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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. Sparse Matrices. é. ù. 0. 0. 11. 0. ê. ú. 12. 5. 0. 0. ê. ú. -. ê.

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

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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

### Sparse Matrices

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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.

down

right

next

row

col

down

entry

right

value

### Sparse Matrix Nodes

# of head nodes = # of rows + # of columns

entry node

tag

j

i

aij

aij

tag is used to tell entry, head and aij nodes part

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### 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];

### 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.