tials grow faster than all polynomials property with a 1 1 and k 2 n 2 isO 2n 2

# Tials grow faster than all polynomials property with

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tials grow faster than all polynomials" property with a = 1 . 1 and k = 2 . n 2 is O (2 n 2 + 4) : True. We use big- O notation to strip away constant multiples and lower- order terms, but that doesn’t make expressions like O (2 n 2 + 4) meaningless. n 2 is eventually bounded by 2 n 2 + 4 , which is all that matters. Exercise Solution: Bounding Running Times of Algorithms A simple technique for bounding the running time of an algorithm involves the following steps: 1. For each "primitive" statement (i.e. statements which can execute in isolation), assign a bound on its running time individually, and write it to the right of the statement. 1
COMP2123/2823/9123 Solutions 2. For each "if" statement, bound the amount of time it takes to evaluate the condition, and write it to the right of the statement. You can assume that actually branching to the body of the "if" statement (or the body of an attached "else" statement) takes constant time. 3. To bound the running time of a loop, sum up the time bounds on all statements within the loop (except for those within nested loops), multiply the result by the number of iterations carried out by the loop (or an upper bound thereof), and write it to the right of the loop statement.

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• Alex, Big O notation, Articles with example pseudocode, Tree traversal, Nested set model

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