \n\n",i+1);
    for(j=0;j<;m;j++){
      printf("Enter element no %d: \n",j+1);
      scanf("%d",&arr[i][j]);
      if(arr[i][j]==0){
        count++;
      }
    }
  }

  if (count>((n*m)/2)){
    printf("This is a sparse matrix! ");
    for(i=0;i<;n;i++){
      for(j=0;j<;m;j++){
        if(arr[i][j]!=0){
          sm[s][0]=i;
          sm[s][1]=j;
          sm[s][2]=arr[i][j];
          tm[s][0]=j;
          tm[s][1]=i;
          tm[s][2]=arr[i][j];
          s++;
        }
      }
    }
    printf("\n\nThe non - zero Entries [a.k.a: sparse matrix] are: \n");
    for(i=0;i<;s;i++){
      for(j=0;j<;3;j++){
        printf("%d ",sm[i][j]);
      }
      printf("\n");
    }

    printf("\n\n The Transpose matrix is: \n");
    for(i=0;i<;s;i++){
      for(j=0;j<;3;j++){
        printf("%d ",tm[i][j]);
      }
      printf("\n");
    }
  }
  else{
    printf("This is not a sparse matrix! ");
  }
  return 0;
}

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