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

2. Sparse Matrices ú û ù ê ë é - 15 4 5 12 114 5 12 11
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. tag is used to tell entry, head and aij nodes part
Sparse Matrix Nodes
# of head nodes = # of rows + # of columns
down
head
right
next
head node
down
entry
right
value
row
col
entry node
tag i j
aij
aij
tag is used to tell entry, head and aij nodes part

4. Linked Representation for Matrix4 4 2 11 1 1 1 12 5 2 1 -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.