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Order of complexity. 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.

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Presentation on theme: "Order of complexity. 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."— Presentation transcript:

1 Order of complexity

2 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

3 Naïve summing of integers

4 Smart summing of integers

5 Binary search

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

7 Insertion Sort

8 Quicksort Pivot Value Smaller than the Pivot Larger than the Pivot

9 Quicksort Pivot Value Smaller than the Pivot Larger than the Pivot

10 Quicksort Pivot Value Smaller than the Pivot Larger than the Pivot

11 Quick Sort

12 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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