CS Foundations II: Data Structures and Algorithms

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2. Give an example of a function f(n) such that . f(n) E 0(n3/ loga(n)) and f(n) e (n2 log2 n) but f(n) 6(n3/1082(n)) and f(n) (n2 log2(n)) 3. Give an example of a function f(n) such that: . f(n) e 0(n0.6) and f(n) e ( n log2(n)) but f(n) (r10.6) and f(n) (v that cin2.5 f(n) cn25 for constants c,c2 2 0 for all large n. f(n) e (g(n)) using lim 00 f(n)/g(n) log2(n)) Ti))- 2.5 4. Prove that 3V2n5-2n3+ 23 E (n2.0) using the definition of (n ) as functions f(n) such 5. Let f(n) = 7V7n't 8n(log4 (3n-2))3 and g(n) = 6n log5 (6n3+n) logo(6n+ 13). Prove that 6. Prove the following: If f(n) E (g(n) and f(n) E O(h(n)), then f(n) E O(g(n) +h(n))