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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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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CSCI 570 – Fall 2020 – HW 12 Solution Due November 30st 11:59pm 2020 1. A variation of the satisfiability problem is the MIN 2-SAT problem. The goal in the MIN 2-SAT problem is to find a truth assignment that mini- mizes the number of satisfied clauses. Give the best approximation algo- rithm that you
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Discussion 9 1. We’re asked to help the captain of the USC tennis team to arrange a series of matches against UCLA’s team. Both teams have n players; the tennis rating (a positive number, where a higher number can be interpreted to mean a better player) of the i-th member of USC’s team is ti
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S Sz A CC G G T C G CC AG G T G G C EE’t minutes 3 gaps SEASIDE DISEASE O Say M is either an opt solution XmYn EM or 0PTCi j as theminarty between ay ay Define an fx Y X Xm LY Yul alignment XmYn M I 0 0 i
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Discussion 7 1. When their respective sport is not in season, USC’s student-athletes are very involved in their community, helping people and spreading goodwill for the school. Unfortunately, NCAA regulations limit each student-athlete to at most one community service project per semester, so the athletic department is not always able to help every deserving charity.
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V 0 Amortized costanalysis Binary Binomialheap heap Binayheap Fi eiiniEI.in Decrease key U Amortizes Binominlheap FibHeap 04h u Merge On 4 Construct O n Ocn oifi I 0C Oci Ocu oiii ii Jesse V S Sa 8yo 4 14 13 9 4 S S4 Se s Y z t fsy s S3 552 S y
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