Department of Computer and Information Science, School of Science, IUPUI

1. Department of Computer and Information Science,School of Science, IUPUI CSCI 240 Abstract Data Types Sparse Matrices Dale Roberts, Lecturer IUPUI droberts@cs.iupui.edu

2. Sparse Matrices é ù 0 0 11 0 ê ú 12 5 0 0 ê ú - ê ú 0 4 0 0 ê ú - 0 0 0 15 ë û Sparse matrices have a large number of zero elements in proportion to the number of nonzero elements. Storing in n x n array will have a lot of wasted space. Alternative: circular lists storing only nonzero elements.

3. down head right next row col down entry right value Sparse Matrix Nodes # of head nodes = # of rows + # of columns head node entry node tag j i aij aij tag is used to tell entry, head and aij nodes part

4. Linked Representation for Matrix 4 4 0 2 11 1 1 1 0 12 5 1 2 -4 3 3 -15 Circular linked list

5. Sparse Matrix Data Structure #define MAX_SIZE 50 /* size of largest matrix */typedef enum {head, entry} tagfield;typedef struct matrix_node *matrix_pointer;typedef struct entry_node { int row; int col; int value; };typedef struct matrix_node { matrix_pointer down; matrix_pointer right; tagfield tag; union { matrix_pointer next; entry_node entry; } u; };matrix_pointer hdnode[MAX_SIZE];

6. Try creating your data for this matrix

7. Acknowledgements • All of this code is from Horowitz, Sahni, and Anderson-Freed, Fundamentals of Data Structures in C. • Some slides were originally developed by Chen, Hsin-His.