![One Linear List Per Row
0 0 3 0 4
0 0 5 7 0
0 0 0 0 0
0 2 6 0 0
row1 = [(3, 3), (5,4)]
row2 = [(3,5), (4,7)]
row3 = []
row4 = [(2,2), (3,6)]
valuecolumn](https://image.slidesharecdn.com/sparsematrixanditsrepresentationdatastructure-171125073407/85/Sparse-matrix-and-its-representation-data-structure-8-320.jpg)
Sparse matrix and its representation data structure
- 1. GANDHINAGAR INSTITUTE OF TECHNOLOGY Computer Engineering Department Data Structures (2130702) Sparse matrix and its representation Prepared By : Vardhil Patel Enrolment No : ___________ Guided By: Prof. ___________
- 2. Sparse matrix and its representation Matrics play a very important role in solving many interesting problem in various scientific and engineering application. It is therefore necessary for us to design efficient representation for matrices. Normally matrices are represented in a two dimensional array. In a matrix, if there are m rows and n columns and then the space required to store the numbers will be m*n*s where s is the number of bytes required to store the value. Suppose there are 10 rows and 10 columns and we have to store the integer values then the space complexity will be bytes. 10*10*2=200 bytes.
- 3. Sparse Matrices • Sparse matrix … many elements are zero means sparse matrix has very few non zero elements • Time complexity of the matrix will be O(n^2),because the operations that are carried out on matrices need to sces one row at a time and individual columns in that row, results in use of two nested loops, • Example: if the matrix is of size 100*100and only 10 elements are non zero. Then for accessing these 10 elements one has to make 10000 times scan. also only 10 spaces will be with non zero elements remaining space of matrix will be filled with zeros only. i.e. we have to allocate the memory of 100*100*2=2000.
- 4. Representation of sparse matrix: • The representation of sparse matrix will be a triplet only. • In the sense that basically the sparse matrix means very few non zero elements having in it rest of the spaces are having the values zero which are basically useless values or simply empty values.so in this efficient representation we will consider all the non zero value along with their positions. in a row wise representation of spare matrix (sparse matrix is 2D matrix) the 0th row will store total rows of the matrix, total column of the matrix and total non zero value
- 5. EXAMPLE: 0 0 3 0 4 0 0 5 7 0 0 0 0 0 0 0 2 6 0 0 INDEX ROW NO. COL. NO. VALUES 0 1 3 3 1 1 5 4 2 2 3 5 3 2 4 7 4 4 2 2 5 4 3 6
- 6. Chain Representation row col nextvalue Node structure:
- 7. Single Chain row 1 1 2 2 4 4 list = column 3 5 3 4 2 3 value 3 4 5 7 2 6 1 3 3 1 5 4 2 5 2 7 4 2 4 6 3 4 3 null firstNode 2
- 8. One Linear List Per Row 0 0 3 0 4 0 0 5 7 0 0 0 0 0 0 0 2 6 0 0 row1 = [(3, 3), (5,4)] row2 = [(3,5), (4,7)] row3 = [] row4 = [(2,2), (3,6)] valuecolumn