Week 12 - Friday What did we talk about last time? Sorting - PowerPoint PPT Presentation

Week 12 - Friday

 What did we talk about last time?  Sorting  Insertion sort  Started merge sort

 Lab hours  Wednesdays at 5 p.m. in The Point 113  Saturdays at noon in The Point 113  CS Club  Tuesdays at 5 p.m. in The Point 113 (or next door in The Point 112)

 Take a list of numbers, and divide it in half, then, recursively:  Merge sort each half  After each half has been sorted, merge them together in order

public static void mergeSort(double[] values) { double[] scratch = new double[values.length]; mergeSort(values, scratch, 0, values.length); } private static void mergeSort(double[] values, double[] scratch, int start, int end) { … } private static void merge(double[] values, double[] scratch, int start, int mid, int end) { … }

 Pros:  Best and average case running time of O( n log n )  Very simple implementation  In-place  Ideal for arrays  Cons:  Worst case running time of O( n 2 )  Not stable

1. Pick a pivot 2. Partition the array into a left half smaller than the pivot and a right half bigger than the pivot 3. Recursively, quicksort the left half 4. Recursively quicksort the right half

 Input: array , index , left , right  Set pivot to be array [ index ]  Swap array [ index ] with array [ right ]  Set index to left  For i from left up to right – 1  If array [ i ] ≤ pivot ▪ Swap array [ i ] with array [ index ] ▪ index ++  Swap array [ index ] with array [ right ]  Return index //so that we know where pivot is

7 0 0 0 0 0 0 45 7 7 7 7 7 7 0 45 45 37 37 37 37 54 54 54 45 45 45 45 37 37 37 54 54 54 54 108 108 108 108 108 108 108

 Everything comes down to picking the right pivot  If you could get the median every time, it would be great  A common choice is the first element in the range as the pivot  Gives O( n 2 ) performance if the list is sorted (or reverse sorted)  Why?  Another implementation is to pick a random location  Another well-studied approach is to pick three random locations and take the median of those three  An algorithm exists that can find the median in linear time, but its constant is HUGE

 Lower bound on sorting time  Counting sort  Radix sort

 Keep working on Project 4  Pick teams if you haven't!  Work on Assignment 6  Due tonight!  Read Section 5.3