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NPTEL Computational Number Theory and Algebra Assignment
Algebra plays an important role in both finding algorithms, and understanding the limitations of computation. This course will focus on some of the fundamental algebraic concepts that arise in computation, and the algebraic algorithms that have applications in real life. The course will cover the problems of fast integer (or polynomial) multiplication (or factoring), fast matrix multiplication, primality testing, computing discrete logarithm, error-correcting codes, lattice- based cryptography, etc. The course intends to introduce both basic concepts and practical applications.
Next Week Assignment Answers
This course can have Associate in Nursing unproctored programming communication conjointly excluding the Proctored communication, please check announcement section for date and time. The programming communication can have a weightage of twenty fifth towards the ultimate score.
- Assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
- ( All assignments in a particular week will be counted towards final scoring – quizzes and programming assignments).
- Unproctored programming exam score = 25% of the average scores obtained as part of Unproctored programming exam – out of 100
- Proctored Exam score =50% of the proctored certification exam score out of 100
UNPROCTORED PROGRAMMING EXAM SCORE >=10/25 AND PROCTORED EXAM SCORE >= 20/50.
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Let xx be an element of Z/⟨n⟩Z/⟨n⟩. What is the time complexity (in bit operations) of computing xdxd in Z/⟨n⟩Z/⟨n⟩?
Ans – A
What is the time complexity of multiplying two n×nn×n lower triangular matrices?
O(n2)O(n2) using n/2×n/2n/2×n/2 sized block multiplication.
O(nlog310)O(nlog310) using n/3×n/3n/3×n/3 sized block multiplication
Θ(M(n))Θ(M(n)), where M(n) is the time complexity of multiplying two general n×nn×n matrices.
o(M(n))o(M(n)), where M(n) is the time complexity of multiplying two general n×nn×n matrices.
Ans – B
Which of the following is false for matrix multiplication of two n×nn×n matrices?
It can be done in O(nlogn)O(nlogn) time.
It can be done in O(nlog27)O(nlog27) time.
It can be done in O(n3)O(n3) time.
It can be done in O(n3logn)O(n3logn) time.
Ans – C
Strassen’s recursive matrix multiplication algorithm reduces the number of multiplications over the naive method in each recursive step. For 2×22×2 matrices A and B, what is the number of multiplications required by the naive method (multiplying each row of A with each column of B) vs Strassen’s method?
8 vs 6
7 vs 6
8 vs 7
7 vs 5
Ans – C
The naive algorithm for multiplying two n×nn×n matrices requires O(n3)O(n3) multiplications. There has been a lot of work to improve this bound. What is the complexity of the current best algorithm?
Ans – B
Revise the definition and facts about Tensors from lectures and answer which of the following is correct?
- Order 33tensor rank computation is NP-hard.
- Rank of an order nntensor lies between n2n2and n3.n3.
Both 1 and 2.
Neither 1 nor 2.
Ans – D