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In which of the following cases, linked list implementations of sparse matrices consumes the same memory space as the conventional way of storing the entire array?
(Assume all data-types need the same amount of storage.)
(Assume all data-types need the same amount of storage.)
- a)5 x 6 matrix with 9 non-zero entries
- b)5 x 6 matrix with 8 non-zero entries
- c)6 x 5 matrix with 8 non-zero entries
- d)6 x 5 matrix with 9 non-zero entries
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In which of the following cases, linked list implementations of sparse...
Conventional way needs a storage of m x n.
In the case of linked list implementation of sparse matrices, storage needed will be m + 3 x (the number of non-zero entries).
Only in case (c), both the methods need the same storage of 30.
In the case of linked list implementation of sparse matrices, storage needed will be m + 3 x (the number of non-zero entries).
Only in case (c), both the methods need the same storage of 30.
Most Upvoted Answer
In which of the following cases, linked list implementations of sparse...
Explanation:
In a conventional way of storing a matrix, we use a 2D array to represent the matrix. Each element of the 2D array occupies a fixed amount of memory space, regardless of whether it is a non-zero or zero element. Therefore, the memory space consumed by a conventional representation is equal to the number of rows multiplied by the number of columns.
However, in a linked list implementation of a sparse matrix, we only store the non-zero elements along with their row and column indices. This saves memory space as we do not need to store the zero elements. The memory space consumed by a linked list representation depends on the number of non-zero elements in the matrix, rather than the total number of elements.
Now let's analyze each case:
a) 5 x 6 matrix with 9 non-zero entries:
In this case, there are 9 non-zero entries in a 5 x 6 matrix. The conventional representation would require a 2D array of size 5 x 6, which is 30 elements. However, the linked list representation only needs to store the 9 non-zero elements. Therefore, the memory space consumed by the linked list representation is less than the conventional representation.
b) 5 x 6 matrix with 8 non-zero entries:
In this case, there are 8 non-zero entries in a 5 x 6 matrix. Similar to the previous case, the memory space consumed by the linked list representation is less than the conventional representation.
c) 6 x 5 matrix with 8 non-zero entries:
In this case, there are 8 non-zero entries in a 6 x 5 matrix. The conventional representation would require a 2D array of size 6 x 5, which is 30 elements. The linked list representation, on the other hand, only needs to store the 8 non-zero elements. Therefore, the memory space consumed by the linked list representation is equal to the conventional representation.
d) 6 x 5 matrix with 9 non-zero entries:
In this case, there are 9 non-zero entries in a 6 x 5 matrix. Similar to the previous case, the memory space consumed by the linked list representation is less than the conventional representation.
Therefore, the only case where the linked list implementation of a sparse matrix consumes the same memory space as the conventional way of storing the entire array is when we have a 6 x 5 matrix with 8 non-zero entries.
In a conventional way of storing a matrix, we use a 2D array to represent the matrix. Each element of the 2D array occupies a fixed amount of memory space, regardless of whether it is a non-zero or zero element. Therefore, the memory space consumed by a conventional representation is equal to the number of rows multiplied by the number of columns.
However, in a linked list implementation of a sparse matrix, we only store the non-zero elements along with their row and column indices. This saves memory space as we do not need to store the zero elements. The memory space consumed by a linked list representation depends on the number of non-zero elements in the matrix, rather than the total number of elements.
Now let's analyze each case:
a) 5 x 6 matrix with 9 non-zero entries:
In this case, there are 9 non-zero entries in a 5 x 6 matrix. The conventional representation would require a 2D array of size 5 x 6, which is 30 elements. However, the linked list representation only needs to store the 9 non-zero elements. Therefore, the memory space consumed by the linked list representation is less than the conventional representation.
b) 5 x 6 matrix with 8 non-zero entries:
In this case, there are 8 non-zero entries in a 5 x 6 matrix. Similar to the previous case, the memory space consumed by the linked list representation is less than the conventional representation.
c) 6 x 5 matrix with 8 non-zero entries:
In this case, there are 8 non-zero entries in a 6 x 5 matrix. The conventional representation would require a 2D array of size 6 x 5, which is 30 elements. The linked list representation, on the other hand, only needs to store the 8 non-zero elements. Therefore, the memory space consumed by the linked list representation is equal to the conventional representation.
d) 6 x 5 matrix with 9 non-zero entries:
In this case, there are 9 non-zero entries in a 6 x 5 matrix. Similar to the previous case, the memory space consumed by the linked list representation is less than the conventional representation.
Therefore, the only case where the linked list implementation of a sparse matrix consumes the same memory space as the conventional way of storing the entire array is when we have a 6 x 5 matrix with 8 non-zero entries.
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In which of the following cases, linked list implementations of sparse matrices consumes the same memory space as the conventional way of storing the entire array?(Assume all data-types need the same amount of storage.)a)5 x 6 matrix with 9 non-zero entriesb)5 x 6 matrix with 8 non-zero entriesc)6 x 5 matrix with 8 non-zero entriesd)6 x 5 matrix with 9 non-zero entriesCorrect answer is option 'C'. Can you explain this answer?
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In which of the following cases, linked list implementations of sparse matrices consumes the same memory space as the conventional way of storing the entire array?(Assume all data-types need the same amount of storage.)a)5 x 6 matrix with 9 non-zero entriesb)5 x 6 matrix with 8 non-zero entriesc)6 x 5 matrix with 8 non-zero entriesd)6 x 5 matrix with 9 non-zero entriesCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about In which of the following cases, linked list implementations of sparse matrices consumes the same memory space as the conventional way of storing the entire array?(Assume all data-types need the same amount of storage.)a)5 x 6 matrix with 9 non-zero entriesb)5 x 6 matrix with 8 non-zero entriesc)6 x 5 matrix with 8 non-zero entriesd)6 x 5 matrix with 9 non-zero entriesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In which of the following cases, linked list implementations of sparse matrices consumes the same memory space as the conventional way of storing the entire array?(Assume all data-types need the same amount of storage.)a)5 x 6 matrix with 9 non-zero entriesb)5 x 6 matrix with 8 non-zero entriesc)6 x 5 matrix with 8 non-zero entriesd)6 x 5 matrix with 9 non-zero entriesCorrect answer is option 'C'. Can you explain this answer?.
In which of the following cases, linked list implementations of sparse matrices consumes the same memory space as the conventional way of storing the entire array?(Assume all data-types need the same amount of storage.)a)5 x 6 matrix with 9 non-zero entriesb)5 x 6 matrix with 8 non-zero entriesc)6 x 5 matrix with 8 non-zero entriesd)6 x 5 matrix with 9 non-zero entriesCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about In which of the following cases, linked list implementations of sparse matrices consumes the same memory space as the conventional way of storing the entire array?(Assume all data-types need the same amount of storage.)a)5 x 6 matrix with 9 non-zero entriesb)5 x 6 matrix with 8 non-zero entriesc)6 x 5 matrix with 8 non-zero entriesd)6 x 5 matrix with 9 non-zero entriesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In which of the following cases, linked list implementations of sparse matrices consumes the same memory space as the conventional way of storing the entire array?(Assume all data-types need the same amount of storage.)a)5 x 6 matrix with 9 non-zero entriesb)5 x 6 matrix with 8 non-zero entriesc)6 x 5 matrix with 8 non-zero entriesd)6 x 5 matrix with 9 non-zero entriesCorrect answer is option 'C'. Can you explain this answer?.
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