Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 11.1, Problem 2E
Program Plan Intro
To describe the application of bit
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Write in C Language
Description
A sparse matrix is a matrix in which most of the elements are zero. Representing a sparse matrix by a 2D array leads to wastage of lots of memory as zeroes in the matrix are of no use in most of the cases. So, we can compress the sparse matrix by only store non-zero elements. This means storing non-zero elements with triples- (Row, Column, value).
0 0 0 0 0 0
0 3 0 0 0 0
0 0 0 6 0 0
0 0 9 0 0 0
0 0 0 0 12 0
Here is a 5X6 matrix, there are 4 element non-zero, we using three number represent it
5 6 4
After the three number are (Row, Column, value):
row col val
1 1 3
2 3 6
3 2 9
4 4 12
Write a program to read the compressed matrix and print out the original matrix.
Input
First line consists 3 integers. First and second integers shows the dimensions of original matrix. Third integer k shows number of non-zero elements. Followed k lines are content of the sparse matrix. Each line consists 3 integers, row number, column number, and data.
Output
Output…
Write in C Language
Description
A sparse matrix is a matrix in which most of the elements are zero. Representing a sparse matrix by a 2D array leads to wastage of lots of memory as zeroes in the matrix are of no use in most of the cases. So, we can compress the sparse matrix by only store non-zero elements. This means storing non-zero elements with triples- (Row, Column, value).
0 0 0 0 0 0
0 3 0 0 0 0
0 0 0 6 0 0
0 0 9 0 0 0
0 0 0 0 12 0
Here is a 5X6 matrix, there are 4 element non-zero, we using three number represent it
5 6 4
After the three number are (Row, Column, value):
row col val
1 1 3
2 3 6
3 2 9
4 4 12
Write a program to read the compressed matrix and print out the original matrix.
Input
First line consists 3 integers. First and second integers shows the dimensions of original matrix. Third integer k shows number of non-zero elements. Followed k lines are content of the sparse matrix. Each line consists 3 integers, row number, column number, and data.
Output
Output…
#!/usr/bin/env python 3
Suppose we have very large sparse vectors, which contains a lot of
zeros and double.
find a data structure to store them
get the dot product of them
def vector_to_index_value_list(vector):
return [(i, v) for i,v in enumerate(vector) if v != 0.0]
def dot product (iv_list1, iv_list2):
product = 0
p1=len (iv_list1)-1
p2 = len (iv_list2) - 1
while p1 >= 0 and p2 >= 0:
i1, v1 = iv_list1 [p1]
i2, v2 = iv_list2 [p2]
if i1
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