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 http://cs.slu.edu/~goldwasser/demos/Quicksort/

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

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

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