Hiroki Yasuga, Elisabeth Kolp, Andreas Lang. 25th September 2014, Scientific Programming
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1 Hiroki Yasuga, Elisabeth Kolp, Andreas Lang 25th September 2014, Scientific Programming
2 What is sorting and complexity? Big O notation Sorting algorithms: Merge sort Quick sort Comparison: Merge sort & Quick sort Searching algorithms Benchmark: Merge sort vs. Quick sort
3 What is sorting and complexity? Big O notation Sorting algorithms: Merge sort Quick sort Comparison: Merge sort & Quick sort Searching algorithms Benchmark: Merge sort vs. Quick sort
4 Sorting in Kindergarten Bottle tops Complexity depends on how to sort
5 Sorting algorithm puts elements of a list in a certain order There are a number of sorting algorithms e.g. Quicksort, Mergesort Choosing efficient sorting algorithm is important Time complexity of sorting algorithm is required time (best, worst and average) To know the complexity, Big O notation
6 What is sorting and complexity? Big O notation Sorting algorithms: Merge sort Quick sort Comparison: Merge sort & Quick sort Searching algorithms Benchmark: Merge sort vs. Quick sort
7 Describes a asymptotic behavior of a function is the dominant term. Ex) 4 22 In time Big-O complexities, this notation indicate how long it takes to complete a sorting
8 What is sorting and complexity? Big O notation Sorting algorithms: Merge sort Quick sort Comparison: Merge sort & Quick sort Searching algorithms Benchmark: Merge sort vs. Quick sort
9 Divide-and-Conquer algorithm Data structure: Array with n elements Stable sort Complexity: Best Average Worst O(n log(n)) O(n log(n)) O(n log(n))
10 Divide-steps Merge-steps
11 Divide-and-Conquer algorithm Data structure: Array with n elements Not a stable sort Complexity: Best Average Worst O(n log(n)) O(n log(n)) O(n²)
12 current pivot fixed element
13 Similarities: - Divide-and-Conquer algorithm - Recursion - Same average complexity Differences: - Quick sort: sorting step is done during the splitting, no merging step - Merge sort: stable sort, better worst case complexity
14 What is sorting and complexity? Big O notation Sorting algorithm: Merge sort Quick sort Comparison: Merge sort & Quick sort Searching algorithms Benchmark: Merge sort vs. Quick sort
15 Binary Search Linear (Brute ( Force Search) - Sorted arrays of n elements - Complexity - unsorted & sorted arrays of n elements - Complexity Average Worst Average Worst O(log(n)) O(log(n)) O(n) O(n)
16 What is sorting and complexity? Big O notation Sorting algorithms: Merge sort Quick sort Comparison: Merge sort & Quick sort Searching algorithms Benchmark: Merge sort vs. Quick sort
17
18 How would you sort a terabyte of data? What about parallelization? What if you are running out of RAM?
19 - Heap sort - Insertion sort - Bubble sort - Select sort - Bucket sort - Radix sort
20 Stable sort: if two items compare as equal [ ] then their relative order will be preserved, so that if one came before the other in the input, it will also come before the other in the output. ( e.g.: sorting a list of employees twice (first: department, second: lastname)
21
Sorting Pearson Education, Inc. All rights reserved.
1 19 Sorting 2 19.1 Introduction (Cont.) Sorting data Place data in order Typically ascending or descending Based on one or more sort keys Algorithms Insertion sort Selection sort Merge sort More efficient,
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