1. Two Dimensional Arrays Rohit Khokher

2. Two dimensional Arrays
A vector can be represented as an one dimensional array
A matrix can be represented as a two dimensional array
A[8][10]
Columns
Rows
A[5][6]
Array element

3. The value of sales of three items by four sales person1 2 3
A[0][0]
A[0][1]
A[0][2]
A[1][0]
A[1][1]
A[1][2]
A[2][0]
A[2][1]
A[2][2] 4
A[3][0]
A[3][1]
A[3][2]
Sales Persons

4. 2-D array 2-Day Array Declaration #define ROWS 2 #define COLS 31
float A[ROWS ][COLS];
Compile time Initialization
int A[ROWS ][COLS]= {0,0,0,1,1,1}; or
int A[ROWS ][COLS]= ({0,0,0},{1,1,1});

5. Compile time initialization1
int A[ROWS ][COLS]= {{0,0,0},
{1,1,1}};
int A[ ][COLS]= {
{0,0,0},
{1,1,1} }; 1 2
int A[ROWS][COLS]= {
{0,0},
{2} };
The missing values are initialized to zero automatically

6. Runtime Initialization for (i=0; i<ROWS; i++)
for (j=0; i<COLS; j++)
a[i][j]=0;
Reading the elements of 2-D array
Read data row-wise
for (i=0; i<ROWS; i++)
for (j=0; j<COLS; j++)
scanf (“%d”, &a[i][j]);
Priniting the elements of 2-D array
for (i=0; i<ROWS; i++) {
Print a row
for (j=0; j<COLS; j++)
printf (“%d”, &a[i][j]);
Change line
printf (“\n”); }

7. Matrix manipulation Read a matrix A (4,4) of real numbers and compute:
sum of each row entries
sum of each column entries
sum of the main diagonal entries
sum of the secondary diagonal entries

8. Compute row sum for (i=0; i<ROWS; i++) { R[i]=0; Initialize R[i]
for (j=0; j<COLS; j++)
R[i]=R[i]+A[i][j]; }

9. Compute Column sum for (j=0; j<COLS; j++) { C[j]=0;
A[0][0]
A[0][1]
A[0][2]
A[0][3]
A[1][0]
A[1][1]
A[1][2]
A[1][3]
A[2][0]
A[2][1]
A[2][2]
A[2][3]
A[3][0]
A[3][1]
A[3][2]
A[3][3]
for (j=0; j<COLS; j++)
{ C[j]=0;
for (i=0; i<ROWS; i++)
C[j]=C[j]+A[i][j]; }
Initialize C[j]
C[0]=
A[0][0] +
A[1][0] +
A[2][0] +
A[3][0]
C[1]=
A[0][1] +
A[1][1] +
A[2][1] +
A[3][1]
C[2]=
A[0][2] +
A[1][2] +
A[2][2] +
A[3][2]
C[3]=
A[0][3] +
A[1][3] +
A[2][3] +
A[3][3]

10. Compute diagonal sum D =0; for (j=0; j<COLS; j++) D= D+ A[j][j]; OR
for (i=0; i<ROWS; i++)
D=D+A[i][i]; D=
A[0][0] +
A[1][1] +
A[2][2] +
A[3][3]

11. Compute second diagonal sum
for (i=0; i<ROWS; i++)
D= D+ A[i][COLS-i]; D=
A[0][3] +
A[1][2] +
A[2][1] +
A[3][0]

12. Practice question
Write a C program to find the largest element of each row of a 2D array.
Write a C program to find the row and column numbers of the smallest element of a 2D array and count the sum of its neighbors. In a 2D array an element A[i][j] may have up to eight neighbors defined as:
i-1,j-1
i-1,j
i-1, j+1
I,j-1
i,j
i,j+1
i+1,j-1
i+1,j
i+1,j+1

13. Add two matrices for (i=0; i<ROWS; i++) for (j=0; j<COLS; j++)
C[i][j]=A[i][j]+B[i][j];

14. Multiplication of two matrices
c11=a11 x b11 + a12 x b21
c12=a11 x b12 + a12 x b22
c13=a11 x b13 + a12 x b23
for (i=0; i<ROWSA; i++)
c21=a21 x b11 + a22 x b21
for (j=0; j<COLSB; j++)
c22=a21 x b12 + a22 x b22
c23=a21 x b13 + a22 x b23
{ C[i][j]=0;
c31=a31 x b11 + a32 x b21
for (k=0; j<COLSA; j++)
C[i][j]= C[i][j]+A[i][k]+B[k][j]; }
c22=a31 x b12 + a32 x b22
c33=a31 x b13 + a32 x b23

15. Practice problem
To verify the correctness the matrix multiplication algorithm described before compute:

16. Practice problem
A square 2D array is called a magic square if sums of each row, each column, and both the diagonals of the array are equal. A 3 x 3 magic square is shown below. Read more about magic square at Write a program that reads a 2D array and determines whether the array is a magic square or not.

17. Project
Read about the tic-tac-toe game at . Find the simplest algorithm that can be implemented in C using 1D and 2D arrays.