# 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 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:

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 of n sorted items 4.An insertion sort of n items

Naïve summing of integers

Smart summing of integers

Binary search

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

Insertion Sort

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

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

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

Quick Sort

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

Similar presentations