order of complexity. consider four algorithms 1.the naïve way of adding the numbers up to n 2.the...
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 items4. 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 doesn’t matter, constant– Smart summing
• O(log2n) – Logarithmic - Binary search
• O(n) – linear – increases with size– Naïve summing
• O(n2) – Polynomial – increases with square of the size– Insertion sort