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sparse matrix in data structure
This document discusses sparse matrices. It defines a sparse matrix as a matrix with more zero values than non-zero values. Sparse matrices can save space by only storing the non-zero elements and their indices rather than allocating space for all elements. Two common representations for sparse matrices are the triplet representation, which stores the non-zero values and their row and column indices, and the linked representation, which connects the non-zero elements. Applications of sparse matrices include solving large systems of equations.
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Overview of sparse matrices indicating their significance in data structures.
A sparse matrix is defined as a matrix with more zero values than non-zero values, represented by m rows and n columns.
Example of a 100x100 matrix with only 10 non-zero elements, illustrating space inefficiency.
Introduction to different representations of sparse matrices, namely triplet and linked representations.
Explains the triplet representation including storage of non-zero values and their indices in a sparse matrix.
Brief mention of the applications of sparse matrices in computational tasks.
Provides a source for further reading on sparse matrices.
sparse matrix in data structure
- 1. தரவ கடடடமமபடப -சசதறசய அலடலத அடரடதடதசயறடற அணசகளட Data Structures- Sparse Matrix P Mahalakshmi
- 2. Data Structures- Sparse Matrix PMahalakshmi
- 3. What is SparseMatrix? ● A matrix can be defined with a 2-dimensional array. ● Any array with 'm' rows and 'n' columns represent a m X n matrix ● There may be a situation in which a matrix contains more number of ZERO values than NON-ZERO values. Such matrix is known as sparse matrix. ● Sparse matrix is a matrix which contains very few non-zero elements.
- 4. Example ● Consider amatrix of size 100 X 100 containing only 10 non-zero elements. ● In this matrix, only 10 spaces are filled with non-zero values and remaining spaces of the matrix are filled with zero. ● Totally we allocate 100 X 100 X 2 = 20000 bytes of space to store this integer matrix. ● To access these 10 non-zero elements we have to make scanning for 10000 times.
- 5. Sparse Matrix Representations ●Triplet Representation (Array Representation) ● Linked Representation
- 6. Triplet Representation (Array Representation) ●In this representation, we consider only non-zero values along with their row and column index values. ● the 0th row stores the total number of rows, total number of columns and the total number of non-zero values in the sparse matrix. ● For example, consider a matrix of size 5 X 6 containing 6 number of non-zero values.
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