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Order of complexity

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Consider four algorithms 1.The naïve way of adding the numbers up to n 2.The smart way of adding the numbers up to n 3.A binary search of n sorted items 4.An insertion sort of n items

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Naïve summing of integers

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Smart summing of integers

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Binary search

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Insertion Sort Outer loop, increases the sorted section Inner loop, steps backwards to find The right place to swap the unsorted elements

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Insertion Sort

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Quicksort Pivot Value Smaller than the Pivot Larger than the Pivot http://cs.slu.edu/~goldwasser/demos/Quicksort/

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Quicksort Pivot Value Smaller than the Pivot Larger than the Pivot http://cs.slu.edu/~goldwasser/demos/Quicksort/

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Quicksort Pivot Value Smaller than the Pivot Larger than the Pivot http://cs.slu.edu/~goldwasser/demos/Quicksort/

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Quick Sort

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Big O notation O(1) – size doesnt matter, constant –Smart summing O(log 2 n) – Logarithmic - Binary search O(n) – linear – increases with size –Naïve summing O(n 2 ) – Polynomial – increases with square of the size –Insertion sort

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