COMPUTER SCIENCE AND ENGINEERING
DATA STRUCTURES
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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O(n)
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O(log n)
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O(n3)
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O(n2)
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Detailed explanation-1: -As of October 2022, the best announced bound on the asymptotic complexity of a matrix multiplication algorithm is O(n2.37188) time, given by Duan, Wu and Zhou announced in a preprint. This improves on the bound of O(n2.3728596) time, given by Josh Alman and Virginia Vassilevska Williams.
Detailed explanation-2: -The standard way of multiplying an m-by-n matrix by an n-by-p matrix has complexity O(mnp).
Detailed explanation-3: -If all three matrices were square, then the fastest known algorithm for multiplying two of them has complexity ≈O(N2.3729); this means that multiplying three N×N matrices will have complexity just under O(N4.75).
Detailed explanation-4: -Time Complexity-We are using three nested for loops, each of which is iterating roughly O ( n ) O(n) O(n) times. Hence, the overall time complexity is O ( n 3 ) O(n^3) O(n3).
Detailed explanation-5: -Multiplication of matrix does take time surely. Time complexity of matrix multiplication is O(n^3) using normal matrix multiplication. And Strassen algorithm improves it and its time complexity is O(n^(2.8074)).