Class 25: Sorting and Searching (guest lecture by Yuchi Tian)

cs1120: Introduction to Computing
Explorations in Language, Logic, and Machine
University of Virginia, Spring 2016

http://xplorecs.org/class25

Class 25:
Problems and Algorithms
Sorting
Selection Sort
Best-First Sort
Insertion Sort

1. Class 25 - Sorting and Searching Yuchi Tian
2. Algorithm vs. Computer program Algorithm: a systematic approach for solving a specific problem. Computer program: a code for solving a problem but written in a language understandable by computer or compiler. a specific implementation of an algorithm.
3. How to define a problem? Examples: Sorting problem; Searching problem; Go playing.
4. Properties of an algorithm finiteness: The algorithm must always terminate after a finite number of steps. definiteness: Each step must be precisely defined. input: An algorithm has zero or more inputs, taken from a specified set of objects. output: An algorithm has one or more outputs, which have a specified relation to the inputs. effectiveness: An algorithm must give correct answer (output).
5. Sorting problem Input: list of elements, comparison function Output: new list containing the same elements A sorting algorithm is an algorithm that solves the sorting problem.
6. Selection Sort def selection_sort(alist): for index in range(0, len(alist)): minpos = index minvalue = alist[index] for index1 in range(index, len(alist)): if (alist[index1] < minvalue): minpos = index1 minvalue = alist[index1] temp = alist[index] alist[index] = alist[minpos] alist[minpos] = temp
7. What is the asymptotic running time of selection_sort? def selection_sort(alist): for index in range(0, len(alist)): minpos = index minvalue = alist[index] for index1 in range(index, len(alist)): if (alist[index1] < minvalue): minpos = index1 minvalue = alist[index1] temp = alist[index] alist[index] = alist[minpos] alist[minpos] = temp
8. Best-First Sort def list_find_best (p): if p[1:]==[]: return 0 else: bestpos = list_find_best (p[1:]) if p[0] < p[1 + bestpos]: return 0 else: return 1 + bestpos def list_sort_best_first (p): if len(p)==0: return p else: bestpos = list_find_best (p) bestel = p.pop(bestpos) return [bestel] + \ list_sort_best_first (p)
9. Time complexity for best-first sort Best case running time: Average case running time: Worst case running time:
10. Insertion Sort def list_insert_one (el, p): if len(p)==0: return [el] if el < p[0]: return [el] + p return [p[0]] + list_insert_one (el, p[1:]) def list_sort_insert (p): if len(p)==0: return p return list_insert_one (p[0], list_sort_insert (p[1:]))
11. Time complexity for insertion sort Best case running time: Worst case running time:
12. Generalizing Comparison def list_insert_one (cf, el, p): if len(p)==0: return [el] if cf(el, p[0]): return [el] + p return [p[0]] + list_insert_one (el, p[1:]) def list_sort_insert (cf, p): if len(p)==0: return p return list_insert_one (cf, p[0], list_sort_insert (cf,p[1:]))
13. Generalizing Comparison def cmp(el1, el2): return el1%10 < el2%10
14. Sorting Problem: What is the time complexity for sorting problem? Is sorting problem in O(n^2)? Is sorting problem in (n)? Is sorting problem in (n^2)?
15. Permutation Sort import itertools def permutation_sort (alist): for i in itertools.permutations(alist): if (check_in_order (list(i))): return i def check_in_order (alist): for i in range(len(alist)-1): if alist[i]>alist[i+1]: return False return True
16. Quicker Sort Is there any sorting algorithm faster than O(n^2)? Yes. Quick Sort O(nlogn). Merge Sort O(nlogn). Heap Sort O(nlogn). Bucket Sort O(m+n)