**Array - single dimension**. Two dimension array is actually extension of idea of single dimension array.

Since single dimension array is linear and memory is also linear, array and memory organisation was straight forward. When it comes to two dimension array, way memory is allocated is different. Since two dimension array mimic the matrix very well. Below is example of matrix addition.

Writing C program that would do the same

#include <stdio.h> int main() { int a[2][3] = { { 1, 2, 3}, { 4, 5, 6}}; int b[2][3] = { { 5, 2, 6}, { 1, 9, 2}}; int c[2][3]; int row, col; for(row = 0; row < 2; row++) { for(col = 0; col < 3; col++) { c[row][col] = a[row][col] + b[row][col]; printf(" %d ", c[row][col]); } printf("\n"); } return 0; }

Output of the above program is

6 4 9 5 14 8

*Explanation**Declaration*

int a[MAX_ROW][MAX_COL] = { { 1, 2, 3}, { 4, 5, 6}};

Here MAX_ROW is maximum number of rows array would have and MAX_COL is maximum number of columns array would have.

The initialization as follows

- {1, 2, 3} corresponds to initial values of first row.
- {4, 5, 6} corresponds to initial values of second row.

Note the syntax of how initialization is done. If partial initialization is done then other elements in the matrix are initialized to zero. Here same rules for single dimension array is extended to Two dimension array.

*Accessing the elements*

Elements can be accessed as follows

a[row][col]

- row is the row index. Note that row index starts from 0, Not 1.
- col is the column index. also column index starts from 0, Not 1.

#include <stdio.h> int main() { int a[2][3] = { { 1, 2, 3}, { 4, 5, 6}}; int b[3][2] = { { 7, 8}, {9, 10}, {11, 12}}; int c[2][2]; int row, col; int dot_idx; for(row = 0; row < 2; row++) { for(col = 0; col < 2; col++) { int sum = 0; for(dot_idx = 0; dot_idx < 3; dot_idx++) { sum = sum + a[row][dot_idx] * b[dot_idx][col]; } c[row][col] = sum;; printf(" %d ", c[row][col]); } printf("\n"); } return 0; }

Output of the above program is

58 64 139 154

Explanation

- Resultant matrix is 2 x 2, if you have not understood this you need to go through link again.
- First loop goes through row of the result matrix, we already know it is 2 in size.
- Second loop goes through column of the result matrix, which is 2.
- Third loop is doing the dot product of row of matrix a with column of matrix b.
- See how nicely the dot product is calculated.
- sum = sum + a[row][dot_idx] * b[dot_idx][col];
- Think about it, you will appreciate the usage of array.

#include <stdio.h> int main() { int a[2][3] = { { 1, 2, 3}, { 4, 5, 6}}; int row, col; printf("Address of a is %p\n", &a); for(row = 0; row < 2; row++) { for(col = 0; col < 3; col++) { printf("Row - %d, Col - %d, Value - %d, Address - %p \n", row, col, a[row][col], &a[row][col]); } } return 0; }

Output of above program is

Address of a is 0x7fff0590c100 Row - 0, Col - 0, Value - 1, Address - 0x7fff0590c100 Row - 0, Col - 1, Value - 2, Address - 0x7fff0590c104 Row - 0, Col - 2, Value - 3, Address - 0x7fff0590c108 Row - 1, Col - 0, Value - 4, Address - 0x7fff0590c10c Row - 1, Col - 1, Value - 5, Address - 0x7fff0590c110 Row - 1, Col - 2, Value - 6, Address - 0x7fff0590c114

*Explanation*Below picture will explain all

Same concept can be extended more than two dimensions, but they are seldom used.

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