Analysis of Algorithms, I CSOR W4231.002 Computer Science Department Copyright By PowCoder代写 加微信 powcoder Columbia University Satisfiability problems: SAT, 3SAT, Circuit-SAT 1 Complexity classes The class NP The class of NP-complete problems 2 Satisfiability: a fundamental NP-complete problem 3 The art of proving NP-completeness Circuit-SAT ≤P SAT 3SAT ≤P IS(D) 1 Complexity classes The class […]
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CSCI 570 Homework 5 Solution 1. Give the asymptotic running time of the following recurrences if they can be solved with the Master Theorem. Otherwise, indicate that the Master Theorem does not apply. a. T(n) = 3T(n/3) + b. T(n) = 2T(n/2)+nlogn. c. T (n) = 7T (n/3) + n2 + 2n. d. T(n) =
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Discussion 1 1. Prove that every execution of the G-S algorithm (when men are proposing) results in the same stable matching regardless of the order in which men propose. Solution is the textbook. This is done by showing that regardless of the order of men proposing, men always end up with their best valid partners.
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Discussion 2 1. Arrange the following functions in increasing order of growth rate with g(n) following f(n) in your list if and only if f(n) = O(g(n)) log nn, n2, nlog n, n log log n, 2log n, log2 n, n√2 Solution: First separate functions into logarithmic, polynomial, and exponential Logarithmic: log2 n Exponential: nlog
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CS570 Fall 2019: Analysis of Algorithms Exam III Points Points Problem 1 20 Problem 4 20 Problem 2 15 Problem 5 15 Problem 3 15 Problem 6 15 Total 100 Instructions: 1. This is a 2-hr exam. Closed book and notes 2. If a description to an algorithm or a proof is required please limit
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Review oftheasymptoticnotation bMd Egan no Hii is EAnyCubicx x 0u2 Any quadraticfunction I Any brain 0cm OH I E Any linear I Any cubic function is No μ re fW Ring R SL Any quadratic function in Cri n NO I Any quadraticfunction is 0 uz 0cm E E Anycubic x is 062 Any linear
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Discussion 12 1. The bin packing problem is as follows. You have an infinite supply of bins, each of which can hold M maximum weight. You also have n objects, each of which has a (possibly distinct) weight wi (any given wi is at most M). Our goal is to partition the objects into bins,
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CSCI 570 – HW 10 Due: November 20th Graded Problems 1. State True/False (a) Assume P ̸= NP. Let A and B be decision problems. If A ∈ NPC andA≤p B,thenB∈P. False. IfBwereinP,thenA≤p BwouldimplyA∈P. Since A∈NPC,∀D∈NP,D≤p A. SinceA≤p B,thisimplies ∀D ∈ NP,D ∈ P which contradicts P ̸= NP. (b) If someone proves P=NP, then
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Discussion 8 1. You have successfully computed a maximum s-t flow f for a network G = (V; E) with integer edge capacities. Your boss now gives you another network G’ that is identical to G except that the capacity of exactly one edge is decreased by one. You are also explicitly given the edge
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1 1. 2. 3. CSCI 570 – Fall 2020 – HW6 Due October 14th 11:59 p.m. Graded problems From the lecture, you know how to use dynamic programming to solve the 0-1 knapsack problem where each item is unique and only one of each kind is available. Now let us consider knapsack problem where you
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