Polynomial-time problems | Unsolved problems in computer science | Computational geometry
In computational complexity theory, the 3SUM problem asks if a given set of real numbers contains three elements that sum to zero. A generalized version, k-SUM, asks the same question on k numbers. 3SUM can be easily solved in time, and matching lower bounds are known in some specialized models of computation. It was conjectured that any deterministic algorithm for the 3SUM requires time.In 2014, the original 3SUM conjecture was refuted by Allan Grønlund and Seth Pettie who gave a deterministic algorithm that solves 3SUM in time.Additionally, Grønlund and Pettie showed that the 4-linear decision tree complexity of 3SUM is .These bounds were subsequently improved.The current best known algorithm for 3SUM runs in time.Kane, Lovett, and Moran showed that the 6-linear decision tree complexity of 3SUM is . The latter bound is tight (up to a logarithmic factor). It is still conjectured that 3SUM is unsolvable in expected time. When the elements are integers in the range , 3SUM can be solved in time by representing the input set as a bit vector, computing the set of all pairwise sums as a discrete convolution using the fast Fourier transform, and finally comparing this set to . (Wikipedia).
How to Perform Matrix Multiplication with Two 3x3 Matrices
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From playlist Linear Algebra
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From playlist Linear Algebra
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From playlist The Daily Programmer
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From playlist Linear Algebra
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In this episode of Python Programming Practice: LeetCode #15 -- 3Sum Link to the problem here: https://leetcode.com/problems/3sum/ If you don't know Python, you can learn the basics of Python for data analysis by following along with this YouTube guide I created: https://www.youtube.com
From playlist Python Programming Practice
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From playlist MIT 6.890 Algorithmic Lower Bounds, Fall 2014
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From playlist Linear Algebra
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From playlist CALCULUS 3 CH 10 TENSORS