Matrices

Two-dimensional data as an array of rows

In algorithmic problems, a matrix can conveniently be represented as a two-dimensional array. The first index selects a row, and the second selects a column.

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

int value = matrix[1][2]; // 6

For this matrix, matrix.length is the number of rows, while matrix[row].length is the number of elements in a particular row. This distinction matters: in Java, a two-dimensional array is technically an array of arrays, so row lengths may differ.

Traversing rows and columns

A full matrix traversal usually uses two nested loops: the outer loop selects a row, and the inner loop visits its elements.

int sum = 0;

for (int row = 0; row < matrix.length; row++) {
    for (int col = 0; col < matrix[row].length; col++) {
        sum += matrix[row][col];
    }
}

If a matrix has rows rows and cols columns, a full traversal of a rectangular matrix takes O(rows × cols) time because every cell is visited.

Neighboring cells and boundaries

Many problems require inspecting neighbors of the current cell: above, below, left, or right. Before accessing a neighbor, you must check that its coordinates remain inside the matrix.

int row = 1;
int col = 1;

if (row > 0) {
    int top = matrix[row - 1][col];
}

if (col + 1 < matrix[row].length) {
    int right = matrix[row][col + 1];
}

These checks may look minor, but correct coordinate handling becomes the foundation for more advanced algorithms on tables and grids.