C++ Sparse Matrix Multiplication using Linked Lists

This C++ code implements a function to multiply two sparse matrices represented as linked lists. The function multiplyMatrices takes two sparse matrices matrixA and matrixB, represented as linked lists, along with the dimensions of the matrices (rowsA, colsA, and colsB) and stores the result in the result matrix, also represented as a linked list.

void multiplyMatrices(HeadNode* matrixA, HeadNode* matrixB, HeadNode* result, int rowsA, int colsA, int colsB) {
    initializeMatrix(&result, rowsA, colsB);

    for (int i = 0; i < rowsA; i++) {
        Node* rowNodeA = matrixA[i].rowHead;

        for (int j = 0; j < colsB; j++) {
            Node* colNodeB = matrixB[j].colHead;

            int sum = 0;
            while (rowNodeA != NULL && colNodeB != NULL) {
                if (rowNodeA->col < colNodeB->row) {
                    rowNodeA = rowNodeA->right;
                } else if (rowNodeA->col > colNodeB->row) {
                    colNodeB = colNodeB->down;
                } else {
                    sum += rowNodeA->value * colNodeB->value;
                    rowNodeA = rowNodeA->right;
                    colNodeB = colNodeB->down;
                } 
            }
            insertNode(result, i, j, sum);
        }
    }
}

The code first initializes the result matrix using the initializeMatrix function. Then, it iterates through each row of matrixA and each column of matrixB, using nested loops. For each row and column combination, it calculates the sum of the products of the corresponding non-zero elements in the row and column. It achieves this by traversing the non-zero elements in both linked lists using two pointers (rowNodeA and colNodeB). If the column index in the row (rowNodeA->col) is less than the row index in the column (colNodeB->row), it moves the rowNodeA pointer to the right (to the next element in the row). Similarly, if the column index is greater than the row index, it moves the colNodeB pointer down (to the next element in the column). If the indices match, it multiplies the values of the corresponding elements and adds the product to the sum. Finally, it inserts the calculated sum into the result matrix at the corresponding row and column using the insertNode function.

This approach leverages the sparsity of the matrices by only iterating through the non-zero elements, making the multiplication process efficient. The use of linked lists allows for a flexible representation of the sparse matrices and simplifies the traversal process. This code provides a practical and efficient way to perform matrix multiplication for sparse matrices, which are often encountered in various applications such as image processing, data analysis, and computer graphics.