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notes70 - Asymptotic Notation Goal To simplify analysis by...

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Asymptotic Notation Goal: To simplify analysis by getting rid of unneeded infromation. It tels us how an algorithm "scales up", that is, how it behaves with large inputs. Example: Execution time of an algorithm = 0.000001n 2 + 10n + 1000 = O(n 2 ) It is also O(n 3 ), O(n 4 ), etc. However, You use O(n 2 ) because it better describes how the execution time grows with n. Special classes of algorithms O(1) - Constant time o Example: adding, accessing memory, array indexing O(n) - Linear Time o Example: Traverse list O(log n) - Logarithmic time o Example: Traversing balanced tree O(n log n) - n log n o Example: Sorting O(n 2 ) - Quadratic time o Example: Bubble sort O(n k ) - Polynomial time O(a n ), n > 1 - Exponential time o Example: np complete problem, travelling salesman problem, optimal solution for chess game, stock market analysis, etc. O(?) o Example: Problem with no solution, making a program that will correct any input. Example: Obtain time compexity (asymptotic time) of obtaining the maximum of an array of numbers:
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