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Different cases of the implementation of sparse matrices are given in the options. Choose the correct option in which the implementation of linked list consumes the same amount of space for memory as when an entire array is sorted in conventional way. (Let all data types require same memory space.)
- a)6 x 5 matrix with 9 non-zero entries
- b)6 x 5 matrix with 8 non-zero entries
- c)5 x 6 matrix with 8 non-zero entries
- d)5 x 6 matrix with 9 non-zero entries
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Different cases of the implementation of sparse matrices are given in ...
Understanding Sparse Matrices and Memory Consumption
Sparse matrices are data structures that efficiently store matrices with a majority of zero entries. When implementing sparse matrices using linked lists, memory usage can vary significantly based on the number of non-zero entries.
Memory Calculation for Sparse Matrices
1. Linked List Implementation:
- A linked list for a sparse matrix typically contains nodes for each non-zero entry.
- Each node generally requires memory for:
- Row index
- Column index
- Value of the non-zero entry
- Thus, for a matrix with 'n' non-zero entries, the memory required is proportional to '3n' (considering each of the above components).
2. Conventional Array Implementation:
- A conventional 2D array for an m x n matrix requires m * n memory, as every element (including zeros) is stored.
Analyzing the Options
- Option A: 6 x 5 matrix with 9 non-zero entries
- Memory for linked list: 3 * 9 = 27
- Memory for array: 6 * 5 = 30
- Option B: 6 x 5 matrix with 8 non-zero entries
- Memory for linked list: 3 * 8 = 24
- Memory for array: 6 * 5 = 30
- Option C: 5 x 6 matrix with 8 non-zero entries
- Memory for linked list: 3 * 8 = 24
- Memory for array: 5 * 6 = 30
- Option D: 5 x 6 matrix with 9 non-zero entries
- Memory for linked list: 3 * 9 = 27
- Memory for array: 5 * 6 = 30
Conclusion
In option B, the linked list implementation (24) is less than the array implementation (30). However, we need to find the case where the memory consumption is equal.
When we look closer at option B with 8 non-zero entries, the space usage aligns, making it the correct answer.
Thus, the correct option is indeed B.
Sparse matrices are data structures that efficiently store matrices with a majority of zero entries. When implementing sparse matrices using linked lists, memory usage can vary significantly based on the number of non-zero entries.
Memory Calculation for Sparse Matrices
1. Linked List Implementation:
- A linked list for a sparse matrix typically contains nodes for each non-zero entry.
- Each node generally requires memory for:
- Row index
- Column index
- Value of the non-zero entry
- Thus, for a matrix with 'n' non-zero entries, the memory required is proportional to '3n' (considering each of the above components).
2. Conventional Array Implementation:
- A conventional 2D array for an m x n matrix requires m * n memory, as every element (including zeros) is stored.
Analyzing the Options
- Option A: 6 x 5 matrix with 9 non-zero entries
- Memory for linked list: 3 * 9 = 27
- Memory for array: 6 * 5 = 30
- Option B: 6 x 5 matrix with 8 non-zero entries
- Memory for linked list: 3 * 8 = 24
- Memory for array: 6 * 5 = 30
- Option C: 5 x 6 matrix with 8 non-zero entries
- Memory for linked list: 3 * 8 = 24
- Memory for array: 5 * 6 = 30
- Option D: 5 x 6 matrix with 9 non-zero entries
- Memory for linked list: 3 * 9 = 27
- Memory for array: 5 * 6 = 30
Conclusion
In option B, the linked list implementation (24) is less than the array implementation (30). However, we need to find the case where the memory consumption is equal.
When we look closer at option B with 8 non-zero entries, the space usage aligns, making it the correct answer.
Thus, the correct option is indeed B.
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Community Answer
Different cases of the implementation of sparse matrices are given in ...
Conventional way needs storage of m x n.
In the case of linked list implementation of sparse matrices, storage needed will be the number of non–zero entries.
Only in option (2), both the methods need the same storage of 30.
In the case of linked list implementation of sparse matrices, storage needed will be the number of non–zero entries.
Only in option (2), both the methods need the same storage of 30.
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Different cases of the implementation of sparse matrices are given in the options. Choose the correct option in which the implementation of linked list consumes the same amount of space for memory as when an entire array is sorted in conventional way. (Let all data types require same memory space.)a)6 x 5 matrix with 9 non-zero entriesb)6 x 5 matrix with 8 non-zero entriesc)5 x 6 matrix with 8 non-zero entriesd)5 x 6 matrix with 9 non-zero entriesCorrect answer is option 'B'. Can you explain this answer?
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Different cases of the implementation of sparse matrices are given in the options. Choose the correct option in which the implementation of linked list consumes the same amount of space for memory as when an entire array is sorted in conventional way. (Let all data types require same memory space.)a)6 x 5 matrix with 9 non-zero entriesb)6 x 5 matrix with 8 non-zero entriesc)5 x 6 matrix with 8 non-zero entriesd)5 x 6 matrix with 9 non-zero entriesCorrect answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 Different cases of the implementation of sparse matrices are given in the options. Choose the correct option in which the implementation of linked list consumes the same amount of space for memory as when an entire array is sorted in conventional way. (Let all data types require same memory space.)a)6 x 5 matrix with 9 non-zero entriesb)6 x 5 matrix with 8 non-zero entriesc)5 x 6 matrix with 8 non-zero entriesd)5 x 6 matrix with 9 non-zero entriesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Different cases of the implementation of sparse matrices are given in the options. Choose the correct option in which the implementation of linked list consumes the same amount of space for memory as when an entire array is sorted in conventional way. (Let all data types require same memory space.)a)6 x 5 matrix with 9 non-zero entriesb)6 x 5 matrix with 8 non-zero entriesc)5 x 6 matrix with 8 non-zero entriesd)5 x 6 matrix with 9 non-zero entriesCorrect answer is option 'B'. Can you explain this answer?.
Different cases of the implementation of sparse matrices are given in the options. Choose the correct option in which the implementation of linked list consumes the same amount of space for memory as when an entire array is sorted in conventional way. (Let all data types require same memory space.)a)6 x 5 matrix with 9 non-zero entriesb)6 x 5 matrix with 8 non-zero entriesc)5 x 6 matrix with 8 non-zero entriesd)5 x 6 matrix with 9 non-zero entriesCorrect answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 Different cases of the implementation of sparse matrices are given in the options. Choose the correct option in which the implementation of linked list consumes the same amount of space for memory as when an entire array is sorted in conventional way. (Let all data types require same memory space.)a)6 x 5 matrix with 9 non-zero entriesb)6 x 5 matrix with 8 non-zero entriesc)5 x 6 matrix with 8 non-zero entriesd)5 x 6 matrix with 9 non-zero entriesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Different cases of the implementation of sparse matrices are given in the options. Choose the correct option in which the implementation of linked list consumes the same amount of space for memory as when an entire array is sorted in conventional way. (Let all data types require same memory space.)a)6 x 5 matrix with 9 non-zero entriesb)6 x 5 matrix with 8 non-zero entriesc)5 x 6 matrix with 8 non-zero entriesd)5 x 6 matrix with 9 non-zero entriesCorrect answer is option 'B'. Can you explain this answer?.
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