4.2 2D Arrays and Sequence Statistics

A two-dimensional array can represent a table, matrix, or board. It has row and column indexes.

int grid[2][3] = {
    {1, 2, 3},
    {4, 5, 6}
};

printf("%d\n", grid[1][2]);  // 6

grid[1][2] means: take row 1, then take column 2 inside that row. Both indexes start from 0.

Matrix addition can be done with nested loops. The outer loop controls rows, and the inner loop controls columns.

Matrix addition and subtraction require two matrices with the same shape. If $A$ and $B$ are both $m \times n$ matrices, then the result matrix is also $m \times n$. "Element by element" means row $i$, column $j$ is only combined with row $i$, column $j$ from the other matrix.

int A[3][2] = {
    {1, 3},
    {1, 0},
    {1, 2}
};

int B[3][2] = {
    {0, 0},
    {7, 5},
    {2, 1}
};

int C[3][2];

printf("Matrix Addition\n");
for (int i = 0; i < 3; i++) {
    for (int j = 0; j < 2; j++) {
        C[i][j] = A[i][j] + B[i][j];
        printf("%3d", C[i][j]);
    }
    printf("\n");
}

Result:

Matrix Addition
  1  3
  8  5
  3  3

Common array statistics include sum, average, maximum, and minimum.

int scores[] = {88, 91, 76, 95, 83};
int n = sizeof(scores) / sizeof(scores[0]);
int max = scores[0];

for (int i = 1; i < n; i++) {
    if (scores[i] > max) {
        max = scores[i];
    }
}

sizeof(scores) / sizeof(scores[0]) only works while scores is still an array in the current scope.