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Two matrices M1 and M2 are to be stored in arrays A and B respectively. Each array can be stored either in row-major or column-major order in contiguous memory locations. The time complexity of an algorithm to compute M1*M2 will be
- a)best if A is in row-major, and B is in column-major order
- b)best if both are in row-major order
- c)best if both are in column-major order
- d)independent of the storage scheme
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two matrices M1 and M2 are to be stored in arrays A and B respectively...
D is correct
Here time complexity is asked, for each access of array element it will be constant,
So the time complexity will not depend upon storage. If at all program execution time is asked
a is true
Here time complexity is asked, for each access of array element it will be constant,
So the time complexity will not depend upon storage. If at all program execution time is asked
a is true
Most Upvoted Answer
Two matrices M1 and M2 are to be stored in arrays A and B respectively...
Understanding Matrix Multiplication Complexity
Matrix multiplication involves multiplying elements of rows from the first matrix with columns of the second matrix. The time complexity primarily depends on the algorithms used rather than the storage order of the matrices.
Storage Orders: Row-Major vs. Column-Major
- Row-Major Order: Stores rows of a matrix in contiguous memory locations.
- Column-Major Order: Stores columns of a matrix in contiguous memory locations.
Memory Access Patterns
- In matrix multiplication, accessing elements from both matrices is crucial.
- The algorithm iterates through rows of the first matrix and columns of the second matrix, leading to multiple accesses.
Independence of Storage Scheme
- Regardless of whether the matrices are stored in row-major or column-major order, the number of operations remains the same.
- The multiplication involves O(n^3) operations for two n x n matrices, where n is the dimension of the matrices.
Cache Efficiency
- While memory access patterns might affect cache performance, they do not change the theoretical time complexity.
- Optimizations can be made for better cache utilization, but these are implementation-specific and do not affect the fundamental complexity.
Conclusion
- The time complexity for computing matrix multiplication is theoretically independent of the storage scheme.
- Thus, the correct answer is option 'D': the time complexity is independent of the storage scheme used for the matrices.
Matrix multiplication involves multiplying elements of rows from the first matrix with columns of the second matrix. The time complexity primarily depends on the algorithms used rather than the storage order of the matrices.
Storage Orders: Row-Major vs. Column-Major
- Row-Major Order: Stores rows of a matrix in contiguous memory locations.
- Column-Major Order: Stores columns of a matrix in contiguous memory locations.
Memory Access Patterns
- In matrix multiplication, accessing elements from both matrices is crucial.
- The algorithm iterates through rows of the first matrix and columns of the second matrix, leading to multiple accesses.
Independence of Storage Scheme
- Regardless of whether the matrices are stored in row-major or column-major order, the number of operations remains the same.
- The multiplication involves O(n^3) operations for two n x n matrices, where n is the dimension of the matrices.
Cache Efficiency
- While memory access patterns might affect cache performance, they do not change the theoretical time complexity.
- Optimizations can be made for better cache utilization, but these are implementation-specific and do not affect the fundamental complexity.
Conclusion
- The time complexity for computing matrix multiplication is theoretically independent of the storage scheme.
- Thus, the correct answer is option 'D': the time complexity is independent of the storage scheme used for the matrices.
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Two matrices M1 and M2 are to be stored in arrays A and B respectively. Each array can be stored either in row-major or column-major order in contiguous memory locations. The time complexity of an algorithm to compute M1*M2 will bea)best if A is in row-major, and B is in column-major orderb)best if both are in row-major orderc)best if both are in column-major orderd)independent of the storage schemeCorrect answer is option 'D'. Can you explain this answer?
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Two matrices M1 and M2 are to be stored in arrays A and B respectively. Each array can be stored either in row-major or column-major order in contiguous memory locations. The time complexity of an algorithm to compute M1*M2 will bea)best if A is in row-major, and B is in column-major orderb)best if both are in row-major orderc)best if both are in column-major orderd)independent of the storage schemeCorrect answer is option 'D'. 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 Two matrices M1 and M2 are to be stored in arrays A and B respectively. Each array can be stored either in row-major or column-major order in contiguous memory locations. The time complexity of an algorithm to compute M1*M2 will bea)best if A is in row-major, and B is in column-major orderb)best if both are in row-major orderc)best if both are in column-major orderd)independent of the storage schemeCorrect answer is option 'D'. 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 Two matrices M1 and M2 are to be stored in arrays A and B respectively. Each array can be stored either in row-major or column-major order in contiguous memory locations. The time complexity of an algorithm to compute M1*M2 will bea)best if A is in row-major, and B is in column-major orderb)best if both are in row-major orderc)best if both are in column-major orderd)independent of the storage schemeCorrect answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice Two matrices M1 and M2 are to be stored in arrays A and B respectively. Each array can be stored either in row-major or column-major order in contiguous memory locations. The time complexity of an algorithm to compute M1*M2 will bea)best if A is in row-major, and B is in column-major orderb)best if both are in row-major orderc)best if both are in column-major orderd)independent of the storage schemeCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
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