HW1FA15-Solutions.pdf - CS 325 HW 1 Solutions Examples Problem Points 1 1 2 NOT GRADED 3 3 4 2 5 3 6 5 7 6 Since some problems have multiple right

# HW1FA15-Solutions.pdf - CS 325 HW 1 Solutions Examples...

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CS 325 - HW 1 Solutions Examples Problem 1 2 3 4 5 6 7 Points 1 NOT GRADED 3 2 3 5 6 Since some problems have multiple right answers I have compiled some possible correct solutions submitted by students. Problem 1: 1 point - must include either a graph, table or some explanation as to how they got the result n < 44. CS 325 - HW 1 Solutions Examples Problem 2: Not Graded CS 325 - HW 1 Solutions Examples Problem 3: 3 points total- 3 points = Base case, inductive hypothesis and induction correct 2 points = One of the above incorrect 1 point = Two of the above incorrect See sample solutions below. You can assume that n is a power of 2. CS 325 - HW 1 Solutions Examples 4. 2 points - 0.25 point deduction for each one missed. a. f(n) = n 0.25 ; g(n) = n 0.5 f(n) is O(g(n)) b. f(n) = n; g(n) = log 2 n f(n) is Ω(g(n)) c. f(n) = log n; g(n) = lg n f(n) is Θ(g(n)) d. f(n) = e n ; g(n) = 2 n f(n) is (g(n)) e. f(n) = 2 n ; g(n) = 2 n+1 f(n) is Θ(g(n)) f. f(n) = 2 n ; g(n) = 2 2 𝑛 f(n) is O(g(n)) g. f(n) = 2 n ; g(n) = n! f(n) is O(g(n)) h. f(n) = (n+1)!; g(n) = n! f(n) is Ω(g(n)) CS 325 - HW 1 Solutions Examples CS 325 - HW 1 Solutions Examples 5)  • • • 